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.
['Seyed Parsa Beheshti', 'Fady Alajaji', 'Tamás Linder']
Optimal Joint Decoding of Correlated Data Over Orthogonal Multiple-Access Channels With Memory