Optimal Joint Decoding of Correlated Data Over Orthogonal Multiple Access Channels with Memory

Abstract

Motivated by the structure of basic sensor networks, we study an optimal joint decoding problem in which the real-valued outputs of two correlated Gaussian sources are scalar quantized, bit assigned, and transmitted, without applying channel coding or interleaving, over a multiple-access channel that consists of two orthogonal point-to-point time-correlated Rayleigh fading subchannels used with soft-decision demodulation. Each fading subchannel is modeled by a nonbinary Markov noise discrete channel that was recently shown to effectively represent it. The correlated sources have memory captured by a time-varying correlation coefficient governed by a two-state first-order Markov process. At the receiver side, we design a joint sequence maximum a posteriori (MAP) decoder to exploit the correlation between the two sources, their temporal memory, and the redundancy left in the quantizers' indexes, the channels' soft-decision outputs, and noise memory. Under the simple practical case of using two-level source quantization, we propose a Markov model to estimate the joint behavior of the quantized sources. We then establish necessary and sufficient conditions under which the delay-prone joint sequence MAP decoder can be reduced to a simple instantaneous symbol-by-symbol decoder. We illustrate our analytical results by system simulation and demonstrate that joint MAP decoding can appropriately harness source and channel characteristics to achieve improved signal-to-distortion ratio performance for a wide range of system conditions.