Group-Theoretic Construction and Analysis of Generalized Coset Codes for Symmetric/asymmetric Distributed Source Coding.

Group-theoretic construction and analysis of generalized coset codes for symmetric/asymmetric distributed source coding. Abstract | In this paper we consider the problem of distributed source coding with symmetric and asym-metric rates of transmission with a constructive and practical approach, referred to as DIstributed Source Coding Using Syndromes (DISCUS). We employ generalized coset codes constructed in a group-theoretic setting, for this approach and show that the performance of symmetric encoding systems matches that of asymmetric systems. This approach is very general and encompasses large class of coding techniques such as trellis codes and lattice codes. We give several examples for the illustration of the concepts. I. Introduction Remote encoding of correlated distributed sources (referred to as distributed source coding) was rst considered in 1] where it was shown primarily that any pair of discrete mem-oryless sources X and Y can be separately (remotely) compressed at a rate approaching their joint entropy 2]. This was extended to the case of encoding of sources with a delity criterion in 3, 4], where source encoding in the presence of side information (in the form of a correlated source) at the decoder is considered: this was referred to as source coding with side information. Another extension of distributed source coding in a sensor network setting was tackled in 5], where the encoders observe independent noisy versions of a source X and separately encode their observed data to a remote joint decoder to get the best joint estimate of X. Further extensions are studied in 6]. Practical construction of encoders and decoders for such problems was considered in 7], where a trellis-based code construction was formulated and analyzed under the name of DIstributed Source Coding Using Syndromes (DISCUS). The construction in 7] is an asymmetric version of the problem where one of the correlated sources is available at the decoder with \full resolution" and the other source is encoded with nite rate. This problem has been tackled in the more general symmetric setting in 8], where a constructive approach to distributed encoding of correlated sources with arbitrary achievable rate pairs, directly based on linear codes, was introduced. In 8], a trellis-and lattice-based construction of codes for symmetric encoding of correlated sources with a delity criterion was introduced and their performance was analyzed. In this paper we formulate the distributed source coding problem in a general setting, which encompasses the trellis