Abstract
We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion and queue-based channel models, which were recently shown to approximate well binary modulated correlated fading channels used with hard-decision demodulation. We establish conditions on the codes and channels parameters under which ML and minimum Hamming distance decoding are equivalent. We also present results on the optimality of classical perfect and quasi-perfect codes when used over the channels under ML decoding. Finally, we briefly apply these results to the dual problem of syndrome source coding with and without side information.
Highlights
T HE fundamental results in coding theory are primarily derived under the assumption that communication channels are memoryless in the sense that their noise is an independent and identically distributed process
In a previous related work [15], it is proven that strict MD (SMD) and strict maximum likelihood (ML) (SML) decoding are equivalent for perfect codes of minimum distance 3 over the first-order Markov noise channel
We first present the results for the infinite memory contagion channel (IMCC) and for the queue-based channel (QBC) with M ≥ n together and we present the results for the QBC with M = 1, 2
Summary
T HE fundamental results in coding theory are primarily derived under the assumption that communication channels are memoryless in the sense that their noise is an independent and identically distributed process (e.g., see [1]). The finite memory contagion channel (FMCC) and the QBC (which generalizes the FMCC) both feature ergodic Mth-order Markov noise processes and have a single-letter capacity expression They were shown to accurately model (in terms of replicating channel capacity and noise autocorrelation function) ergodic discrete fading channels composed of a binary modulator, a timecorrelated flat Rayleigh or Rician fading channel and a harddecision demodulator [7], [11]. For general binary codes of block length n sent over the IMCC or the QBC with memory M ≥ n, we establish both necessary and sufficient conditions for which minimum distance (MD) and ML decoding are equivalent. In a previous related work [15], it is proven that SMD and strict ML (SML) decoding are equivalent for perfect codes of minimum distance 3 over the first-order Markov noise channel (i.e., the FMCC or QBC with M = 1).
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