Analysis and Code Design for the Binary CEO Problem under Logarithmic Loss

TL;DR

This paper introduces an efficient coding scheme for the binary CEO problem under logarithmic loss, achieving near-theoretical rate-distortion bounds using compound LDGM-LDPC codes and iterative decoding.

Contribution

It presents a novel encoding and decoding scheme based on LDGM and LDPC codes that closely approaches the theoretical rate-distortion bound for the binary CEO problem.

Findings

The proposed scheme outperforms majority-based estimation methods.

Numerical results show performance close to the theoretical bound.

An iterative decoding algorithm effectively reconstructs source bits.

Abstract

In this paper, we propose an efficient coding scheme for the binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. Courtade and Weissman obtained the exact rate-distortion bound for a two-link binary CEO problem under this criterion. We find the optimal test-channel model and its parameters for the encoder of each link by using the given bound. Furthermore, an efficient encoding scheme based on compound LDGM-LDPC codes is presented to achieve the theoretical rates. In the proposed encoding scheme, a binary quantizer using LDGM codes and a syndrome-decoding employing LDPC codes are applied. An iterative decoding is also presented as a fusion center to reconstruct the observation bits. The proposed decoder consists of a sum-product algorithm with a side information from other decoder and a soft estimator. The output of the CEO decoder is the probability of source bits conditional to the received sequences of both links. This method outperforms the majority-based estimation of the source bits utilized in the prior studies of the binary CEO problem. Our numerical examples verify a close performance of the proposed coding scheme to the theoretical bound in several cases.