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Double Error Correction

IP.com Disclosure Number: IPCOM000075301D
Original Publication Date: 1971-Aug-01
Included in the Prior Art Database: 2005-Feb-24
Document File: 1 page(s) / 12K

Publishing Venue

IBM

Related People

Hsiao, MY: AUTHOR [+2]

Abstract

This error correction scheme detects and corrects single and double errors in a data word having n bits, k thereof being information bits and (n-k) check bits. The Bose-Chaudhuri class of codes is applicable.

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Double Error Correction

This error correction scheme detects and corrects single and double errors in a data word having n bits, k thereof being information bits and (n-k) check bits. The Bose-Chaudhuri class of codes is applicable.

From the received data word represented as vector v, the syndrome S is determined by multiplication of v with the parity-check matrix H which comprises n rows and (n-k) columns. Syndrome S is thus an (n-k) component vector. If all syndrome components are zero, the received data vector is error-free. An odd parity of the syndrome components (odd S-parity) indicates an odd number of erroneous positions in the data vector, while an even S-parity indicates an even number. Assuming the received data vector has a maximum of two or less erroneous positions, an odd S-parity indicates a single error while an even S- parity indicates a double error.

For single-error correction, syndrome S is compared with the rows of parity- check matrix H. Assuming the i-th row of matrix H equals S, the i-th position in the data vector is erroneous and is corrected.

For double-error correction syndrome S is added (= Exclusive OR in logical algebra) to the different rows of matrix H in subsequent steps. This logical operation is performed for each component of S with matrix elements of the same position. Addition of S to the k-th row of matrix H yields compare vector R(k). This vector R(k) is then compared with the rows of parity-check matrix H. Assuming the j-...