An improved pre-factor for the random coding bound is proved. Specifically,
for channels with critical rate not equal to capacity, if a regularity
condition is satisfied (resp. not satisfied), then for any ϵ>0 a
pre-factor of O(N−21(1−ϵ+ρˉR∗)) (resp. O(N−21)) is achievable for rates above the
critical rate, where N and R is the blocklength and rate, respectively. The
extra term ρˉR∗ is related to the slope of the random coding
exponent. Further, the relation of these bounds with the authors' recent
refinement of the sphere-packing bound, as well as the pre-factor for the
random coding bound below the critical rate, is discussed.Comment: Submitted to IEEE Trans. Inform. Theor