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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: 1) Cover’s superposition codes and 2) 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 multiuser 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(n \log n) , where n of the average block error probability where 0 < \beta < {1}/{2} . Reproducible experiments for finite block lengths n = 512, 1024, 2048$ corroborate the theory. [ABSTRACT FROM AUTHOR]