Polar Codes for Broadcast Channels

Polar codes are introduced for discrete memoryless broadcast channels. For m-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from m independent messages to one codeword while satisfying broadcast constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: i) Cover’s superposition codes; ii) Marton’s codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multi-user setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is O(nlogn) where n is the block length. In addition, polar code sequences obtain a stretched-exponential decay of O(2−nβ) of the average block error probability where 0 < β < 1 2. Reproducible experiments for finite bloc