BCH Soft Decoding Beyond Half-Distance Error Limits
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Solution Overview
Problem
Existing Bose-Chaudhuri-Hocquenghem (BCH) code decoding algorithms are limited in their ability to handle error patterns beyond the (d−1)/2 Hamming distance, requiring a large number of operations and being unable to decode when the number of weak bit errors is less than r+1, which restricts their raw bit error rate (BER) coverage.
Innovation Solution
The proposed method involves finding a dimension bound for linear space solutions of key equations, reducing core processing to a small evaluation set linked to an r-size linear basis, enabling vast computational sharing and combinatorial ordering to solve related linear equations, allowing decoding with fewer errors and reducing complexity, specifically using r operations per iteration and decoding when the number of weak bit errors is ≥r−1.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If prior-art fast Chase decoders use partial decoding per iteration, then processing speed is improved, but the decoder covers a smaller range of error patterns
Solution Approach 1:
The patent applies partial action by performing partial decoding on only the subset of weak bits rather than processing the entire codeword. This is achieved by identifying a subset of bits with the lowest reliability metrics and limiting the decoding operations to this subset, thereby reducing computational complexity while maintaining the ability to correct errors in the most problematic positions.
Solution Approach 2:
The patent implements local quality by applying different processing strategies to different parts of the data. Specifically, full decoding is applied to the subset of weak bits while other bits receive minimal or no processing. This localized approach concentrates computational resources where they are most needed, improving both speed and error pattern coverage.
2Reliability
If prior-art algorithms process entire error-locator-polynomial-type polynomials, then decoding capability is maintained, but computational complexity increases
Solution Approach 1:
The patent extracts only the essential components needed for decoding by focusing on a subset of weak bits rather than processing entire error-locator-polynomial-type polynomials. This extraction reduces the problem size from the full codeword to a manageable subset, significantly lowering computational complexity while preserving decoding capability for the most critical error patterns.
Solution Approach 2:
The patent segments the decoding problem by dividing the codeword into subsets based on reliability metrics. Instead of processing the entire polynomial, the algorithm segments the work to handle only the subset of weak bits that contribute most to the error pattern, thereby reducing computational complexity while maintaining reliability.
3Reliability
If Chase soft decoding is used to increase soft decoding capability, then error correction capability is improved, but the requirement of at least r+1 weak bit errors limits applicability
Solution Approach 1:
The patent introduces dynamics by adaptively adjusting the decoding threshold based on the actual number of weak bit errors detected. Instead of requiring a fixed minimum of r+1 weak bit errors, the algorithm dynamically determines the appropriate threshold based on reliability metrics, allowing it to effectively handle a broader range of error patterns including cases with fewer than r+1 weak bit errors.
Solution Approach 2:
The patent changes the parameter of the decoding threshold from a fixed value (r+1) to a dynamic value determined by reliability metrics. This parameter change allows the algorithm to adapt to different error scenarios, improving versatility while maintaining the high error correction capability of Chase soft decoding.
Data Source
AI summary
A method for Bose-Chaudhuri-Hocquenghem (BCH) soft error decoding includes receiving a codeword x, wherein the received codeword x has τ=t+r errors for some r≥1; computing a minimal monotone basis {λi(x)}1≤i≤r+1⊆F[x] of an affine space V={λ(x)∈F[x]:λ(x)·S(x)=λ′(x) (mod x2t), λ(0)=1, deg(λ(x)≤t+r}, wherein λ(x) is an error locator polynomial and S(x) is a syndrome; computing a matrix A≡(λj(βi))i∈[w],j∈[r+1], wherein W={β1, . . . , βw} is a set of weak bits in x; constructing a submatrix of r+1 rows from sub matrices of r+1 rows of the subsets of A such that the last column is a linear combination of the other columns; forming a candidate error locating polynomial using coefficients of the minimal monotone basis that result from the constructed submatrix; performing a fast Chien search to verify the candidate error locating polynomial; and flipping channel hard decision at error locations found in the candidate error locating polynomial.