Distributed source coding using syndromes (DISCUS): design and construction

TLDR

Distributed source coding seeks to compress correlated sources that are not co‑located or cannot cooperate, a problem studied under Slepian‑Wolf for lossless coding and rate‑distortion with side information for lossy coding. The authors introduce DISCUS, a constructive practical framework based on algebraic trellis codes for distributed source coding. DISCUS employs trellis‑based quantization and coset construction, and is evaluated through simulations on i.i.d. Gaussian sources with noisy side information available at the decoder.

Abstract

We address the problem of compressing correlated distributed sources, i.e., correlated sources which are not co-located or which cannot cooperate to directly exploit their correlation. We consider the related problem of compressing a source which is correlated with another source that is available only at the decoder. This problem has been studied in the information theory literature under the name of the Slepian-Wolf (1973) source coding problem for the lossless coding case, and as "rate-distortion with side information" for the lossy coding case. We provide a constructive practical framework based on algebraic trellis codes dubbed as DIstributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings. Simulation results are presented for source coding of independent and identically distributed (i.i.d.) Gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded. Our results reveal the promise of this approach: using trellis-based quantization and coset construction, the performance of the proposed approach is 2-5 dB from the Wyner-Ziv (1976) bound.