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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]

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arikan's polarization technique applied individually to each user transforms independent uses of an m-user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: 1) the “uniform sum-rate” of the original MAC is preserved, 2) the extremal MACs have uniform rate regions that are not only polymatroids but matroids, and thus, 3) their uniform sum-rate can be reached by each user transmitting either uncoded or fixed bits; in this sense, they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of O(n \log n) (where n is the block length), a block error probability of o(\exp (- n^1/2 - \varepsilon)), and capable of achieving the uniform sum-rate of any binary input MAC with arbitrary many users. Applications of this polar code construction to channels with a finite field input alphabet and to the additive white Gaussian noise channel are also discussed. [ABSTRACT FROM PUBLISHER]