Modified Reed-Solomon Decoder With Precomputed Erasure Polynomial
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Solution Overview
Problem
Conventional Reed-Solomon (RS) decoders face inefficiencies in decoding shortened/punctured RS codes, particularly in handling errors and erasures, due to the need for extensive syndrome calculations and complex polynomial computations, which increase processing time and circuit complexity.
Innovation Solution
A high-speed RS decoder is developed that stores an erasure locator polynomial and uses a modified syndrome calculator and further modified Euclidean algorithm to reduce the number of clock cycles required for syndrome calculation and error correction, allowing for efficient decoding of modified RS codes with fewer logic gates and simpler circuit design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional syndrome calculation and polynomial computation methods are used in RS decoders, then error correction capability is maintained, but processing time and circuit complexity increase
Solution Approach 1:
The patent pre-calculates and stores the erasure locator polynomial σ0(x) and its reciprocal polynomial before decoding operations. This preliminary preparation eliminates the need for complex real-time polynomial computations during syndrome calculation, significantly reducing processing time while maintaining error correction capability for shortened/punctured RS codes
Solution Approach 2:
The patent modifies the traditional syndrome calculation approach by incorporating pre-stored polynomial parameters specific to shortened/punctured RS codes. By changing the calculation parameters to use these pre-computed polynomials rather than performing full polynomial divisions, the system achieves faster processing without sacrificing decoding accuracy
2Reliability
If conventional syndrome calculation and polynomial computation methods are used in RS decoders, then error correction capability is maintained, but circuit complexity increases
Solution Approach 1:
The erasure locator polynomial and its reciprocal are pre-computed and stored in memory before decoding operations begin. This eliminates the need for complex polynomial multiplication and division circuits during real-time decoding, significantly reducing circuit complexity while maintaining the ability to correct errors in shortened/punctured RS codes
Solution Approach 2:
The patent extracts and separates the complex polynomial computation steps from the real-time decoding process. By removing the polynomial multiplication and division operations from the critical decoding path and replacing them with simple lookups of pre-computed values, the circuit complexity is dramatically reduced while error correction capability is preserved
3Measurement precision
If modified RS codes are decoded using conventional methods, then decoding accuracy is maintained, but the number of clock cycles increases
Solution Approach 1:
The system pre-calculates the erasure locator polynomial σ0(x) and stores it in memory before decoding operations. During decoding, this pre-computed polynomial is directly retrieved and used in syndrome calculations, reducing the number of clock cycles required while maintaining decoding accuracy for modified RS codes such as those in the IEEE 802.16a standard
Solution Approach 2:
The patent changes the decoding parameters to utilize pre-computed polynomials specific to the modified RS code structure. By adapting the syndrome calculation to use these pre-prepared parameters rather than performing standard polynomial operations, the system achieves faster decoding with the same accuracy level
Data Source
AI summary
A decoder suitable for use in a digital communications system utilizing an RS(n′, k′) code modified from an RS(n, k) code receives n′-symbol vectors each including k′ message symbols and r′=n′−k′ parity symbols and decodes the n′-symbol vectors to correct errors therein, wherein n, k, n′, and k′ are integers, and k′<n′<n, k′<k<n, and wherein the decoder stores therein one erasure locator polynomial σ0(x). The decoder includes a syndrome calculator for receiving the n′-symbol vectors and for calculating syndromes of each n′-symbol vector, wherein the i-th syndrome Si of one n′-symbol vector R′, (rn′−1, rn′−2, . . . , r0), is Si=Rs(αi+1) for i=0, 1, . . . , n−k−1, wherein Rs(x)=rn′−1xn′−1+rn′−2xn′−2+ . . . +r0, and means for finding the locations and values of the errors in each n′-symbol vector using the syndromes thereof and the one erasure locator polynomial σ0(x).