Reed-Muller Soft Decision Decoding with Optimal Decomposition
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Solution Overview
Problem
High-speed communication networks, such as optical networks, face challenges in achieving coding gains while maintaining low encoding and decoding complexity, particularly in decoding soft information from receive signals.
Innovation Solution
The method involves performing soft decision decoding of Euclidean space Reed-Muller codes using maximum likelihood and maximum a posteriori decoders, with optimal decomposition variables determined through log-likelihood ratio calculations and Plotkin decomposition, enabling efficient decoding of higher order Reed-Muller codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If soft decision decoding is used to improve decoding performance and coding gain, then decoding accuracy is improved, but decoding complexity increases
Solution Approach 1:
The decoding process is segmented into multiple stages: syndrome calculation, error pattern identification, and soft decision refinement. Each stage processes only the necessary information for that specific task, breaking down the complex soft decision decoding into manageable segments that reduce overall computational burden while maintaining accuracy.
Solution Approach 2:
The patent applies partial soft decision processing by performing full soft decision decoding only on critical portions of the data where error correction is most needed, while using simpler hard decision methods for less critical portions. This selective approach achieves sufficient decoding accuracy without the full computational cost of complete soft decision decoding.
2Reliability
If higher order Reed-Muller codes are used to achieve coding gain close to Shannon limit, then error correction performance is improved, but encoding and decoding complexity increases
Solution Approach 1:
Higher order Reed-Muller codes are decomposed into multiple lower order subcodes through systematic segmentation. The encoding and decoding processes are divided into separate stages, each handling a specific subset of the code structure. This segmentation allows complex higher order codes to be processed using simpler, repeated applications of lower order decoding algorithms, reducing overall complexity while maintaining the coding gain benefits.
3Reliability
If complex error correcting codes are used to provide coding gain, then reliability is improved, but latency increases due to additional decoding processing
Solution Approach 1:
Syndrome calculations and error pattern pre-identification are performed as preliminary actions before the main soft decision decoding process. By pre-computing these intermediate results, the patent reduces the processing time required during the critical decoding path, thereby reducing overall latency while maintaining the reliability benefits of complex error correcting codes.
Data Source
AI summary
Soft decision decoding of a codeword of a Reed-Muller (RM) code byselecting an optimal decomposition variable i using a likelihood calculation. A code RM(r, m) is expressed as {(u, uv)|uεRM(r, m−1) and vεRM(r−1, m−1)}, where uv denotes a component-wise multiplication of u and v, and (u, uv)=(r1, r2). A receive codeword is separated into r1=u and r2=uv based on the optimal decomposition variable, and r2 is decoded according to the optimal decomposition variable, using a RM(r−1, m−1) decoder to obtain a decoded v and a first set of decoded bits. The decoded v is combined with r1 using (r1+r2v)/2, and(r1+r2v)/2 is decoded using a RM(r, m−1) decoder to obtain a decoded u and a second set of decoded bits.