On the asymptotic properties of sparse matrix codes in the CEO problem

Abstract

This paper provides the asymptotic analysis for the sparse matrix codes in the CEO problem. In this problem, a firm's chief executive officer (CEO) is interested in the data sequence which cannot be observed directly. Therefore, the CEO deploys a team of L agents who encodes his/her noisy observation of the data sequence without sharing any information. The CEO then collects all the L codeword sequences to recover the data sequence, where the combined data rate R at which the agents can communicate with the CEO is limited. In our scenario, each agent is supposed to use his/her LDPC-like code for lossy compression, while the CEO estimates each data bit by a majority vote of the L reproductions. The replica ansatz and the central limit theorem allow us to derive an analytical description of the problem in the case of large L. Here, the expected error frequency can be numerically evaluated for a given R, indicating that the optimum decentralization strategy depends largely on the bandwidth, as well as the observation noise level