Recursive projection-aggregation framework for decoding Reed-Muller codes in digital communication systems

Background

In the field of digital communications, error-correcting codes are essential for ensuring data integrity over noisy channels. Reed-Muller (RM) codes are a foundational class of linear block codes recognized for their simple, universal, and channel-independent construction. As modern communication networks, such as 5G and the Internet of Things (IoT), continue to evolve, there is a critical need for highly reliable data transmission. Specifically, these advanced applications require robust error correction mechanisms that can operate efficiently at short to medium block lengths and low code rates to maintain seamless connectivity.

Despite the theoretical appeal of RM codes, current decoding approaches face significant limitations. Existing RM decoding algorithms, including Reed’s method, recursive list-decoding, and Berlekamp-Welch, struggle to deliver competitive error-correcting performance. At short to medium block lengths and low code rates, these traditional RM decoders fail to match the efficacy of state-of-the-art polar code decoders. Conversely, while polar codes achieve high performance and channel capacity, they suffer from suboptimal scaling at short block lengths and require complex, channel-dependent constructions. This creates a critical gap where neither existing RM decoders nor polar codes provide an optimal, universally applicable solution.

Technology

The Recursive Projection-Aggregation (RPA) decoding framework is an advanced error-correction solution for processing Reed-Muller codes in digital communications. It operates by projecting received codewords onto cosets of subspaces to create lower-order representations. These projections are decoded recursively and recombined using aggregation methods, such as majority voting or log-likelihood ratio summation, iteratively converging on the correct codeword. The system enhances accuracy through list decoding, which evaluates bit patterns for unreliable bits, and code concatenation, which uses an outer code for verification. Its recursive architecture inherently supports parallel execution across multiple processing units.

This solution is highly differentiated by its superior performance and channel-independent universality, outperforming state-of-the-art polar code decoders at short block lengths and low code rates. Unlike polar codes requiring channel-specific constructions, this framework’s universal design simplifies deployment across varying conditions. It achieves faster polarization and sharper error probability transitions, yielding up to a 0.75 dB gain and significantly lower error rates. Furthermore, the framework’s natural parallelization enables exceptional throughput and low-latency processing in hardware or software. These advantages make it uniquely suited for demanding modern applications, including 5G and Internet of Things networks.

Benefits

• Delivers superior error-correcting performance and accuracy compared to state-of-the-art polar codes, particularly at short to medium block lengths and low code rates.
• Enables high-throughput and low-latency decoding through a recursive architecture that naturally supports parallel execution across multiple hardware or software processing units.
• Simplifies deployment across varying network environments due to its universal, channel-independent code construction.
• Provides an ideal error-correction solution for modern digital communication systems, such as 5G and IoT, which frequently rely on short block lengths.
• Enhances overall system reliability by utilizing list decoding and code concatenation to identify unreliable bits and verify results.
• Offers broad adaptability, allowing the framework to be extended to other vector space structure codes like BCH, Reed-Solomon, and expander codes.

Applications

• 5G mobile communication networks
• Internet of Things networks
• Satellite data transmission systems
• Low latency wireless communications
• Digital data storage systems

Additional info

The Recursive Projection-Aggregation (RPA) framework decodes Reed-Muller codes by projecting received signals onto subspace cosets to create lower-order representations. These are processed recursively and recombined through aggregation techniques like majority voting or log-likelihood ratio summation. Augmented by list decoding and code concatenation, this parallelizable architecture enables high-speed, high-accuracy error correction in digital communications, surpassing polar code performance at short to medium block lengths.