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：我们考虑了离散无记忆信道（DMC）在一种新型成本约束下的信道编码问题，该约束同时限制了码字的成本均值和方差。我们证明，在新成本公式下，最大（渐近）可达速率等于容量-成本函数；特别地，强逆定理成立。我们进一步刻画了这些成本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，通过使用一种新的胆怯/大胆编码变体，二阶编码性能在有反馈时得到严格提升，显著扩展了胆怯/大胆编码方案从无约束复合弥散信道到所有成本约束信道的适用性。我们还给出了最小平均错误概率的等价结果。