Arıkan's polar codes (2009) achieve channel capacity by recursively combining channels. The transform G_N = B_N F^⊗n splits N synthetic channels into "good" (capacity→1) and "bad" (capacity→0) — send data on good channels, freeze bad ones to 0.
Capacity C = — | Good channels: — | Rate: —
Combine: I(U₁) = I(W)² (bad) | Split: I(U₂|U₁) ≈ 2I(W)−I(W)² (good) → polarization after n steps