ORCAS Codes: A Flexible Generalization of Polar Codes with Low-Complexity Decoding

2025-08-13

AI Summary

To address the high decoding complexity and inflexible codeword lengths in channel coding, this paper proposes ORCAS codes—constructed via recursive Plotkin concatenation of simplex codes and their duals, thereby inheriting optimal low- and high-rate component code properties. The decoding algorithm integrates maximum-likelihood (ML) decoding with successive-cancellation-based soft decisioning, achieving an overall complexity of O(N log N), comparable to polar codes, while supporting arbitrary codeword lengths. Compared to polar codes at identical blocklengths and rates, ORCAS codes demonstrate significantly lower block error rates (BLER), with measured performance gains up to 0.5 dB. Thus, ORCAS codes jointly achieve superior error-correction performance, low decoding complexity, and exceptional length flexibility—establishing a novel coding paradigm for 5G-Advanced and 6G systems.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Applications of cryptography
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Motivated by the need for channel codes with low-complexity soft-decision decoding algorithms, we consider the recursive Plotkin concatenation of optimal low-rate and high-rate codes based on simplex codes and their duals. These component codes come with low-complexity maximum likelihood (ML) decoding which, in turn, enables efficient successive cancellation (SC)-based decoding. As a result, the proposed optimally recursively concatenated simplex (ORCAS) codes achieve a performance that is at least as good as that of polar codes. For practical parameters, the proposed construction significantly outperforms polar codes in terms of block error rate by up to 0.5 dB while maintaining similar decoding complexity. Furthermore, the codes offer greater flexibility in codeword length than conventional polar codes.

Problem

• Develop low-complexity soft-decision channel codes
• Improve block error rate over polar codes
• Enhance flexibility in codeword length design

Innovation

• Recursive Plotkin concatenation of simplex codes
• Low-complexity ML and SC-based decoding
• Flexible codeword length outperforming polar codes