{"id":"palomar/PALOMAR-2026-08-26-000006","url":"https://github.com/g-pichler/bsc-averaging/tree/288a1d8787c68010534969b53dcf01ba223e085e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-26-000006-v3.json","repo":"https://github.com/g-pichler/bsc-averaging","tags":["cs.IT","math.IT","msc:94A17","msc:94A15","msc:94A40","msc:94A34","msc:26D07","information-theory","channel-coding","binary-channels"],"score":0,"title":"BSCAveraging","trust":"high","domain":"cs.IT","source":"palomar","authors":["Georg Pichler"],"reviews":0,"subject":"cs.IT","summary":"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…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"verified":true,"discussed":0,"published":"2026-09-15","reactions":{},"formalized":true}