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RFC 2435

Obsoletes RFC 2035

Network Working Group                                            L. Berc
Request for Comments: 2435                 Digital Equipment Corporation
Obsoletes: 2035                                                W. Fenner
Category: Standards Track                                     Xerox PARC
                                                            R. Frederick
                                                              Xerox PARC
                                                              S. McCanne
                                            Lawrence Berkeley Laboratory
                                                              P. Stewart
                                                              Xerox PARC
                                                            October 1998

              RTP Payload Format for JPEG-compressed Video

Status of this Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (1998).  All Rights Reserved.

Abstract

   This memo describes the RTP payload format for JPEG video streams.
   The packet format is optimized for real-time video streams where
   codec parameters change rarely from frame to frame.

   This document is a product of the Audio-Video Transport working group
   within the Internet Engineering Task Force.  Comments are solicited
   and should be addressed to the working group's mailing list at rem-
   conf@es.net and/or the author(s).

Changes from RFC 2035

   Most of this memo is identical to RFC 2035.  The changes made to the
   protocol are summarized in Appendix D.

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RFC 2435              RTP Payload Format for JPEG           October 1998

Key Words

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [9].

1.  Introduction

   The Joint Photographic Experts Group (JPEG) standard [1,2,3] defines
   a family of compression algorithms for continuous-tone, still images.
   This still image compression standard can be applied to video by
   compressing each frame of video as an independent still image and
   transmitting them in series.  Video coded in this fashion is often
   called Motion-JPEG.

   We first give an overview of JPEG and then describe the specific
   subset of JPEG that is supported in RTP and the mechanism by which
   JPEG frames are carried as RTP payloads.

   The JPEG standard defines four modes of operation: the sequential DCT
   mode, the progressive DCT mode, the lossless mode, and the
   hierarchical mode.  Depending on the mode, the image is represented
   in one or more passes.  Each pass (called a frame in the JPEG
   standard) is further broken down into one or more scans.  Within each
   scan, there are one to four components, which represent the three
   components of a color signal (e.g., "red, green, and blue", or a
   luminance signal and two chrominance signals).  These components can
   be encoded as separate scans or interleaved into a single scan.

   Each frame and scan is preceded with a header containing optional
   definitions for compression parameters like quantization tables and
   Huffman coding tables.  The headers and optional parameters are
   identified with "markers" and comprise a marker segment; each scan
   appears as an entropy-coded bit stream within two marker segments.
   Markers are aligned to byte boundaries and (in general) cannot appear
   in the entropy-coded segment, allowing scan boundaries to be
   determined without parsing the bit stream.

   Compressed data is represented in one of three formats: the
   interchange format, the abbreviated format, or the table-
   specification format.  The interchange format contains definitions
   for all the tables used by the entropy-coded segments, while the
   abbreviated format might omit some assuming they were defined out-
   of-band or by a "previous" image.

   The JPEG standard does not define the meaning or format of the
   components that comprise the image.  Attributes like the color space
   and pixel aspect ratio must be specified out-of-band with respect to

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   the JPEG bit stream.  The JPEG File Interchange Format (JFIF) [4] is
   a de-facto standard that provides this extra information using an
   application marker segment (APP0).  Note that a JFIF file is simply a
   JPEG interchange format image along with the APP0 segment.  In the
   case of video, additional parameters must be defined out-of-band
   (e.g., frame rate, interlaced vs. non-interlaced, etc.).

   While the JPEG standard provides a rich set of algorithms for
   flexible compression, cost-effective hardware implementations of the
   full standard have not appeared.  Instead, most hardware JPEG video
   codecs implement only a subset of the sequential DCT mode of
   operation.  Typically, marker segments are interpreted in software
   (which "re-programs" the hardware) and the hardware is presented with
   a single, interleaved entropy-coded scan represented in the YUV color
   space.

   The scan contains an ordered sequence of Minimum Coded Units, or
   MCUs, which are the smallest group of image data coded in a JPEG bit
   stream.  Each MCU defines the image data for a small rectangular
   block of the output image.

   Restart markers in the JPEG data denote a point where the decoder
   should reset its state.  As defined by JPEG, restart markers are the
   only type of marker that may appear embedded in the entropy-coded
   segment, and they may only appear on an MCU boundary.  A "restart
   interval" is defined to be a block of data containing a restart
   marker followed by some fixed number of MCUs.  An exception is made
   for the first restart interval in each frame, which omits the initial
   restart marker and just begins with the MCU data.  When these markers
   are used, each frame is composed of some fixed number of back-to-back
   restart intervals.

2.  JPEG Over RTP

   To maximize interoperability among hardware-based codecs, we assume
   the sequential DCT operating mode [1,Annex F] and restrict the set of
   predefined RTP/JPEG "type codes" (defined below) to single-scan,
   interleaved images.  While this is more restrictive than even
   baseline JPEG, many hardware implementation fall short of the
   baseline specification (e.g., most hardware cannot decode non-
   interleaved scans).

   In practice, most of the table-specification data rarely changes from
   frame to frame within a single video stream.  Therefore RTP/JPEG data
   is represented in abbreviated format, with all of the tables omitted
   from the bit stream where possible.  Each frame begins immediately
   with the (single) entropy-coded scan.  The information that would
   otherwise be in both the frame and scan headers is represented

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   entirely within the RTP/JPEG header (defined below) that lies between
   the RTP header and the JPEG payload.

   While parameters like Huffman tables and color space are likely to
   remain fixed for the lifetime of the video stream, other parameters
   should be allowed to vary, notably the quantization tables and image
   size (e.g., to implement rate-adaptive transmission or allow a user
   to adjust the "quality level" or resolution manually).  Thus explicit
   fields in the RTP/JPEG header are allocated to represent this
   information.  Since only a small set of quantization tables are
   typically used, we encode the entire set of quantization tables in a
   small integer field.  Customized quantization tables are accommodated
   by using a special range of values in this field, and then placing
   the table before the beginning of the JPEG payload.  The image width
   and height are encoded explicitly.

