Third-order Analysis of Channel Coding in the Moderate Deviations Regime
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The channel coding problem in the moderate deviations regime is studied; here, the error probability decays sub-exponentially to zero, and the rate approaches the capacity slower than O(1/√(n)). Our result refines Altuğ and Wagner's moderate deviations result by deriving lower and upper bounds on the third-order term in the asymptotic expansion of the maximum achievable message set size. The third-order term of our expansion employs a new quantity here called the channel skewness. For the binary symmetric channel and most practically important (n, ϵ) pairs, including n ∈ [100, 500] and ϵ∈ [10^-10, 10^-1], an approximation up to the channel skewness is the most accurate among several expansions in the literature.
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