Polar Codes For Broadcast Channels

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: 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 $O(n\ast logn)$ where $n$ is the block length. In addition, polar code sequences obtain a stretched-exponential decay of $O(2^{-n^{\beta }})$ of the average block error probability where $0<\beta <0.5$.

25 pages, double-column, 7 figures

References in corpus (3)

• Nested Polar Codes for Wiretap and Relay Channels
• A Comparison of Superposition Coding Schemes
• Achieving Marton's Region for Broadcast Channels Using Polar Codes

Cited by in corpus (8)

• Relaxed Polar Codes
• Polar Codes' Simplicity, Random Codes' Durability
• The Broadcast Approach in Communication Networks
• Alignment of Polarized Sets
• Channel Polarization through the Lens of Blackwell Measures
• Strong Coordination over Noisy Channels
• Time-Shifted Alternating Gelfand-Pinsker Coding for Broadcast Channels
• Joint Coordination-Channel Coding for Strong Coordination over Noisy Channels Based on Polar Codes