Multiple-bases Belief-Propagation and Permutation Decoding for Block Codes

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This patent describes an advanced method and system for decoding digital data transmitted or stored using block codes, especially in noisy environments. The invention utilizes multiple belief-propagation (BP) decoders operating in parallel, each based on different parity-check matrices or modified received words using code automorphisms. A selector then chooses the best reconstructed message from the decoder outputs. This approach, called Multiple-Bases Belief-Propagation (MBBP) and Permutation Decoding, improves error correction performance by efficiently handling error patterns that standard decoders may fail to resolve.

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• Wireless communication systems (e.g., 5G, Wi-Fi, satellite communications) where robust error correction is crucial.
• Data storage devices (e.g., SSDs, hard drives, flash memory) to improve data integrity and prevent loss due to noise or corruption.
• Broadcast systems (e.g., digital TV, satellite broadcasting) for enhanced reliability in harsh transmission conditions.
• Deep space communication, where signal noise and data loss can be significant.
• Any system using block codes (BCH, LDPC, Golay, etc.) that requires high-performance or low-latency error correction.
• Sophisticated digital communication protocols, such as those in automotive networks or avionics.

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• Improved error correction by using several decoding bases and collective decision-making, leading to performance close to maximum likelihood decoding.
• Reduced decoding delay and lower data latency because fewer iterations per decoder are needed, especially with parallel processing.
• Greater resilience against problematic error patterns (stopping sets), which standard belief-propagation decoders may struggle with.
• Flexibility in balancing computational complexity (number of decoders and iterations) with performance and latency needs, offering practical deployment options.
• Applicability to a range of code types (including high-rate codes and LDPC codes) and noisy channel scenarios (e.g., binary erasure, AWGN).
• Scalable for implementation in both hardware and software, and compatible with modern digital communication and storage systems.

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Patent Abstract

A decoder (100) for decoding a noisy received word to obtain an estimate of a transmitted word, the noisy received word being based on an encoding rule enabling at least a first and a second parity-check criterion. The decoder (100) comprises the first decoder (110) for decoding the noisy received word based on the first parity-check criterion and to obtain a first estimate of the transmitted code and a second decoder (120) for decoding the noisy transmitted word based on the second parity-check criterion and to obtain a second estimate of the transmitted word or for modifying a noisy received word according to an automorphism of the encoding rule to obtain a modified received word and for decoding the modified received word based on the first parity-check criterion and to obtain the second estimate of the transmitted word. The decoder (100) further comprises a selector (130) for selecting the first or the second estimate of the transmitted word as the estimate of the transmitted word based on the noisy received word.