Doubly-Irregular Repeat-Accumulate Codes over Integer Rings for Multi-user Communications
Fangtao Yu, Tao Yang, Qiuzhuo Chen

TL;DR
This paper introduces doubly irregular repeat-accumulate (D-IRA) codes over integer rings for multi-user communication, achieving near-capacity performance and enabling practical lattice-based network information theory applications.
Contribution
The paper proposes a novel D-IRA ring code structure that optimizes belief-propagation decoding and applies to multi-user setups like compute-forward and dirty paper coding.
Findings
D-IRA codes perform within 0.29 dB of capacity for point-to-point channels.
D-IRA codes reduce gap to capacity in multi-user scenarios, achieving 0.24 dB and 0.91 dB gaps.
Analysis of zero-divisors impacts on iterative decoding and the design of optimized code structures.
Abstract
Structured codes based on lattices were shown to provide enlarged capacity for multi-user communication networks. In this paper, we study capacity-approaching irregular repeat accumulate (IRA) codes over integer rings for -PAM signaling, . Such codes feature the property that the integer sum of codewords belongs to the extended codebook (or lattice) w.r.t. the base code. With it, \emph{% structured binning} can be utilized and the gains promised in lattice based network information theory can be materialized in practice. In designing IRA ring codes, we first analyze the effect of zero-divisors of integer ring on the iterative belief-propagation (BP) decoding, and show the invalidity of symmetric Gaussian approximation. Then we propose a doubly IRA (D-IRA) ring code structure, consisting of \emph{irregular multiplier distribution} and…
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Error Correcting Code Techniques
