Consider a source that produces independent copies of a triplet of jointly distributed random variables{Xi,Yi,Zi}z =1∞. The process{Xi} is observed at the encoder, and is supposed to be reproduced at two decoders, decoder Y and decoder Z, where{Yi} and{Zi} are observed, respectively, in either a causal or noncausal manner. The communication between the encoder and the decoders is carried in two successive stages. In the first stage, the transmission is available to both decoders and they reconstruct the source according to the received bit-stream and the individual side information ({Zi} or{Yi}). In the second stage, additional information is sent to both decoders and they refine the reconstructions of the source according to the available side information and the transmissions at both stages. It is desired to find the necessary and sufficient conditions on the communication rates between the encoder and decoders, so that the distortions incurred (at each stage) will not exceed given thresholds. For the case of causal availability of side information at the decoders, an exact single-letter characterization of the achievable region is derived for the case of pure source-coding. Then, for the case of communication between the encoder and decoders carried over independent memoryless discrete channels with random states known causally/noncausally at the encoder and with causal side information about the source at the decoders, a single-letter characterization of all achievable distortion in both stages is provided and it is shown that the separation theorem holds. The results are derived without assuming any structural restrictions on side information, such as a Markov structure, etc. Finally, for noncausal degraded side information, inner and outer bounds to the achievable rate-distortion region are derived. These bounds are shown to be tight for certain cases of reconstruction requirements at the decoders. Due to the system setup, these results also shed some light on a problem of successive refinement with side information which is not degraded in the usual sense.

Consider a process, {XiYi,Zi}infini=1producing independent copies of a triplet of jointly distributed random variables (RVs). The part of the process - the source - is observed at the encoder, and is supposed to be reproduced at two decoders, decoder 1 and decoder 2, where the {Zi} and the {Yi} parts of the process are observed, respectively, in a causal manner. The communication between the encoder and the decoders is carried out across two memoryless channels in two successive communication stages. In the first stage, the compressed transmission is available to both decoders, but only decoder 1 reconstructs the source (according to the received data stream and its causal side information (SI){Zi}). In the second stage, the second decoder reconstructs the source according to {Yi} and the transmissions of the encoder at both stages. It is desired to find necessary and sufficient conditions such that the distortions incurred (in each stage) will not exceed given thresholds. First, a single-letter characterization of achievable rates is derived for a pure source-coding problem with successive refinement and causal SI at the decoders. Then, for a joint source-channel coding setting, a separation theorem is proved, asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bit streams, regardless of the source. Next, conditions for a source to be successively refinable in two different senses are established, and finally, it is shown that the binary-symmetric source is successively refinable.

Consider a source, {Xi, Yi, Zi}i=1infin, producing independent copies of a triplet of jointly distributed random variables (RVs). The {Xi} part of the process is observed at the encoder, and is supposed to be reproduced at two decoders, decoder 1 and decoder 2 , where the {Yi} and the {Zi} parts of the process are observed, respectively, in either a causal or a non-causal manner. The communication between the encoder and the decoders is carried in two successive communication stages. In the first stage, the transmission is available to both decoders and the decoders reconstruct the source according to the received stream and individual side information ({Zi} or {Yi}). In the second stage, additional information is sent to both decoders and the decoders refine the reconstruction of the source according to the side information available to it and the transmissions in both stages. It is desired to find the necessary and sufficient conditions on communication between the encoder and decoders, so that the distortions incurred (at each stage) will not exceed given thresholds. For such a multi-decoder coding setting with successive refinement and non-causal degraded side information, we derive inner and outer bounds to the achievable rate-distortion region. Then, for the case of general causal side information at the decoders, we derive a single-letter characterization of the achievable region for a multi-decoder source-coding problem with successive refinement.

