Capacity-Achieving BBT Polar Codes with Interleaver-Assisted BP Decoding

2026-03-20

AI Summary

This work addresses the challenges of polar codes in supporting arbitrary block lengths and suffering from high decoding latency. It proposes a channel transformation based on binary balanced trees (BBT), achieving capacity-approaching polarization for any block length—a first in the field. Furthermore, an interleaving-aided belief propagation (BP) decoding architecture is developed, integrating subgraph interleaving, optimized posterior probability modules, and weight spectrum analysis to significantly accelerate BP convergence. The resulting IBBT polar codes maintain near-maximum-likelihood performance while substantially reducing decoding latency, thereby offering both flexibility in code length and high decoding efficiency.

Technology Category

Cognitive Modeling & Cognitive Systems: Neural Spike CodingMachine Learning: Hardware-aware MLSearch and Optimization: Learning to Search

Application Category

Security and Privacy: Privacy-enhancing technologiesGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In this paper, we introduce a binary balanced tree (BBT) channel transformation that extends Arıkan's channel transformation to arbitrary block lengths. We prove that the proposed transformation induces channel polarization, thereby establishing that BBT polar codes achieve the capacity of binary-input memoryless symmetric (BMS) channels. To characterize the finite-length performance of BBT polar codes, we further develop an efficient method for estimating the weight spectrum by exploiting the hierarchical tree structure, and derive analytical upper and lower bounds on the frame error rate (FER) under maximum-likelihood (ML) decoding. For practical low-latency implementations, we propose interleaved BBT (IBBT) polar codes together with a belief-propagation (BP) decoding algorithm. Specifically, based on the normal-graph representation of BBT polar codes, interleavers are introduced between adjacent layers to modify the message-passing schedule. In addition, we propose to perform BP decoding on an IBBT sub-normal graph and replace partial BP processing modules with a posteriori probability (APP) calculation modules, thereby reducing the number of message-passing steps required per iteration. Numerical results demonstrate that the proposed interleaving strategy improves decoding convergence, while the sub-normal-graph-based BP decoding algorithm significantly reduces decoding latency while maintaining comparable error-rate performance.

Problem

• polar codes
• channel polarization
• arbitrary block lengths
• low-latency decoding
• belief-propagation decoding

Innovation

• BBT polar codes
• interleaver-assisted BP decoding
• channel polarization
• sub-normal graph
• low-latency decoding