The paper considers channel coding for discrete memoryless channels (DMCs) with a novel cost constraint that bounds both the mean and the variance of the cost of the codewords. The key insights are:
The maximum (asymptotically) achievable rate under the new cost formulation is equal to the capacity-cost function, and the strong converse holds.
The optimal second-order coding rate (SOCR) is finite and can be characterized in terms of a function K(r, V) that depends on the mean (r) and variance (V) constraints on the codeword costs.
Feedback can strictly improve the SOCR compared to the optimal SOCR without feedback. The feedback scheme is a new variant of timid/bold coding that does not require multiple capacity-cost-achieving distributions or i.i.d. codewords.
The (Γ, V) cost constraint allows i.i.d. channel inputs with a bounded variance V > 0, preserving the advantage of previous cost constraints that permitted i.i.d. codewords. However, the (Γ, V) formulation can also handle cases where i.i.d. P* codewords are not admissible.
The converse and achievability results provide matching upper and lower bounds on the optimal SOCR in terms of the function K(r, V).
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by Adeel Mahmoo... : arxiv.org 05-07-2024
https://arxiv.org/pdf/2401.16417.pdfDaha Derin Sorular