Channel Capacity — Blahut-Arimoto

Shannon's channel capacity C = max_{p(x)} I(X;Y) is the supreme reliable communication rate. The Blahut-Arimoto algorithm (1972) computes C via alternating optimization: q(x|y) ← p(x)·exp(∑_y p(y|x)log q(x|y)) then normalize p(x). Each iteration increases I(X;Y) monotonically. For the BSC with crossover ε: C = 1 - H_b(ε). The Z-channel shows how asymmetric channels have non-uniform capacity-achieving distributions.