Consider a process, {Xi, Yi, Zi}-infini=1, producing independent copies of a triplet of jointly distributed random variables (RVs). The {Xi} part of the process - the source, is observed at the encoder, and is supposed to be reproduced at two decoders, decoder 1 and decoder 2 , where the {Zi} and the {Yi} parts of the process are observed, respectively in a causal manner. The communication between the encoder and the decoders is carried out across two memoryless channels in two successive communication stages. In the first stage, the compressed transmission is available to both decoders, but only decoder 1 reconstructs the source (according to the received data-stream and its causal side information {Zi}0. In the second stage, the second decoder reconstructs the source according to {Yi} and the transmissions of the encoder in both stages. It is desired to find the necessary and sufficient conditions on communication between the encoder and decoders, so that the distortions incurred (in each round) will not exceed given thresholds. We first derive a single-letter characterization of achievable rates for a pure source-coding problem with successive refinement and causal side information at the decoders. Then, for a joint source-channel coding setting, we prove a separation theorem, asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source

Consider a source, {X/sub i/,Y/sub i/}/sub i=1//sup /spl infin//, producing independent copies of a pair of jointly distributed random variables (RVs). The {X/sub i/} part of the process is observed at some location, say A, and is supposed to be reproduced at a different location, say B, where the {Y/sub i/} part of the process is observed. Similarly, {Y/sub i/} should be reproduced at location A. The communication between the two locations is carried out across two memoryless channels in K iterative bi-directional rounds. In each round, the source components are reconstructed at the other locations based on the information exchanged in all previous rounds and the source component known at that location, and it is desired to find the amount of information that should be exchanged between the two locations in each round, so that the distortions incurred (in each round) will not exceed given thresholds. Our setting extends the results of Steinberg and Merhav as well as Kaspi, combining the notion of successive refinement with this of two-way interactive communication. We first derive a single-letter characterization of achievable rates for a pure source-coding problem with successive refinement. Then, for a joint source-channel coding setting, we prove a separation theorem, asserting that in the limit of long blocks, no optimality is lost by first applying lossy (two-way) successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source.

Consider a source, {Xi, Yi}i=1infin, producing independent copies of a pair of jointly distributed RVs. The {Xi} part of the process is observed at some location, say A, and is supposed to be reproduced at a different location, say B, where the {Yi} part of the process is observed. Similarly, {Yi} should be reproduced at location A. The communication between the two locations is carried out across two memoryless channels in K iterative bidirectional rounds. In each round, the source components are reconstructed at the other locations based on the information exchanged in all previous rounds and the source component known at that location, and it is desired to find the amount of information that should be exchanged between the two locations in each round, so that the distortions incurred (in each round) would not exceed given thresholds. We first derive a single-letter characterization of achievable rates for a pure source-coding problem with successive refinement. Then, for a joint source-channel coding setting, we prove a separation theorem, asserting that in the limit of long blocks, no optimality is lost by first applying lossy (two-way) successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source

We consider the problem of optimum joint information embedding and lossy compression with respect to a fidelity criterion. The goal is to find the minimum achievable compression (composite) rate R/sub c/ as a function of the embedding rate R/sub e/ and the average distortion level /spl Delta/ allowed, such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length. We characterize the minimum achievable composite rate for both the public and the private versions of the problem and demonstrate how this minimum can be approached in principle. We also provide an alternative single-letter expression of the maximum achievable embedding rate (embedding capacity) as a function of R/sub c/ and /spl Delta/, above which there exist no reliable embedding schemes.

We consider the problem of optimum joint public information embedding and lossy compression with respect to a fidelity criterion. The decompressed composite sequence (stegotext) is distorted by a stationary memoryless attack, resulting in a forgery which in turn is fed into the decoder, whose task is to retrieve the embedded information. The goal of this paper is to characterize the maximum achievable embedding rate R/sub e/ (the embedding capacity C/sub e/) as a function of the compression (composite) rate R/sub c/ and the allowed average distortion level /spl Delta/, such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length. We characterize the embedding capacity and demonstrate how it can be approached in principle. We also provide a single-letter expression of the minimum achievable composite rate as a function of R/sub e/ and /spl Delta/, below which there exists no reliable embedding scheme.

In this paper, the best achievable tradeoffs between /spl Delta/, R/sub e/ and R/sub c/, that maintain reliable estimation of V is characterized. The attack-free version of the public problem of joint information embedding and entropy coding, where the covertext, the watermark and the stegotext are drawn from finite alphabets. It is possible to attribute a different watermark to each codebook, and thus, the watermark can be correctly retrieved according to the codebook to which the composite sequence belongs. The achievable rate region can also be expressed in terms of the maximum achievable embedding capacity. The watermark by the joint typicality property of the decompressed composite sequence with the source sequence and the watermark are evaluated.