Reed-Solomon Hard Decision Decoding with Early Error Detection
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Solution Overview
Problem
Existing Reed-Solomon decoding processes are inefficient due to the high complexity caused by the repeated application of the Berlekamp-Massey algorithm and Chien search, especially when the number of erasures is significantly larger than the number of errors, leading to impractical implementation challenges.
Innovation Solution
The proposed system bypasses unnecessary processing steps by detecting the presence of errors early and using a polynomial that reflects only the number of errors, rather than the sum of erasures and errors, thereby reducing complexity and optimizing the BM algorithm and Chien search operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Berlekamp-Massey algorithm is applied repeatedly to update the erasure locator polynomial for both erasures and errors, then the decoding can handle both types of noise, but the computational complexity becomes impractically high when the number of erasures is much larger than the number of errors
Solution Approach 1:
The patent segments the decoding process into two independent parts: (1) erasure correction using the known erasure locations and an erasure decoder, and (2) error correction using the Berlekamp-Massey algorithm only for the remaining errors. This segmentation allows the complex BM algorithm to be applied only to the smaller error component rather than the sum of erasures and errors, significantly reducing computational complexity while maintaining the ability to correct both noise types
Solution Approach 2:
The patent performs preliminary identification and correction of erasure locations before applying the Berlekamp-Massey algorithm. By first constructing the erasure locator polynomial from known erasure positions and correcting erasures in advance, the system reduces the problem to a smaller error-only correction task, thereby avoiding the computational burden of applying BM algorithm to the full sum of erasures and errors
2Measurement precision
If the degree of the auxiliary ELP is increased to account for both erasures and errors, then the decoder can identify more error locations, but the hardware requirements and processing complexity increase significantly
Solution Approach 1:
The patent extracts the erasure correction function into a separate, preliminary processing stage that operates independently before the main error correction stage. By removing erasures from the error correction problem and handling them separately using their known locations, the system reduces the degree of the auxiliary ELP needed in the BM algorithm from (E0+E1) to only E1, thereby reducing hardware complexity while maintaining accurate error location identification
Solution Approach 2:
The patent applies different processing strategies to different types of noise: erasures are handled using a specialized erasure decoder that exploits known location information, while errors are handled using the general-purpose Berlekamp-Massey algorithm. This local optimization allows each noise type to be corrected with the most efficient method, reducing overall hardware requirements compared to applying a single unified approach to both
3Measurement precision
If the Chien search algorithm is applied to find zeros in the auxiliary ELP, then the locations of errors can be identified, but the processing time increases when the degree of the polynomial is large
Solution Approach 1:
The patent performs preliminary erasure correction before applying the Chien search algorithm. By first removing the effect of erasures from the received codeword and updating the syndrome accordingly, the system reduces the degree of the auxiliary ELP that needs to be searched. This preliminary action reduces the number of iterations required in the Chien search from the full polynomial degree to a smaller degree corresponding only to error locations, thereby reducing processing time while maintaining accurate error location detection
Data Source
AI summary
A processing circuit is configured to: construct a first locator polynomial for a Reed-Solomon codeword to identify locations of erasures in the Reed-Solomon codeword; determine a first syndrome of the Reed-Solomon codeword; calculate a first error evaluator polynomial from the first syndrome and the first locator polynomial; and perform error detection based on the first error evaluator polynomial to determine presence of errors in the Reed-Solomon codeword. When presence of errors in the Reed-Solomon codeword is not detected in the error detection, the processing circuit bypasses updating the first locator polynomial and proceeds to completing decoding of the Reed-Solomon codeword, but when presence of errors in the Reed-Solomon codeword is detected in the error detection, the system first updates the first locator polynomial to a second locator polynomial in a process with reduced complexity compared to the common one, before completing decoding of the Reed-Solomon codeword.