Capacity of Burst Noise-Erasure Channels With and Without Feedback and Input Cost

A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to have a so-called “quasi-symmetry” property under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel’s block mutual information, resulting in a closed-form formula for its non-feedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that feedback does not increase capacity and generalizing prior related results. The capacity-cost function of the channel with and without feedback is also investigated. A sequence of finite-letter upper bounds for the capacity-cost function without feedback is derived. Finite-letter lower bonds for the capacity-cost function with feedback are obtained using a specific encoding rule. Based on these bounds, it is demonstrated both numerically and analytically that feedback can increase the capacity-cost function for a class of channels with Markov noise-erasure processes. Index Terms Channels with burst errors and erasures, channels with memory, channel symmetry, non-feedback and feedback capacities, non-feedback and feedback capacity-cost functions, input cost constraints, stationary ergodic and Markov processes. The authors are with the Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada (Emails: [email protected], {fady, linder}@mast.queensu.ca). This work was supported in part by NSERC of Canada. Parts of this work will be presented at the 2017 IEEE International Symposium on Information Theory. May 5, 2017 DRAFT ar X iv :1 70 5. 01 59 6v 1 [ cs .I T ] 3 M ay 2 01 7