Refinements of the third-order term in the fixed error asymptotics of constant-composition codes

This paper studies the fixed-error asymptotics of constant-composition codes for discrete memoryless channels. An achievable asymptotic expansion is derived with a third-order term that can be as high as 1/2 log n, while being lower when (i) a certain feasibility-decoding condition fails, or (ii) the channel is a sum channel. Converse bounds are used to provide conditions under which each of these losses is unavoidable.