BSCAveraging
Three theorems about binary channels on a doubly symmetric binary source: a pair (𝑋, 𝑌) of Bernoulli(1/2) bits with P(𝑋 ≠ 𝑌) = 𝑝, together with Markov chains 𝑈 - 𝑋 - 𝑌 - 𝑉 in which 𝑈 and 𝑉 are the outputs of two independent binary channels applied to 𝑋 and to 𝑌. Let 𝒜 be the set of rate triples (𝑅₀, 𝑅₁, 𝑅₂) with 𝐼(𝑈;𝑋) ≤ 𝑅₁, 𝐼(𝑌;𝑉) ≤ 𝑅₂ and 𝑅₀ ≤ 𝐼(𝑈;𝑉) attainable by arbitrary binary channels on the two sides, and ℬ the same set with both channels restricted to be binary symmetric. (1) conv 𝒜 = conv ℬ for every 𝑝 in [0,1]. (2) At 𝑝 = 0, no pair of binary channels whose rates do not exceed…
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