Bounds on the Error Probability over Finite-State Erasure Channels

Abstract

We analyze the block error probability of linear block codes when used to transmit over a finite-state Markov erasure channel (FSMEC). We introduce a density evolution analysis that allows to derive the distribution of the number of erasures over a finite number of uses of the FSMEC. The DE result is used to derive upper and lower bounds on the block error probability achievable by the best (n, k) linear block code. We show that the upper bound can be generalized to specific codes (and code ensembles) for which the distance spectrum is known. An example of application to a three-state Markov erasure channel (MEC) is presented, for which the upper and the lower bounds show to be very close, hence proving an accurate estimate of the performance achievable by optimum erasure codes.