Universality for the noisy Slepian-Wolf problem via spatial coupling

Abstract

Abstract-We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded and transmitted over two independent binary memoryless symmetric channels. Each channel capacity is assumed to be characterized by a single parameter which is not known at the transmitter. The receiver has knowledge of both the source correlation and the channel parameters. We call a system universal if it retains near-capacity performance without channel knowledge at the transmitter.Kudekar et al. recently showed that terminated low-density parity-check (LDPC) convolutional codes (a.k.a. spatially-coupled LDPC ensembles) can have belief-propagation thresholds that approach their maximum a-posteriori thresholds. This was proven for binary erasure channels and shown empirically for binary memoryless symmetric channels. They also conjectured that the principle of spatial coupling is very general and the phenomenon of threshold saturation applies to a very broad class of graphical models. In this work, we derive an area theorem for the joint decoder and empirically show that threshold saturation occurs for this problem. As a result, we demonstrate near-universal performance for this problem using the proposed spatiallycoupled coding system. A similar result is also discussed briefly for the 2-user multiple-access channel.

Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation

“…It has been shown to apply to a variety of problems in communications, computer science, signal processing, and physics. To mention some concrete examples, the threshold saturation effect (dynamical/algorithmic threshold of the system being equal to the static or condensation threshold) of coupled graphical models has been observed for rate-less codes by Aref and Urbanke [78], for channels with memory and multiple access channels with erasure by Kudekar and Kasai [79], [80], for CDMA channels by Takeuchi, Tanaka, and Kawabata [81], for relay channels with erasure by Uchikawa, Kasai, and Sakaniwa [82], for the noisy Slepian-Wolf problem by Yedla, Pfister, and Narayanan [83], and for the BEC wiretap channel by Rathi, Urbanke, Andersson, and Skoglund [84]. Uchikawa, Kurkoski, Kasai, and Sakaniwa recently showed an improvement of the BP threshold has also for transmission over the unconstrained AWGN channel using low-density lattice codes [85].…”

Adaptive Slepian-Wolf Decoding Based on Expectation Propagation

“…In this paper, our problem is to estimate timevarying crossover probability given observations from neighboring factor nodes (see (3) and (6)). Thus, EP is extended to approximate a mixture of Beta distributions instead of Gaussian distributions in our problem.…”

“…INTRODUCTION Slepian-Wolf (SW) coding is a technique to losslessly compress correlated remote sources separately and decompress them jointly [1]. Numerous channel coding based SW coding schemes have been proposed [2], [3]. However, the fundamental assumption is that the correlation statistics needs to be known accurately a priori.…”

Decentralized power control for random access with iterative multi-user detection

“…Fig. 2 shows the feasible region (see [14] for a similar example) of the system in (2) with a codeword-length 10 4 (3, 6) regular LDPC code [15]- [16] followed by QPSK and iterative LMMSE receiver.…”