   Because JPEG frames are typically larger than the underlying
   network's maximum packet size, frames must often be fragmented into
   several packets.  One approach is to allow the network layer below
   RTP (e.g., IP) to perform the fragmentation.  However, this precludes
   rate-controlling the resulting packet stream or partial delivery in
   the presence of loss, and frames may be larger than the maximum
   network layer reassembly length (see [10] for more information).  To
   avoid these limitations, RTP/JPEG defines a simple fragmentation and
   reassembly scheme at the RTP level.

3.  RTP/JPEG Packet Format

   The RTP timestamp is in units of 90000Hz.  The same timestamp MUST
   appear in each fragment of a given frame.  The RTP marker bit MUST be
   set in the last packet of a frame.

3.1.  JPEG header

   Each packet contains a special JPEG header which immediately follows
   the RTP header.  The first 8 bytes of this header, called the "main
   JPEG header", are as follows:

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   | Type-specific |              Fragment Offset                  |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |      Type     |       Q       |     Width     |     Height    |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

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   All fields in this header except for the Fragment Offset field MUST
   remain the same in all packets that correspond to the same JPEG
   frame.

   A Restart Marker header and/or Quantization Table header may follow
   this header, depending on the values of the Type and Q fields.

3.1.1.  Type-specific: 8 bits

   Interpretation depends on the value of the type field.  If no
   interpretation is specified, this field MUST be zeroed on
   transmission and ignored on reception.

3.1.2.  Fragment Offset: 24 bits

   The Fragment Offset is the offset in bytes of the current packet in
   the JPEG frame data. This value is encoded in network byte order
   (most significant byte first). The Fragment Offset plus the length of
   the payload data in the packet MUST NOT exceed 2^24 bytes.

3.1.3.  Type: 8 bits

   The type field specifies the information that would otherwise be
   present in a JPEG abbreviated table-specification as well as the
   additional JFIF-style parameters not defined by JPEG.  Types 0-63 are
   reserved as fixed, well-known mappings to be defined by this document
   and future revisions of this document.  Types 64-127 are the same as
   types 0-63, except that restart markers are present in the JPEG data
   and a Restart Marker header appears immediately following the main
   JPEG header.  Types 128-255 are free to be dynamically defined by a
   session setup protocol (which is beyond the scope of this document).

3.1.4.  Q: 8 bits

   The Q field defines the quantization tables for this frame.  Q values
   0-127 indicate the quantization tables are computed using an
   algorithm determined by the Type field (see below).  Q values 128-255
   indicate that a Quantization Table header appears after the main JPEG
   header (and the Restart Marker header, if present) in the first
   packet of the frame (fragment offset 0).  This header can be used to
   explicitly specify the quantization tables in-band.

3.1.5.  Width: 8 bits

   This field encodes the width of the image in 8-pixel multiples (e.g.,
   a width of 40 denotes an image 320 pixels wide).  The maximum width
   is 2040 pixels.

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3.1.6.  Height: 8 bits

   This field encodes the height of the image in 8-pixel multiples
   (e.g., a height of 30 denotes an image 240 pixels tall). When
   encoding interlaced video, this is the height of a video field, since
   fields are individually JPEG encoded. The maximum height is 2040
   pixels.

3.1.7.  Restart Marker header

   This header MUST be present immediately after the main JPEG header
   when using types 64-127.  It provides the additional information
   required to properly decode a data stream containing restart markers.

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |       Restart Interval        |F|L|       Restart Count       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The Restart Interval field specifies the number of MCUs that appear
   between restart markers.  It is identical to the 16 bit value that
   would appear in the DRI marker segment of a JFIF header.  This value
   MUST NOT be zero.

   If the restart intervals in a frame are not guaranteed to be aligned
   with packet boundaries, the F (first) and L (last) bits MUST be set
   to 1 and the Restart Count MUST be set to 0x3FFF.  This indicates
   that a receiver MUST reassemble the entire frame before decoding it.

   To support partial frame decoding, the frame is broken into "chunks"
   each containing an integral number of restart intervals. The Restart
   Count field contains the position of the first restart interval in
   the current "chunk" so that receivers know which part of the frame
   this data corresponds to.  A Restart Interval value SHOULD be chosen
   to allow a "chunk" to completely fit within a single packet.  In this
   case, both the F and L bits of the packet are set to 1.  However, if
   a chunk needs to be spread across multiple packets, the F bit will be
   set to 1 in the first packet of the chunk (and only that one) and the
   L bit will be set to 1 in the last packet of the chunk (and only that
   one).

3.1.8.  Quantization Table header

   This header MUST be present after the main JPEG header (and after the
   Restart Marker header, if present) when using Q values 128-255.  It
   provides a way to specify the quantization tables associated with
   this Q value in-band.

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RFC 2435              RTP Payload Format for JPEG           October 1998

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |      MBZ      |   Precision   |             Length            |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                    Quantization Table Data                    |
   |                              ...                              |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The Length field is set to the length in bytes of the quantization
   table data to follow.  The Length field MAY be set to zero to
   indicate that no quantization table data is included in this frame.
   See section 4.2 for more information.  If the Length field in a
   received packet is larger than the remaining number of bytes, the
   packet MUST be discarded.

   When table data is included, the number of tables present depends on
   the JPEG type field.  For example, type 0 uses two tables (one for
   the luminance component and one shared by the chrominance
   components).  Each table is an array of 64 values given in zig-zag
   order, identical to the format used in a JFIF DQT marker segment.

