Patent ID: 9203438
Filing Date: 2015-12-01
Classification: H03M

Abstract:
1. A method for error correction decoding, comprising: a processing circuit receiving a plurality of signals representing a codeword of a cyclic code with a fixed length with a minimum distance between codewords determined by an n-valued shift register based coder prior to transmission, the received codeword consisting of p n-valued symbols with n greater than 2 of which k n-valued symbols are information symbols and (p−k) n-valued symbols are check symbols with p>1 and k>1 and p>k, each n-valued check symbol is determined prior to transmission by an n-valued logic expression, which is not a polynomial expression of a degree greater than 1, with at least two n-valued information symbols as variables and wherein at least one n-valued symbol of the received codeword is in error; and wherein the n-valued logic expression is determined by the shift register based coder; the processing circuit determining an n-valued check symbol from the received k n-valued information symbols that indicates that an error has occurred in the received codeword; the processing circuit generating non-iteratively in a deterministic manner a plurality of calculated codewords from the received codeword, each calculated codeword in the plurality of calculated codewords being associated with the n-valued shift register based coder and including a calculated n-valued symbol, and wherein a value of the calculated n-valued symbol in each of the calculated codewords is generated by the processing circuit evaluating a pre-determined n-valued logic expression that outputs the value, the predetermined n-valued expression is associated with a location of the calculated symbol in a calculated codeword in which it is calculated; the processing circuit selecting one of the plurality of calculated codewords as a correct codeword and providing at least one corrected symbol of the one of the plurality of calculated codewords on an output of the device, wherein the device is part of the group consisting of communication apparatus, data storage apparatus, and medium display apparatus; and, determining a correctness of at least one calculated codeword by comparing it to the received codeword and adding to a score when an n-valued symbol in the at least one calculated codeword is identical to an n-valued symbol in a corresponding position in the received codeword.