Channel Coding with Mean and Variance Cost Constraints
CoRR(2024)
摘要
We consider channel coding for discrete memoryless channels (DMCs) with a
novel cost constraint that constrains both the mean and the variance of the
cost of the codewords. We show that the maximum (asymptotically) achievable
rate under the new cost formulation is equal to the capacity-cost function; in
particular, the strong converse holds. We further characterize the optimal
second-order coding rate of these cost-constrained codes; in particular, the
optimal second-order coding rate is finite. We then show that the second-order
coding performance is strictly improved with feedback using a new variation of
timid/bold coding, significantly broadening the applicability of timid/bold
coding schemes from unconstrained compound-dispersion channels to all
cost-constrained channels. Equivalent results on the minimum average
probability of error are also given.
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