A refinement of the random coding bound

An improved pre-factor for the random coding bound is proved. Specifically, for positive dispersion channels, if a certain regularity condition is satisfied, then for any ϵ > 0 a pre-factor of O(N
^{-1/2(1-ϵ+ρ*w(R))}
) is achievable for rates above the critical rate, where ρ*w (R) is related to the slope of the random coding bound at rate R. If the regularity condition is not satisfied, then a pre-factor of O(N
^-1/2
) is achievable. Recent work of the authors shows that the former case is nearly the best possible.