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A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length N, code rate R, and error probability P is analyzed. Given a tradeoff between N,P and a tradeoff between N,R, we return an interpolating tradeoff among N,R,P (Theorem 5). CapacityQuantitatively, if P=(-N^β^*) is possible for some β^* and if R=-N^1/μ^* is possible for some 1/μ^*, then (P,R)=((-N^β'),-N^-1/μ') is possible for some pair (β',1/μ')arXiv:1812.08112v1 fatcat:eobjw5c5k5abxofjfdug4ublse