   For each quantization table present, a bit in the Precision field
   specifies the size of the coefficients in that table.  If the bit is
   zero, the coefficients are 8 bits yielding a table length of 64
   bytes.  If the bit is one, the coefficients are 16 bits for a table
   length of 128 bytes.  For 16 bit tables, the coefficients are
   presented in network byte order.  The rightmost bit in the Precision
   field (bit 15 in the diagram above) corresponds to the first table
   and each additional table uses the next bit to the left.  Bits beyond
   those corresponding to the tables needed by the type in use MUST be
   ignored.

   For Q values from 128 to 254, the Q value to quantization table data
   mapping MUST be static, i.e., the receivers are guaranteed that they
   only need to read the table data once in order to correctly decode
   frames sent with that Q value.  A Q value of 255 denotes that the
   quantization table mapping is dynamic and can change on every frame.
   Decoders MUST NOT depend on any previous version of the tables, and
   need to reload these tables on every frame.  Packets MUST NOT contain
   Q = 255 and Length = 0.

3.1.9.  JPEG Payload

   The data following the RTP/JPEG headers is an entropy-coded segment
   consisting of a single scan.  The scan header is not present and is
   inferred from the RTP/JPEG header.  The scan is terminated either
   implicitly (i.e., the point at which the image is fully parsed), or

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   explicitly with an EOI marker.  The scan may be padded to arbitrary
   length with undefined bytes.  (Some existing hardware codecs generate
   extra lines at the bottom of a video frame and removal of these lines
   would require a Huffman-decoding pass over the data.)

   The type code determines whether restart markers are present.  If a
   type supports restart markers, the packet MUST contain a non-zero
   Restart Interval value in a Restart Marker Header and restart markers
   MUST appear on byte aligned boundaries beginning with an 0xFF between
   MCUs at that interval.  Additional 0xFF bytes MAY appear between
   restart intervals.  This can be used in the packetization process to
   align data to something like a word boundary for more efficient
   copying.  Restart markers MUST NOT appear anywhere else in the JPEG
   payload.  Types which do not support restart makers MUST NOT contain
   restart markers anywhere in the JPEG payload. All packets MUST
   contain a "stuffed" 0x00 byte following any true 0xFF byte generated
   by the entropy coder [1, Sec.  B.1.1.5].

4.  Discussion

4.1.  The Type Field

   The Type field defines the abbreviated table-specification and
   additional JFIF-style parameters not defined by JPEG, since they are
   not present in the body of the transmitted JPEG data.

   Three ranges of the type field are currently defined. Types 0-63 are
   reserved as fixed, well-known mappings to be defined by this document
   and future revisions of this document. Types 64-127 are the same as
   types 0-63, except that restart markers are present in the JPEG data
   and a Restart Marker header appears immediately following the main
   JPEG header. Types 128-255 are free to be dynamically defined by a
   session setup protocol (which is beyond the scope of this document).

   Of the first group of fixed mappings, types 0 and 1 are currently
   defined, along with the corresponding types 64 and 65 that indicate
   the presence of restart markers.  They correspond to an abbreviated
   table-specification indicating the "Baseline DCT sequential" mode,
   8-bit samples, square pixels, three components in the YUV color
   space, standard Huffman tables as defined in [1, Annex K.3], and a
   single interleaved scan with a scan component selector indicating
   components 1, 2, and 3 in that order.  The Y, U, and V color planes
   correspond to component numbers 1, 2, and 3, respectively.  Component
   1 (i.e., the luminance plane) uses Huffman table number 0 and
   quantization table number 0 (defined below) and components 2 and 3
   (i.e., the chrominance planes) use Huffman table number 1 and
   quantization table number 1 (defined below).

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RFC 2435              RTP Payload Format for JPEG           October 1998

   Type numbers 2-5 are reserved and SHOULD NOT be used.  Applications
   based on previous versions of this document (RFC 2035) should be
   updated to indicate the presence of restart markers with type 64 or
   65 and the Restart Marker header.

   The two RTP/JPEG types currently defined are described below:

                            horizontal   vertical   Quantization
           types  component samp. fact. samp. fact. table number
         +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
         |       |  1 (Y)  |     2     |     1     |     0     |
         | 0, 64 |  2 (U)  |     1     |     1     |     1     |
         |       |  3 (V)  |     1     |     1     |     1     |
         +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
         |       |  1 (Y)  |     2     |     2     |     0     |
         | 1, 65 |  2 (U)  |     1     |     1     |     1     |
         |       |  3 (V)  |     1     |     1     |     1     |
         +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   These sampling factors indicate that the chrominance components of
   type 0 video is downsampled horizontally by 2 (often called 4:2:2)
   while the chrominance components of type 1 video are downsampled both
   horizontally and vertically by 2 (often called 4:2:0).

   Types 0 and 1 can be used to carry both progressively scanned and
   interlaced image data.  This is encoded using the Type-specific field
   in the main JPEG header.  The following values are defined:

      0 : Image is progressively scanned.  On a computer monitor, it can
          be displayed as-is at the specified width and height.

      1 : Image is an odd field of an interlaced video signal.  The
          height specified in the main JPEG header is half of the height
          of the entire displayed image.  This field should be de-
          interlaced with the even field following it such that lines
          from each of the images alternate.  Corresponding lines from
          the even field should appear just above those same lines from
          the odd field.

      2 : Image is an even field of an interlaced video signal.

      3 : Image is a single field from an interlaced video signal, but
          it should be displayed full frame as if it were received as
          both the odd & even fields of the frame.  On a computer
          monitor, each line in the image should be displayed twice,
          doubling the height of the image.

