Reed-Solomon Two-Level Decoding With Probabilistic Soft Switching
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Solution Overview
Problem
Reed-Solomon code decoding processes, such as the Berlekamp-Massey method, suffer from high latency in on-the-fly applications due to sequential stages like syndrome computation, error locator polynomial computation, and Chien search, which can be improved without significantly increasing power consumption or decoding failure rates.
Innovation Solution
A probabilistic transition rule is introduced to initiate soft-decision decoding after the error locator polynomial computation, based on the length of the error locator polynomial's linear feedback shift register, reducing the need for the Chien search and thereby decreasing overall decoding latency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If conventional two-level decoding is used with sequential stages (syndrome computation, error locator polynomial computation, Chien search), then decoding reliability is maintained, but decoding latency is high
Solution Approach 1:
The patent applies preliminary action by performing soft-decision decoding before completing the traditional hard-decision decoding process. Specifically, after computing the error locator polynomial, the system probabilistically transitions to soft-decision decoding using the Forney algorithm before the Chien search is completed. This preliminary transition to soft-decision decoding reduces latency by avoiding the completion of unnecessary sequential stages while maintaining decoding reliability through the probabilistic transition rule that determines whether to switch based on the current decoding state.
2Use of energy by moving object
If soft-decision decoding is performed only after hard-decision decoding fails, then power consumption is reduced, but decoding latency increases due to sequential processing
Solution Approach 1:
The patent applies dynamics by making the decoding process adaptive rather than static. The system dynamically transitions between hard-decision and soft-decision decoding modes based on a probabilistic transition rule that evaluates the current decoding state. This dynamic approach allows the system to switch to soft-decision decoding mid-process when beneficial, rather than following a fixed sequential path, thereby reducing latency without proportionally increasing power consumption.
Solution Approach 2:
The patent applies parameter changes by modifying the decoding strategy based on the degree of the error locator polynomial and the number of errors detected. The probabilistic transition rule uses these parameters to determine whether to switch from hard-decision to soft-decision decoding. By changing the decoding mode parameter dynamically based on observed parameters, the system optimizes the balance between power consumption and latency.
3Measurement precision
If the Chien search is completed fully before transitioning to soft-decision decoding, then decoding accuracy is maintained, but overall processing time increases
Solution Approach 1:
The patent applies the taking out principle by extracting the essential error correction functionality from the complete Chien search process. Instead of requiring full completion of the Chien search, the system extracts sufficient information from the error locator polynomial and syndromes to make an informed decision about transitioning to soft-decision decoding. This extraction of necessary information allows the system to achieve adequate decoding accuracy without completing unnecessary processing stages.
Solution Approach 2:
The patent applies partial action by performing only the necessary portion of the hard-decision decoding process before transitioning to soft-decision decoding. The probabilistic transition rule determines that partial completion of the Chien search, combined with soft-decision decoding, is sufficient to achieve the required decoding accuracy. This partial action approach avoids the excessive processing time of completing the full Chien search while maintaining adequate accuracy through the complementary soft-decision decoding.
Data Source
AI summary
Decoding data is disclosed, including computing a syndrome polynomial for Reed-Solomon encoded data, applying the Berlekamp-Massey method to solve key equations associated with the syndrome polynomial, comparing a linear feedback shift register (LSFR) length LΛ associated with an error locator polynomial Λ(x) with an error correction capability t, and based on the comparison, determining whether to perform soft decision decoding or a Chien search.