Polar codes for broadcast channels

Naveen Goela, Emmanuel Abbe, Michael Gastpar

Research output: Contribution to journalArticle

33 Scopus citations

Abstract

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 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 block lengths n = 512, 1024, 2048 corroborate the theory.

Original languageEnglish (US)
Article number6975233
Pages (from-to)758-782
Number of pages25
JournalIEEE Transactions on Information Theory
Volume61
Issue number2
DOIs
StatePublished - Feb 1 2015

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Marton's region
  • Polar codes
  • broadcast channel
  • random binning
  • superposition codes

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