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RFC 2435              RTP Payload Format for JPEG           October 1998

   Appendix B contains C source code for transforming the RTP/JPEG
   header parameters into the JPEG frame and scan headers that are
   absent from the data payload.

4.2.  The Q Field

   For JPEG types 0 and 1 (and their corresponding types 64 and 65), Q
   values between 1 and 99 inclusive are defined as follows.  Other
   values less than 128 are reserved.  Additional types are encouraged
   to use this definition if applicable.

   Both type 0 and type 1 JPEG require two quantization tables.  These
   tables are calculated as follows.  For 1 <= Q <= 99, the Independent
   JPEG Group's formula [5] is used to produce a scale factor S as:

           S = 5000 / Q          for  1 <= Q <= 50
             = 200 - 2 * Q       for 51 <= Q <= 99

   This value is then used to scale Tables K.1 and K.2 from [1]
   (saturating each value to 8 bits) to give quantization table numbers
   0 and 1, respectively.  C source code is provided in Appendix A to
   compute these tables.

   For Q values 128-255, dynamically defined quantization tables are
   used.  These tables may be specified either in-band or out of band by
   something like a session setup protocol, but the Quantization Table
   header MUST be present in the first packet of every frame. When the
   tables are specified out of band, they may be omitted from the packet
   by setting the Length field in this header to 0.

   When the quantization tables are sent in-band, they need not be sent
   with every frame.  Like the out of band case, frames which do not
   contain tables will have a Quantization Table header with a Length
   field of 0.  While this does decrease the overhead of including the
   tables, new receivers will be unable to properly decode frames from
   the time they start up until they receive the tables.

4.3.  Fragmentation and Reassembly

   Since JPEG frames can be large, they must often be fragmented.
   Frames SHOULD be fragmented into packets in a manner avoiding
   fragmentation at a lower level.  If support for partial frame
   decoding is desired, frames SHOULD be fragmented such that each
   packet contains an integral number of restart intervals (see below).

   Each packet that makes up a single frame MUST have the same
   timestamp, and the RTP marker bit MUST be set on the last packet in a
   frame.  The fragment offset field of each packet is set to the byte

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   offset of its payload data within the original frame.  Packets making
   up a frame SHOULD be sent sequentially and the fragments they contain
   MUST NOT overlap one another.

   An entire frame can be identified as a sequence of packets beginning
   with a packet having a zero fragment offset and ending with a packet
   having the RTP marker bit set.  Missing packets can be detected
   either with RTP sequence numbers or with the fragment offset and
   lengths of each packet.  Reassembly could be carried out without the
   offset field (i.e., using only the RTP marker bit and sequence
   numbers), but an efficient single-copy implementation would not
   otherwise be possible in the presence of misordered packets.
   Moreover, if the last packet of the previous frame (containing the
   marker bit) were dropped, then a receiver could not always detect
   that the current frame is entirely intact.

4.4.  Restart Markers

   Restart markers indicate a point in the JPEG stream at which the
   Huffman decoder and DC predictors are reset, allowing partial
   decoding starting at that point.  To fully take advantage of this,
   however, a decoder must know which MCUs of a frame a particular
   restart interval encodes.  While the original JPEG specification does
   provide a small sequence number field in the restart markers for this
   purpose, it is not large enough to properly cope with the loss of an
   entire packet's worth of data at a typical network MTU size.  The
   RTP/JPEG Restart Marker header contains the additional information
   needed to accomplish this.

   The size of restart intervals SHOULD be chosen to always allow an
   integral number of restart intervals to fit within a single packet.
   This will guarantee that packets can be decoded independently from
   one another.  If a restart interval ends up being larger than a
   packet, the F and L bits in the Restart Marker header can be used to
   fragment it, but the resulting set of packets must all be received by
   a decoder for that restart interval to be decoded properly.

   Once a decoder has received either a single packet with both the F
   and L bits set on or a contiguous sequence of packets (based on the
   RTP sequence number) which begin with an F bit and end with an L bit,
   it can begin decoding.  The position of the MCU at the beginning of
   the data can be determined by multiplying the Restart Count value by
   the Restart Interval value.  A packet (or group of packets as
   identified by the F and L bits) may contain any number of consecutive
   restart intervals.

   To accommodate encoders which generate frames with restart markers in
   them but cannot fragment the data in this manner, the Restart Count

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RFC 2435              RTP Payload Format for JPEG           October 1998

   field may be set to 0x3FFF with the F and L bits both set to 1.  This
   indicates to decoders that the entire frame must be reassembled
   before decoding it.

5.  Security Considerations

   RTP packets using the payload format defined in this specification
   are subject to the security considerations discussed in the RTP
   specification [6], and any appropriate RTP profile (for example [7]).
   This implies that confidentiality of the media streams is achieved by
   encryption. Because the data compression used with this payload
   format is applied end-to-end, encryption may be performed after
   compression so there is no conflict between the two operations.

   A potential denial-of-service threat exists for data encodings using
   compression techniques that have non-uniform receiver-end
   computational load.  The attacker can inject pathological datagrams
   into the stream which are complex to decode and cause the receiver to
   be overloaded.  However, this encoding does not exhibit any
   significant non-uniformity.

   Another potential denial-of-service threat exists around the
   fragmentation mechanism presented here.  Receivers should be prepared
   to limit the total amount of data associated with assembling received
   frames so as to avoid resource exhaustion.

   As with any IP-based protocol, in some circumstances a receiver may
   be overloaded simply by the receipt of too many packets, either
   desired or undesired.  Network-layer authentication may be used to
   discard packets from undesired sources, but the processing cost of
   the authentication itself may be too high.  In a multicast
   environment, pruning of specific sources will be implemented in a
   future version of IGMP [8] and in multicast routing protocols to
   allow a receiver to select which sources are allowed to reach it.

