A communication channel modeled on contagion

Abstract

We introduce a binary additive communication channel with memory. The noise process of the channel is generated according to the contagion model of G. Polya (1923); our motivation is the empirical observation of Stapper et al. (1980) that defects in semiconductor memories are well described by distributions derived from Polya's urn scheme. The resulting channel is stationary but not ergodic, and it has many interesting properties. We first derive a maximum likelihood (ML) decoding algorithm for the channel; it turns out that ML decoding is equivalent to decoding a received vector onto either the closest codeword or the codeword that is farthest away, depending on whether an apparent epidemic has occurred. We next show that the Polya-contagion channel is an averaged channel in the sense of Ahlswede (1968) and others and that its capacity is zero. Finally, we consider a finite-memory version of he Polya-contagion model; this channel is (unlike the original) ergodic with a nonzero capacity that increases with increasing memory. >