Refinement of the Sphere-Packing Bound: Asymmetric Channels

We provide a refinement of the sphere-packing bound for constant composition codes over asymmetric discrete memoryless channels that improves the pre-factor in front of the exponential term. The order of our pre-factor is $Ω(N^{-1/2(1+ε+ ρ_{R}^{\ast})})$ for any $ε>0$, where $ρ_{R}^{\ast}$ is the maximum absolute-value subdifferential of the sphere-packing exponent at rate $R$ and $N$ is the blocklength.

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