Refinement of the random coding bound

الأصل · EN

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-1/2(1 - ε+ ρᵣ)) (resp. O(N⁻¹/²)) is achievable for rates above the critical rate, where N and R is the blocklength and rate, respectively. The extra term ρᵣ 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.