Reed-Solomon Decoder Architecture With Degree-Limited Polynomial
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Solution Overview
Problem
Existing Reed-Solomon decoders are computationally intensive and require significant hardware, leading to inefficiencies in error correction, particularly in applications where latency and power consumption are concerns.
Innovation Solution
The development of scalable Very Large Scale Integration (VLSI) architectures for Reed-Solomon decoders using an inversionless Berlekamp-Massey method with reduced hardware and latency, employing the Horiguchi-Koetter formula for error evaluation and dynamic stopping rules to eliminate unnecessary computations, resulting in a parallel inversionless Berlekamp-Massey method that uses fewer multipliers and registers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional Reed-Solomon decoding methods are used, then error correction capability is achieved, but hardware complexity and computation intensity increase significantly
Solution Approach 1:
The decoding process is divided into distinct modules: syndrome computation unit, error locator polynomial generation unit (using Berlekamp-Massey algorithm), error evaluator polynomial generation unit, and error correction unit. Each module handles a specific aspect of the decoding process, reducing overall hardware complexity through functional segmentation.
Solution Approach 2:
The patent employs dynamic stopping rules in the Berlekamp-Massey algorithm that adaptively terminate iterations based on the actual number of errors detected, rather than always executing the full predetermined number of iterations. This dynamic adaptation reduces computation intensity and hardware resource utilization when fewer errors are present.
2Reliability
If conventional Reed-Solomon decoding methods are used, then error correction is performed, but processing time and latency increase
Solution Approach 1:
The syndrome computation is performed first as a preliminary step to determine the actual number of errors before initiating the full Berlekamp-Massey iteration process. This preliminary action enables the system to skip unnecessary iterations when few errors are present, reducing overall processing time and latency.
Solution Approach 2:
The patent implements dynamic iteration termination in the Berlekamp-Massey algorithm where the number of iterations is adjusted based on the syndrome results. When the syndromes indicate fewer errors than the maximum correction capability, the algorithm terminates early, significantly reducing processing time while maintaining accurate error correction.
3Measurement precision
If conventional Reed-Solomon decoding methods are used, then decoding accuracy is maintained, but power consumption increases
Solution Approach 1:
The patent employs dynamic stopping rules that adaptively control the number of Berlekamp-Massey iterations based on actual error conditions. This dynamic adaptation reduces power consumption by avoiding unnecessary computational iterations while maintaining full decoding accuracy when errors are present within the correction capability.
Solution Approach 2:
The system changes the iteration parameter of the Berlekamp-Massey algorithm dynamically based on syndrome analysis. When syndromes indicate a low error count, the iteration parameter is reduced accordingly, lowering power consumption while preserving decoding accuracy through adaptive parameter adjustment.
Data Source
AI summary
Processing Reed Solomon data is disclosed. A scratch polynomial having a degree is obtained using an inversionless Berlekamp-Massey process. The degree of the scratch polynomial is limited. A magnitude of an error associated with the Reed Solomon data is determined based at least in part on information associated with the degree limited scratch polynomial. In some embodiments, determining the magnitude of an error using the degree limited scratch polynomial enables a smaller device.