An error exponent for lossy source coding with side information at the decoder

Jayaraman, S.; Berger, Toby

doi:10.1109/isit.1995.535778

Cited by 4 publications

(4 citation statements)

References 2 publications

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“…Foremost, in Theorem 2 the innermost optimization is over Q X|Y , so that X, Y, S adhere to the Markov structure, yet in the achievable exponent this Markov constraint is not present. This differing Markov structure is also present in the partial Wyner-Ziv exponent results of Jayaraman and Berger [18], [32] who attribute the gap between the sphere packing and random exponents (present even at low rates) in the binning exponent problem they studied to this type of difference in the Markov structure. The other differences between η L and η U are the range of the inner most optimization, the presence of the binning term in the achievable exponent and the fact that the choice of test channel is restricted in the upper bound.…”

Section: Sccsi Results and Discussionmentioning

confidence: 54%

“…Let F n be as defined in (32). We may move the optimizations appearing in (41) into the exponent and this yields P e · ≤ exp(−n(F n (P XY , R 1 , R 2 ))).…”

Section: We Now Show Thatmentioning

confidence: 99%

“…where in (32) the optimizations are over types/conditional types and in (33) the optimizations are over all distributions, and in both cases the inner optimizations are compatible with the outer ones, i.e. assume…”

Section: B Error Probability Calculationmentioning

confidence: 99%

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Reliability in Source Coding With Side Information

Kelly

Wagner

2012

IEEE Trans. Inform. Theory

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We study error exponents for source coding with side information. Both achievable exponents and converse bounds are obtained for the following two cases: lossless source coding with coded information (SCCSI) and lossy source coding with full side information (Wyner-Ziv). These results recover and extend several existing results on source-coding error exponents and are tight in some circumstances. Our bounds have a natural interpretation as a two-player game between nature and the code designer, with nature seeking to minimize the exponent and the code designer seeking to maximize it. In the Wyner-Ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events. The Gaussian and binary-erasure cases are examined in detail. I. INTRODUCTIONIn a typical lossy data compression problem a source is to be compressed by an encoder at a prescribed rate so that a decoder may reproduce the source to within some desired fidelity (distortion). Sometimes present, in addition to the data to be compressed, is some correlated information that can be utilized by a second encoder, that is able to send a separate message to the decoder. We refer to this kind of problem as source coding with side information (SCSI). The set-up is depicted in Fig. 1, where a source X is compressed by encoder one to a rate R 1 with the decoder having access to encoded side information Y , compressed at rate R 2 by encoder two, as well as the compressed version of X from the first encoder.The SCSI scenario arises in a variety of applications. For example, in video applications [1] X can represent a current frame, and Y a separate correlated frame sent from a second encoder. Y can even represent the frame(s) preceding the current frame X in the stream: while the previous frames are certainly available to the encoder, the encoder's coding scheme can be simplified by not making use of this information and leaving the decoder to exploit the interframe dependence. A second example can be found in communication in networks with relays [2]. A source sends a message X to a sink in a network containing a relay. One mode of operation for the relay is "compress and forward", i.e. for the relay to send a compressed version of its observation, Y , of the source-sink message to the sink. This compressed message can be used by the sink to further aid its decoding. SCSI appears in applications even beyond communication, for example (with minor changes) it has been proposed as a model for rate-constrained pattern recognition [3].For the lossless problem with coded side information (SCCSI) 1 , and the lossy problem with full side information (Wyner-Ziv), the "rate region" problem, i.e. determining the rates required to meet a given average distortion constraint, is solved. In this paper, we study these two problems from an error-exponent standpoint. Our motivation for doing so is three-fold:

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Section: Sccsi Results and Discussionmentioning

confidence: 54%

“…Let F n be as defined in (32). We may move the optimizations appearing in (41) into the exponent and this yields P e · ≤ exp(−n(F n (P XY , R 1 , R 2 ))).…”

Section: We Now Show Thatmentioning

confidence: 99%

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Reliability in Source Coding With Side Information

Kelly

Wagner

2012

IEEE Trans. Inform. Theory

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“…Jayaraman and Berger [10] studied error exponents for the Wyner-Ziv problem, although they restricted their attention to the probability that a binning error occurs. As mentioned earlier, we derived an achievable exponent for the discrete memoryless case and showed that a binning error is only one of two competing error events [4].…”

Section: Other Prior Workmentioning

confidence: 99%

Error exponents and test channel optimization for the Gaussian Wyner-Ziv problem

Kelly

Wagner

Vamvatsikos

2008

2008 IEEE International Symposium on Information Theory

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We consider the quadratic Gaussian Wyner-Ziv problem, i.e., the problem of lossy compression of a Gaussian source with Gaussian side information at the decoder and a quadratic distortion measure. Motivated by applications in video coding, we study how to minimize the probability that the distortion exceeds a given threshold, as opposed to the conventional approach of minimizing the average distortion. We obtain an achievable exponent for this problem, which is positive above the rate distortion function, and expose a tension in the choice of the test channel; the optimal test channel balances two competing error events.

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On reliability of content identification from databases based on noisy queries

Dasarathy

Draper

2011

2011 IEEE International Symposium on Information Theory Proceedings

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An error exponent for lossy source coding with side information at the decoder

Cited by 4 publications

References 2 publications

Reliability in Source Coding With Side Information

Reliability in Source Coding With Side Information

Error exponents and test channel optimization for the Gaussian Wyner-Ziv problem

On reliability of content identification from databases based on noisy queries

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