A Discrete Channel Model for Capturing Memory and Soft-Decision Information: A Capacity Study

Abstract

A discrete (binary-input 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sup> -ary output) communication channel with memory is introduced with the objective to judiciously capture both the statistical memory and the soft-decision information of time-correlated fading channels modulated via binary phase-shift keying and coherently demodulated with an output quantizer of resolution q. It is shown that the discrete channel can be explicitly described in terms of its binary input process and a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sup> -ary noise process. It is also shown that the channel is symmetric and admits a simple expression for its capacity when its noise is stationary ergodic. The 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sup> -ary noise process is next modeled via a generalized version of the recently studied binary queue-based channel (2007) to produce a mathematically tractable stationary ergodic M'th order Markovian noise source with 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sup> + 2 parameters. Numerical results indicate that the capacity of the discrete channel with q = 2, 3 is substantially improved over the cases of perfect channel interleaving (which yields an equivalent memoryless channel) and of hard-decision demodulation (q = 1). These results point to potentially large performance gains achievable by designing coding schemes for this discrete channel that exploit both its memory and soft-decision information, as opposed to ignoring either of them.