A communication channel modeled on contagion

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