Reed-Muller Decoding via Recursive Projection and Aggregation
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Solution Overview
Problem
Reed-Muller codes lack an efficient decoder that is competitive in the low rate/block-length regime, particularly for binary input memoryless channels, which hinders their performance in emerging communication technologies like 5G and IoT applications.
Innovation Solution
The proposed solution involves recursive projection-aggregation decoding methods that exploit the self-similarity of Reed-Muller codes, incorporating list-decoding procedures and outer-code concatenations, to efficiently decode Reed-Muller encoded data over binary input memoryless channels, particularly in short code length and low code rate regimes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional decoding methods are used for Reed-Muller codes, then the decoding process is simple, but the error-correcting performance is insufficient in low rate/block-length regime
Solution Approach 1:
The decoding process is segmented into multiple stages: projection of received word onto cosets of different subspaces, recursive decoding of each projected word, and aggregation of decoded results. This segmentation allows the decoder to achieve near-optimal error correction performance by systematically processing different components of the code structure, while maintaining manageable complexity through modular organization of decoding tasks.
Solution Approach 2:
The decoder employs nested recursive structures where Reed-Muller codes of different orders are decoded hierarchically. The decoding of RM(m,r) codes incorporates decoding of lower-order RM(m-1,r-1) codes through the projection and aggregation process, creating a nested decoding framework that efficiently handles the hierarchical structure of Reed-Muller codes and achieves near-optimal performance without exponential complexity growth.
2Reliability
If efficient decoding algorithms are implemented for Reed-Muller codes, then error-correcting performance improves, but computation and power consumption increase
Solution Approach 1:
By segmenting the decoding process into projection, recursive decoding, and aggregation stages, the computational workload is distributed across multiple simpler operations rather than one complex computation. This segmentation reduces peak power consumption while maintaining overall decoding accuracy, as each stage can be executed with lower instantaneous energy requirements.
Solution Approach 2:
The recursive decoding process operates periodically across different cosets and subspaces, processing projected words in systematic cycles. This periodic action allows for efficient resource utilization and power management, where computational resources are activated in structured intervals rather than continuously, reducing average power consumption while achieving near-optimal decoding performance through repeated refinement.
Data Source
AI summary
Various embodiments are directed to Reed-Muller decoding systems and methods based on recursive projections and aggregations of cosets decoding, exploiting the self-similarity of RM codes, and extended with list-decoding procedures and with outer-code concatenations. Various embodiments are configured for decoding RM codes (and variants thereof) over binary input memoryless channels, such as by, for each received word of RM encoded data, projecting the received word onto each of a plurality of cosets of different subspaces to form thereby a respective plurality of projected words; recursively decoding each of the respective plurality of projected words to form a respective plurality of decoded projected words; and aggregating each of the respective decoded projected words to obtain thereby a decoding of the corresponding received word of RM encoded data.