   A security review of this payload format found no additional
   considerations beyond those in the RTP specification.

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6.  Authors' Addresses

   Lance M. Berc
   Systems Research Center
   Digital Equipment Corporation
   130 Lytton Ave
   Palo Alto CA 94301

   Phone: +1 650 853 2100
   EMail: berc@pa.dec.com

   William C. Fenner
   Xerox PARC
   3333 Coyote Hill Road
   Palo Alto, CA 94304

   Phone: +1 650 812 4816
   EMail: fenner@parc.xerox.com

   Ron Frederick
   Xerox PARC
   3333 Coyote Hill Road
   Palo Alto, CA 94304

   Phone: +1 650 812 4459
   EMail: frederick@parc.xerox.com

   Steven McCanne
   University of California at Berkeley
   Electrical Engineering and Computer Science
   633 Soda Hall
   Berkeley, CA 94720

   Phone: +1 510 642 0865
   EMail: mccanne@cs.berkeley.edu

   Paul Stewart
   Xerox PARC
   3333 Coyote Hill Road
   Palo Alto, CA 94304

   Phone: +1 650 812 4821
   EMail: stewart@parc.xerox.com

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RFC 2435              RTP Payload Format for JPEG           October 1998

7.  References

   [1]  ISO DIS 10918-1. Digital Compression and Coding of Continuous-
        tone Still Images (JPEG), CCITT Recommendation T.81.

   [2]  William B. Pennebaker, Joan L. Mitchell, JPEG: Still Image Data
        Compression Standard, Van Nostrand Reinhold, 1993.

   [3]  Gregory K. Wallace, The JPEG Sill Picture Compression Standard,
        Communications of the ACM, April 1991, Vol 34, No. 1, pp. 31-44.

   [4]  The JPEG File Interchange Format.  Maintained by C-Cube
        Microsystems, Inc., and available in
        ftp://ftp.uu.net/graphics/jpeg/jfif.ps.gz.

   [5]  Tom Lane et. al., The Independent JPEG Group software JPEG
        codec.  Source code available in
        ftp://ftp.uu.net/graphics/jpeg/jpegsrc.v6a.tar.gz.

   [6]  Schulzrinne, H., Casner, S., Frederick, R. and V. Jacobson,
        "RTP: A Transport Protocol for Real-Time Applications", RFC
        1889, January 1996.

   [7]  Schulzrinne, H., "RTP Profile for Audio and Video Conferences
        with Minimal Control", RFC 1890, January 1996.

   [8]  Fenner, W., "Internet Group Management Protocol Version 2", RFC
        2236, November 1997.

   [9]  Bradner, S., "Key words for use in RFCs to Indicate Requirement
        Levels", BCP 14, RFC 2119, March 1997.

   [10] Kent C., and J. Mogul, "Fragmentation Considered Harmful",
        Proceedings of the ACM SIGCOMM '87 Workshop on Frontiers in
        Computer Communications Technology, August 1987.

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RFC 2435              RTP Payload Format for JPEG           October 1998

Appendix A

   The following code can be used to create a quantization table from a
   Q factor:

/*
 * Table K.1 from JPEG spec.
 */
static const int jpeg_luma_quantizer[64] = {
        16, 11, 10, 16, 24, 40, 51, 61,
        12, 12, 14, 19, 26, 58, 60, 55,
        14, 13, 16, 24, 40, 57, 69, 56,
        14, 17, 22, 29, 51, 87, 80, 62,
        18, 22, 37, 56, 68, 109, 103, 77,
        24, 35, 55, 64, 81, 104, 113, 92,
        49, 64, 78, 87, 103, 121, 120, 101,
        72, 92, 95, 98, 112, 100, 103, 99
};

/*
 * Table K.2 from JPEG spec.
 */
static const int jpeg_chroma_quantizer[64] = {
        17, 18, 24, 47, 99, 99, 99, 99,
        18, 21, 26, 66, 99, 99, 99, 99,
        24, 26, 56, 99, 99, 99, 99, 99,
        47, 66, 99, 99, 99, 99, 99, 99,
        99, 99, 99, 99, 99, 99, 99, 99,
        99, 99, 99, 99, 99, 99, 99, 99,
        99, 99, 99, 99, 99, 99, 99, 99,
        99, 99, 99, 99, 99, 99, 99, 99
};

/*
 * Call MakeTables with the Q factor and two u_char[64] return arrays
 */
void
MakeTables(int q, u_char *lqt, u_char *cqt)
{
  int i;
  int factor = q;

  if (q < 1) factor = 1;
  if (q > 99) factor = 99;
  if (q < 50)
    q = 5000 / factor;
  else
    q = 200 - factor*2;

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RFC 2435              RTP Payload Format for JPEG           October 1998

  for (i=0; i < 64; i++) {
    int lq = (jpeg_luma_quantizer[i] * q + 50) / 100;
    int cq = (jpeg_chroma_quantizer[i] * q + 50) / 100;

    /* Limit the quantizers to 1 <= q <= 255 */
    if (lq < 1) lq = 1;
    else if (lq > 255) lq = 255;
    lqt[i] = lq;

    if (cq < 1) cq = 1;
    else if (cq > 255) cq = 255;
    cqt[i] = cq;
  }
}

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RFC 2435              RTP Payload Format for JPEG           October 1998

Appendix B

   The following routines can be used to create the JPEG marker segments
   corresponding to the table-specification data that is absent from the
   RTP/JPEG body.

