RS Syndrome Circuit for Low-Complexity Reed-Solomon Correction
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Solution Overview
Problem
Conventional decoding methods for Reed-Solomon (RS) codes, particularly for shortened RS (12, 9) codes, are complex and fail to correctly handle errors when both data and parity symbols are affected, leading to increased decoding complexity and reduced coding gain in hardware implementations like ASICs.
Innovation Solution
A circuit and method for error correction that includes a Reed-Solomon syndrome generator, a decision unit to determine the presence of zero symbols in the syndrome, and an adder to correct errors by adding the syndrome to the received symbol stream, utilizing error location and correction value tables to simplify decoding and correct errors in both data and parity symbols.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional decoding methods (calculating syndrome roots and performing Chien search) are used for RS codes, then decoding can be performed, but the decoding complexity increases and the method fails to correctly handle errors when both data and parity symbols are affected
Solution Approach 1:
The patent extracts and utilizes only the essential information from the syndrome (the presence of at least N zero symbols) to determine error conditions, rather than performing complete syndrome root calculation and Chien search. This selective extraction of critical syndrome properties simplifies the decoding process while maintaining error correction capability for specific error patterns including cases where both data and parity symbols are affected
Solution Approach 2:
Instead of following the conventional approach of calculating syndrome roots and performing Chien search to identify error locations, the patent inverts the logic by directly checking whether at least N syndrome symbols are zero. This inverted approach determines error conditions and enables correction without the complex intermediate steps of root finding and searching, thereby reducing decoding complexity while improving reliability for certain error patterns
2Reliability
If conventional decoding algorithms are applied to shortened RS (12, 9) code, then decoding can be performed, but the algorithm becomes more complicated and coding gain is reduced
Solution Approach 1:
The patent extracts the critical property of the syndrome (having at least N zero symbols) that indicates error conditions in shortened RS (12, 9) code, and uses this extracted information directly for error correction. This avoids the complicated conventional algorithms while maintaining the ability to detect and correct errors, thereby preserving coding gain and reducing algorithm complexity specifically for shortened RS code applications
3Ease of manufacture
If conventional decoding methods are used, then software implementation is relatively easy, but hardware implementation introduces more complex logic and state machines
Solution Approach 1:
The patent extracts the essential error detection information from the syndrome (the count of zero symbols) and uses this simplified criterion for error correction. This extracted approach requires minimal hardware logic - essentially a counter to count zero syndrome symbols and a decision unit to compare with threshold N - making hardware implementation as simple as software while eliminating the need for complex state machines and root calculation logic
Solution Approach 2:
The patent replaces the mechanical/conventional decoding process (syndrome root calculation, Chien search iterations) with a simpler substitution approach: directly counting zero syndrome symbols and comparing with a threshold. This substitution eliminates the need for complex iterative mechanical processes in hardware, replacing them with simple counting and comparison operations that are equally easy to implement in both software and hardware
Data Source
AI summary
A circuit for error correction comprises a first RS syndrome generator to generate a first RS syndrome for a RS(n, k) code according to a received symbol stream to be decoded, wherein k and n are respective the number of data symbols and the total number of code symbols in the received symbol stream to be decoded; a first decision unit communicatively coupled to the first RS syndrome generator and configured to determine whether there are at least N symbols in the first RS syndrome that equal 0, wherein N is related to a code distance of the RS(n, k) code; and a first adder communicatively coupled to the first decision unit and configured to output a corrected decoded codeword by adding the first RS syndrome to the received symbol stream to be decoded if there are at least N symbols in the first RS syndrome that equal 0.