Decoding error correction codes using a modular single recursion implementation

Abstract

Systems and methods are provided for performing error correction decoding. The coefficients of the error locator polynomial are iteratively determined for each codeword using a modular implementation of a single recursion key-equation solver algorithm. According to this implementation, a plurality of modules are used to calculate the current and previous coefficients of the error locator polynomial. One module is used for each correctable error. The modular single recursion implementation is programmable, because the number of modules can be easily changed to correct any number of correctable errors. Galois field tower arithmetic can be used to calculate the inverse of an error term. Galois field tower arithmetic greatly reduces the size of the inversion unit. The latency time can be reduced by placing the computations of the inverse error term outside the critical path of the error locator polynomial algorithm.

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