u_char lum_dc_codelens[] = {
        0, 1, 5, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
};

u_char lum_dc_symbols[] = {
        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
};

u_char lum_ac_codelens[] = {
        0, 2, 1, 3, 3, 2, 4, 3, 5, 5, 4, 4, 0, 0, 1, 0x7d,
};

u_char lum_ac_symbols[] = {
        0x01, 0x02, 0x03, 0x00, 0x04, 0x11, 0x05, 0x12,
        0x21, 0x31, 0x41, 0x06, 0x13, 0x51, 0x61, 0x07,
        0x22, 0x71, 0x14, 0x32, 0x81, 0x91, 0xa1, 0x08,
        0x23, 0x42, 0xb1, 0xc1, 0x15, 0x52, 0xd1, 0xf0,
        0x24, 0x33, 0x62, 0x72, 0x82, 0x09, 0x0a, 0x16,
        0x17, 0x18, 0x19, 0x1a, 0x25, 0x26, 0x27, 0x28,
        0x29, 0x2a, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39,
        0x3a, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49,
        0x4a, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59,
        0x5a, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69,
        0x6a, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79,
        0x7a, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89,
        0x8a, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98,
        0x99, 0x9a, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7,
        0xa8, 0xa9, 0xaa, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6,
        0xb7, 0xb8, 0xb9, 0xba, 0xc2, 0xc3, 0xc4, 0xc5,
        0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xd2, 0xd3, 0xd4,
        0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xe1, 0xe2,
        0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea,
        0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8,
        0xf9, 0xfa,
};

u_char chm_dc_codelens[] = {
        0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
};

u_char chm_dc_symbols[] = {
        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,

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RFC 2435              RTP Payload Format for JPEG           October 1998

};

u_char chm_ac_codelens[] = {
        0, 2, 1, 2, 4, 4, 3, 4, 7, 5, 4, 4, 0, 1, 2, 0x77,
};

u_char chm_ac_symbols[] = {
        0x00, 0x01, 0x02, 0x03, 0x11, 0x04, 0x05, 0x21,
        0x31, 0x06, 0x12, 0x41, 0x51, 0x07, 0x61, 0x71,
        0x13, 0x22, 0x32, 0x81, 0x08, 0x14, 0x42, 0x91,
        0xa1, 0xb1, 0xc1, 0x09, 0x23, 0x33, 0x52, 0xf0,
        0x15, 0x62, 0x72, 0xd1, 0x0a, 0x16, 0x24, 0x34,
        0xe1, 0x25, 0xf1, 0x17, 0x18, 0x19, 0x1a, 0x26,
        0x27, 0x28, 0x29, 0x2a, 0x35, 0x36, 0x37, 0x38,
        0x39, 0x3a, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48,
        0x49, 0x4a, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58,
        0x59, 0x5a, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68,
        0x69, 0x6a, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78,
        0x79, 0x7a, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87,
        0x88, 0x89, 0x8a, 0x92, 0x93, 0x94, 0x95, 0x96,
        0x97, 0x98, 0x99, 0x9a, 0xa2, 0xa3, 0xa4, 0xa5,
        0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xb2, 0xb3, 0xb4,
        0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xc2, 0xc3,
        0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xd2,
        0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda,
        0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
        0xea, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8,
        0xf9, 0xfa,
};

u_char *
MakeQuantHeader(u_char *p, u_char *qt, int tableNo)
{
        *p++ = 0xff;
        *p++ = 0xdb;            /* DQT */
        *p++ = 0;               /* length msb */
        *p++ = 67;              /* length lsb */
        *p++ = tableNo;
        memcpy(p, qt, 64);
        return (p + 64);
}

u_char *
MakeHuffmanHeader(u_char *p, u_char *codelens, int ncodes,
                  u_char *symbols, int nsymbols, int tableNo,
                  int tableClass)
{
        *p++ = 0xff;

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RFC 2435              RTP Payload Format for JPEG           October 1998

        *p++ = 0xc4;            /* DHT */
        *p++ = 0;               /* length msb */
        *p++ = 3 + ncodes + nsymbols; /* length lsb */
        *p++ = (tableClass << 4) | tableNo;
        memcpy(p, codelens, ncodes);
        p += ncodes;
        memcpy(p, symbols, nsymbols);
        p += nsymbols;
        return (p);
}

u_char *
MakeDRIHeader(u_char *p, u_short dri) {
        *p++ = 0xff;
        *p++ = 0xdd;            /* DRI */
        *p++ = 0x0;             /* length msb */
        *p++ = 4;               /* length lsb */
        *p++ = dri >> 8;        /* dri msb */
        *p++ = dri & 0xff;      /* dri lsb */
        return (p);
}

/*
 *  Arguments:
 *    type, width, height: as supplied in RTP/JPEG header
 *    lqt, cqt: quantization tables as either derived from
 *         the Q field using MakeTables() or as specified
 *         in section 4.2.
 *    dri: restart interval in MCUs, or 0 if no restarts.
 *
 *    p: pointer to return area
 *
 *  Return value:
 *    The length of the generated headers.
 *
 *    Generate a frame and scan headers that can be prepended to the
 *    RTP/JPEG data payload to produce a JPEG compressed image in
 *    interchange format (except for possible trailing garbage and
 *    absence of an EOI marker to terminate the scan).
 */
int MakeHeaders(u_char *p, int type, int w, int h, u_char *lqt,
                u_char *cqt, u_short dri)
{
        u_char *start = p;

        /* convert from blocks to pixels */
        w <<= 3;
        h <<= 3;

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RFC 2435              RTP Payload Format for JPEG           October 1998

        *p++ = 0xff;
        *p++ = 0xd8;            /* SOI */

        p = MakeQuantHeader(p, lqt, 0);
        p = MakeQuantHeader(p, cqt, 1);

        if (dri != 0)
                p = MakeDRIHeader(p, dri);

