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.

翻译：我们研究了离散无记忆信道（DMC）在一种新颖代价约束下的信道编码问题，该约束同时限制了码字的代价均值和方差。我们证明，在新代价公式下（渐近）可达的最大速率等于容量-代价函数；特别地，强逆成立。我们进一步刻画了这些代价约束码的最优二阶编码速率；特别地，最优二阶编码速率是有限的。然后我们证明，通过使用一种新的谨慎/大胆编码变体，反馈能够严格提升二阶编码性能，这将谨慎/大胆编码方案的适用范围从无约束的混合色散信道显著扩展到所有代价约束信道。同时给出了关于最小平均错误概率的等价结果。