Refinement of the Random Coding Bound

The problem of deriving refined bounds on the sub-exponential factor in the random coding bound for discrete memoryless channels is considered. In particular, for independent identically distributed random code ensembles and for rates above the critical rate, we prove that if a regularity condition is satisfied (respectively, not satisfied), then for any ε > 0 a sub-exponential factor of O(N
^-0.5
(1-ε+ρ̅*
_R
(respectively, O(N
^-0.5
)) is achievable, where N and R are the blocklength and rate, respectively. The term ρ̅*
_R
is related to the slope of the random coding exponent at rate R.