        *p++ = 0xff;
        *p++ = 0xc0;            /* SOF */
        *p++ = 0;               /* length msb */
        *p++ = 17;              /* length lsb */
        *p++ = 8;               /* 8-bit precision */
        *p++ = h >> 8;          /* height msb */
        *p++ = h;               /* height lsb */
        *p++ = w >> 8;          /* width msb */
        *p++ = w;               /* wudth lsb */
        *p++ = 3;               /* number of components */
        *p++ = 0;               /* comp 0 */
        if (type == 0)
                *p++ = 0x21;    /* hsamp = 2, vsamp = 1 */
        else
                *p++ = 0x22;    /* hsamp = 2, vsamp = 2 */
        *p++ = 0;               /* quant table 0 */
        *p++ = 1;               /* comp 1 */
        *p++ = 0x11;            /* hsamp = 1, vsamp = 1 */
        *p++ = 1;               /* quant table 1 */
        *p++ = 2;               /* comp 2 */
        *p++ = 0x11;            /* hsamp = 1, vsamp = 1 */
        *p++ = 1;               /* quant table 1 */
        p = MakeHuffmanHeader(p, lum_dc_codelens,
                              sizeof(lum_dc_codelens),
                              lum_dc_symbols,
                              sizeof(lum_dc_symbols), 0, 0);
        p = MakeHuffmanHeader(p, lum_ac_codelens,
                              sizeof(lum_ac_codelens),
                              lum_ac_symbols,
                              sizeof(lum_ac_symbols), 0, 1);
        p = MakeHuffmanHeader(p, chm_dc_codelens,
                              sizeof(chm_dc_codelens),
                              chm_dc_symbols,
                              sizeof(chm_dc_symbols), 1, 0);
        p = MakeHuffmanHeader(p, chm_ac_codelens,
                              sizeof(chm_ac_codelens),
                              chm_ac_symbols,
                              sizeof(chm_ac_symbols), 1, 1);

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RFC 2435              RTP Payload Format for JPEG           October 1998

        *p++ = 0xff;
        *p++ = 0xda;            /* SOS */
        *p++ = 0;               /* length msb */
        *p++ = 12;              /* length lsb */
        *p++ = 3;               /* 3 components */
        *p++ = 0;               /* comp 0 */
        *p++ = 0;               /* huffman table 0 */
        *p++ = 1;               /* comp 1 */
        *p++ = 0x11;            /* huffman table 1 */
        *p++ = 2;               /* comp 2 */
        *p++ = 0x11;            /* huffman table 1 */
        *p++ = 0;               /* first DCT coeff */
        *p++ = 63;              /* last DCT coeff */
        *p++ = 0;               /* sucessive approx. */

        return (p - start);
};

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RFC 2435              RTP Payload Format for JPEG           October 1998

Appendix C

   The following routine is used to illustrate the RTP/JPEG packet
   fragmentation and header creation.

   For clarity and brevity, the structure definitions are only valid for
   32-bit big-endian (most significant octet first) architectures. Bit
   fields are assumed to be packed tightly in big-endian bit order, with
   no additional padding. Modifications would be required to construct a
   portable implementation.

/*
 * RTP data header from RFC1889
 */
typedef struct {
        unsigned int version:2;   /* protocol version */
        unsigned int p:1;         /* padding flag */
        unsigned int x:1;         /* header extension flag */
        unsigned int cc:4;        /* CSRC count */
        unsigned int m:1;         /* marker bit */
        unsigned int pt:7;        /* payload type */
        u_int16 seq;              /* sequence number */
        u_int32 ts;               /* timestamp */
        u_int32 ssrc;             /* synchronization source */
        u_int32 csrc[1];          /* optional CSRC list */
} rtp_hdr_t;

#define RTP_HDR_SZ 12

/* The following definition is from RFC1890 */
#define RTP_PT_JPEG             26

struct jpeghdr {
        unsigned int tspec:8;   /* type-specific field */
        unsigned int off:24;    /* fragment byte offset */
        u_int8 type;            /* id of jpeg decoder params */
        u_int8 q;               /* quantization factor (or table id) */
        u_int8 width;           /* frame width in 8 pixel blocks */
        u_int8 height;          /* frame height in 8 pixel blocks */
};

struct jpeghdr_rst {
        u_int16 dri;
        unsigned int f:1;
        unsigned int l:1;
        unsigned int count:14;
};

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RFC 2435              RTP Payload Format for JPEG           October 1998

struct jpeghdr_qtable {
        u_int8  mbz;
        u_int8  precision;
        u_int16 length;
};

#define RTP_JPEG_RESTART           0x40

/* Procedure SendFrame:
 *
 *  Arguments:
 *    start_seq: The sequence number for the first packet of the current
 *               frame.
 *    ts: RTP timestamp for the current frame
 *    ssrc: RTP SSRC value
 *    jpeg_data: Huffman encoded JPEG scan data
 *    len: Length of the JPEG scan data
 *    type: The value the RTP/JPEG type field should be set to
 *    typespec: The value the RTP/JPEG type-specific field should be set
 *              to
 *    width: The width in pixels of the JPEG image
 *    height: The height in pixels of the JPEG image
 *    dri: The number of MCUs between restart markers (or 0 if there
 *         are no restart markers in the data
 *    q: The Q factor of the data, to be specified using the Independent
 *       JPEG group's algorithm if 1 <= q <= 99, specified explicitly
 *       with lqt and cqt if q >= 128, or undefined otherwise.
 *    lqt: The quantization table for the luminance channel if q >= 128
 *    cqt: The quantization table for the chrominance channels if
 *         q >= 128
 *
 *  Return value:
 *    the sequence number to be sent for the first packet of the next
 *    frame.
 *
 * The following are assumed to be defined:
 *
 * PACKET_SIZE                         - The size of the outgoing packet
 * send_packet(u_int8 *data, int len)  - Sends the packet to the network
 */

u_int16 SendFrame(u_int16 start_seq, u_int32 ts, u_int32 ssrc,
                   u_int8 *jpeg_data, int len, u_int8 type,
                   u_int8 typespec, int width, int height, int dri,
                   u_int8 q, u_int8 *lqt, u_int8 *cqt) {
        rtp_hdr_t rtphdr;
        struct jpeghdr jpghdr;
        struct jpeghdr_rst rsthdr;

