Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 65, Issue 1, Pages 276-291Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2018.2862354
Keywords
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
Funding
- NSERC of Canada
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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 the feedback does not increase capacity and generalizing prior related results. The capacity-cost function of the channel with and without feedback is next 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.
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