Decoding and optimized implementation of SECDED codes over GF(q)
| DWPI Title: Method for determining whether syndrome produced from check symbols with linear code divides column of check matrix used to produce check symbols, involves determining whether parallel multiplication results are equal to one another |
| Abstract: A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic. |
| Use: Method for determining whether syndrome produced from check symbols with linear code divides column of check matrix used to produce check symbols (claimed) for single error correcting, double error detecting (SECDED) codes over GF(q) for use in any data transfer/communication application. |
| Advantage: The construction of distance linear codes is more efficient than by random searching. A simple decoder is provided for linear SECDED codes with an efficient parallel implementation. The amount of logic required to implement the check matrix in circuit logic is reduced since columns for the check matrix is processed. The method provides improved techniques for non-deterministically generating matrix for a linear SECDED code. The method achieves improved computational efficiency. |
| Novelty: The method involves providing (111) pre-computed multiplicative inverses of symbols in column of the check matrix. The multiplicative inverses are multiplied (112) by respectively corresponding symbols of syndrome in parallel to produce parallel multiplication results. The parallel multiplication results (113) are determined whether they are equal to one another. A first/second input is included for providing pre-computed multiplicative inverses of symbols in column of the check matrix and symbols of syndrome respectively. A comparator is coupled to parallel multiplication logic. |
| Filed: 5/19/2014 |
| Application Number: US14281567A |
| Tech ID: SD 11853.2 |
| This invention was made with Government support under Contract No. DE-NA0003525 awarded by the United States Department of Energy/National Nuclear Security Administration. The Government has certain rights in the invention. |
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