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RFC 2435              RTP Payload Format for JPEG           October 1998

        struct jpeghdr_qtable qtblhdr;
        u_int8 packet_buf[PACKET_SIZE];
        u_int8 *ptr;
        int bytes_left = len;
        int seq = start_seq;
        int pkt_len, data_len;

        /* Initialize RTP header
         */
        rtphdr.version = 2;
        rtphdr.p = 0;
        rtphdr.x = 0;
        rtphdr.cc = 0;
        rtphdr.m = 0;
        rtphdr.pt = RTP_PT_JPEG;
        rtphdr.seq = start_seq;
        rtphdr.ts = ts;
        rtphdr.ssrc = ssrc;

        /* Initialize JPEG header
         */
        jpghdr.tspec = typespec;
        jpghdr.off = 0;
        jpghdr.type = type | ((dri != 0) ? RTP_JPEG_RESTART : 0);
        jpghdr.q = q;
        jpghdr.width = width / 8;
        jpghdr.height = height / 8;

        /* Initialize DRI header
         */
        if (dri != 0) {
                rsthdr.dri = dri;
                rsthdr.f = 1;        /* This code does not align RIs */
                rsthdr.l = 1;
                rsthdr.count = 0x3fff;
        }

        /* Initialize quantization table header
         */
        if (q >= 128) {
                qtblhdr.mbz = 0;
                qtblhdr.precision = 0; /* This code uses 8 bit tables only */
                qtblhdr.length = 128;  /* 2 64-byte tables */
        }

        while (bytes_left > 0) {
                ptr = packet_buf + RTP_HDR_SZ;
                memcpy(ptr, &jpghdr, sizeof(jpghdr));

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RFC 2435              RTP Payload Format for JPEG           October 1998

                ptr += sizeof(jpghdr);

                if (dri != 0) {
                        memcpy(ptr, &rsthdr, sizeof(rsthdr));
                        ptr += sizeof(rsthdr);
                }

                if (q >= 128 && jpghdr.off == 0) {
                        memcpy(ptr, &qtblhdr, sizeof(qtblhdr));
                        ptr += sizeof(qtblhdr);
                        memcpy(ptr, lqt, 64);
                        ptr += 64;
                        memcpy(ptr, cqt, 64);
                        ptr += 64;
                }

                data_len = PACKET_SIZE - (ptr - packet_buf);
                if (data_len >= bytes_left) {
                        data_len = bytes_left;
                        rtphdr.m = 1;
                }

                memcpy(packet_buf, &rtphdr, RTP_HDR_SZ);
                memcpy(ptr, jpeg_data + jpghdr.off, data_len);

                send_packet(packet_buf, (ptr - packet_buf) + data_len);

                jpghdr.off += data_len;
                bytes_left -= data_len;
                rtphdr.seq++;
        }
        return rtphdr.seq;
}

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RFC 2435              RTP Payload Format for JPEG           October 1998

Appendix D

   This section outlines the changes between this document and its
   precdecessor, RFC 2035.  The changes to the protocol were made with
   an eye towards causing as few interoperability problems between
   implementations based on the older text and newer implementations,
   and indeed, many of the obsolete conventions can still be
   unambiguously decoded by a newer implementation.  However, use of the
   older conventions in newer implementations is strongly discouraged.

    o   Types 0 and 1 have been augmented to allow for the encoding of
        interlaced video images, using 2 bits of the type-specific
        field.  See section 4.1 for details.

    o   There has been discussion in the working group arguing for more
        flexibility in specifying the JPEG quantization tables.  This
        memo allows table coefficients to be specified explicitly
        through the use of an optional Quantization Table header,
        discussed in sections 3.1.8 and 4.2.

    o   In RFC 2035, the encoding of restart marker information in the
        Type field made it difficult to add new types. Additionally, the
        type- specific field was used for the restart count, making it
        unavailable for other type-specific purposes.  This memo moves
        the restart marker indication to a particular bit in the Type
        field, and adds an optional header to hold the additional
        information required, leaving the type-specific field free for
        its intended purpose.  The handling of partial frame decoding
        was also made more robust against packet loss.  See sections
        3.1.7 and 4.4 for details.

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RFC 2435              RTP Payload Format for JPEG           October 1998

Full Copyright Statement

   Copyright (C) The Internet Society (1998).  All Rights Reserved.

   This document and translations of it may be copied and furnished to
   others, and derivative works that comment on or otherwise explain it
   or assist in its implementation may be prepared, copied, published
   and distributed, in whole or in part, without restriction of any
   kind, provided that the above copyright notice and this paragraph are
   included on all such copies and derivative works.  However, this
   document itself may not be modified in any way, such as by removing
   the copyright notice or references to the Internet Society or other
   Internet organizations, except as needed for the purpose of
   developing Internet standards in which case the procedures for
   copyrights defined in the Internet Standards process must be
   followed, or as required to translate it into languages other than
   English.

   The limited permissions granted above are perpetual and will not be
   revoked by the Internet Society or its successors or assigns.

   This document and the information contained herein is provided on an
   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
   TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
   BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
   HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

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