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

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 ratedistortion 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.M. Nangir and M. Ahmadian-Attari are with the ⋆ CEO if |Q| ≤ 4 and |U i | ≤ |Y i | = 2, for i = 1, 2, are satisfied. To find a complete characterization of the sumrate-distortion function for the two-link binary CEO problem, we should solve the following DRAFT

Successive Wyner-Ziv Coding for the Binary CEO Problem Under Logarithmic Loss

“…We shall derive several analytical results surrounding Definition 5. An investigation along this line was initiated in [28] for the case L = 2.…”

“…These corner points can be achieved via successive Wyner-Ziv coding with decoding order U π(L) → U π(L−1) → · · · → U π(1) (an implementation of this scheme for the case L = 2 can be found in [28]).…”

Successive Wyner-Ziv Coding for the Binary CEO Problem under Log-Loss

“…An improved performance can be achieved by increasing n, l, and also using better source splitters. Based on the numerical and analytical results in [16] for a two-link binary CEO problem, the allocation d 1 = d 2 is not optimal for some values of the sum-rate and distortion, even in the case of equal noise parameters p 1 = p 2 . This surprising result is also true for the multi-link case.…”

“…Furthermore, we assume BSC test-channel models for the encoders in each link, i.e., the Encoder i is modeled by a BSC with the crossover probability d i . Note that as far as the sum-rate distortion function is concerned, the timesharing variable Q can be assumed to be a constant and hence it is eliminated [16]. Under these assumptions, the sum-rate and distortion bounds are derived,…”

“…Since the problem (8) is not convex [16], it can be numerically solved by an l-dimensional exhaustive search in the set [0, 0.5] l . In Section IV, these theoretical bounds are presented for some cases.…”