Polar Codes II
summary
Shows how N independent copies of a binary DMC are combined by a one‑to‑one transform and split via the chain rule into synthetic bit‑channels whose capacities sum to NC(W); simple kernel is G2 with x1 = u1 ⊕ u2 and x2 = u2, producing a worse W− and better W+ (for BEC: W− erasure = 2ε−ε^2, W+ erasure = ε^2). Decoding uses low‑complexity successive‑cancellation in a bit‑reversed order, genie help vanishes as size grows, and convergence is proved by a bounded martingale (examples up to 128 show stepwise polarization).
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