Error Locator Circuit Using Normal Basis for Fast BCH Decoding
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Solution Overview
Problem
Existing error correction methods for BCH codes are iterative and time-consuming, requiring hundreds to thousands of clock cycles to correct two bit errors, which hampers the effective bandwidth of these codes.
Innovation Solution
A non-iterative error locator unit is introduced, utilizing a normalized basis transform to convert squaring operations into circular shifts, allowing for the calculation of two bit error locations in as few as 8 clock cycles, by using a combination of operational units, a normalized basis transform unit, and a conversion unit to process syndromes and coefficients directly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If iterative error correction methods (e.g., Chien's search) are used for BCH codes, then error correction capability is maintained, but the number of clock cycles required increases to hundreds or thousands
Solution Approach 1:
The patent transforms the error locator polynomial from the power basis to the normal basis representation. This parameter change in the mathematical domain allows squaring operations to be replaced with circular shifts, reducing the computational complexity from iterative to non-iterative and decreasing clock cycles from hundreds/thousands to just 8 cycles
Solution Approach 2:
The patent substitutes the iterative mechanical search process (Chien's search) with a direct algebraic solution method. By using the normal basis transformation and solving the quadratic equation directly, the system replaces the step-by-step iterative mechanical approach with a single-step algebraic computation
2Productivity
If faster two bit error correction methods (e.g., Saxena et al., Kustedjo et al.) are used, then decoding speed is improved, but the methods remain iterative requiring hundreds or thousands of clock cycles
Solution Approach 1:
The patent applies a fundamental parameter change by representing the error locator polynomial in the normal basis instead of the power basis. This transformation converts squaring operations into circular shifts, enabling a non-iterative solution that completes in 8 clock cycles versus the hundreds or thousands required by previous iterative methods
Data Source
AI summary
An error locator unit for correcting two bit error. The error locator unit includes a plurality of operational units, a normalized basis transform unit, and a conversion unit. The plurality of operations units calculates coefficients of the polynomial based on the generated syndromes in a first basis of a Galois Field. Operating on the coefficients produces a root definition value vector in the first basis. The normalized basis transform unit transforms the root definition value vector to a normal basis to produce a plurality of roots. The conversion unit converts the plurality of roots to the first basis. A scaling factor calculated based on the coefficients is applied to the output of the conversion unit to produce a plurality of scaled roots for said polynomial in the first basis. The plurality of scaled roots is added to produce error locations for the polynomial.