Reed-Solomon Decoding with Modified Syndromes for High Erasures
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Solution Overview
Problem
The Berlekamp-Massey algorithm (BMA) is ineffective when the number of erasures exceeds the nominal error correction strength of Reed-Solomon (RS) codes, leading to inefficiencies in error and erasure decoding.
Innovation Solution
An apparatus and method that includes a syndrome calculator, erasure locator, syndrome modifier, and error locator to generate partial syndromes, erasure locator polynomials, and error locator polynomials, allowing for efficient error and erasure decoding by leveraging known erasure locations and reducing the number of BMA iterations, thereby improving decoding efficiency and reducing latency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Berlekamp-Massey algorithm is used for error and erasure decoding, then decoding can be performed using standard Reed-Solomon code capabilities, but the algorithm becomes ineffective when the number of erasures exceeds the nominal error correction strength
Solution Approach 1:
The patent segments the decoding process into distinct phases: erasure location identification, syndrome calculation based on known erasure positions, and error location finding using modified syndromes. This segmentation allows the system to handle erasures separately from random errors, enabling effective decoding even when erasure counts exceed traditional limits by treating erasures as known positions that reduce the search space for error locations
Solution Approach 2:
The patent performs preliminary identification and marking of erasure positions before executing the main error decoding process. By pre-locating erasures and incorporating their positions into syndrome calculations, the system prepares modified syndromes that already account for erasure contributions, allowing the Berlekamp-Massey algorithm to focus only on finding remaining error locations rather than dealing with the full complexity of mixed errors and erasures
2Ease of manufacture
If traditional Reed-Solomon decoding is used, then the implementation is straightforward with standard algorithms, but decoding latency increases when erasures exceed error correction strength
Solution Approach 1:
The patent performs preliminary identification and marking of erasure positions before executing the main error decoding process. By pre-locating erasures and incorporating their positions into syndrome calculations, the system prepares modified syndromes that already account for erasure contributions, allowing the Berlekamp-Massey algorithm to focus only on finding remaining error locations rather than dealing with the full complexity of mixed errors and erasures
Solution Approach 2:
The patent modifies the syndrome parameters by calculating syndromes specifically based on known erasure positions and then using these modified syndromes in the error location finding process. This parameter transformation changes the input to the Berlekamp-Massey algorithm from raw syndromes to erasure-adjusted syndromes, reducing the computational burden and iteration requirements while maintaining implementation based on standard algorithms
3Measurement precision
If the Berlekamp-Massey algorithm processes all syndromes, then complete error and erasure information is considered, but the number of iterations increases reducing decoding efficiency
Solution Approach 1:
The patent extracts and separates the erasure position information from the overall decoding problem. By identifying erasure locations in advance and removing their contribution from the syndrome equations, the system creates a simplified sub-problem that only involves finding random error locations. This extraction reduces the number of syndromes that need to be processed by the Berlekamp-Massey algorithm while preserving all necessary information for accurate decoding
Solution Approach 2:
The patent applies partial action by having the Berlekamp-Massey algorithm process only a subset of syndromes - specifically those modified to account for erasures - rather than processing all raw syndromes. This partial processing is sufficient because the erasure contributions have been separately accounted for, allowing the algorithm to converge faster while maintaining complete decoding accuracy
Data Source
AI summary
A codeword may have errors and erasures. In embodiments, an apparatus may include a syndrome calculator configured to generate partial syndromes of the codeword, an erasure locator configured to generate an erasure locator polynomial, and a syndrome modifier configured to generate modified partial syndromes based at least in part on the partial syndromes and the erasure locator polynomial. The apparatus may further include an error locator configured to generate an error locator polynomial using the modified partial syndromes, for error and erasure decoding of the codeword.