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# Paired Error Correcting Scheme

IP.com Disclosure Number: IPCOM000073445D
Original Publication Date: 1970-Dec-01
Included in the Prior Art Database: 2005-Feb-22
Document File: 2 page(s) / 30K

IBM

## Related People

Takayesu, TT: AUTHOR [+2]

## Abstract

Single errors or a class of paired errors can be corrected using a class of specially constructed single error correcting majority decodable codes. This class of codes has (m-1) m information bits and 2m checkbits where m is an integer. For a word of n information bits, b(i), double errors in the information part of the message can be categorized with classes of paired errors (b(i), b(i) + tau), where i = 0, 1, 2,....., n-1. tau is a member of the set of integers from 1 to n-1. Obviously, double adjacent errors (DAE's) is a class of paired errors denoted by (b(i), b(i) + 1). The addition (i + tau) is done in Mod n arithmetic.

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Paired Error Correcting Scheme

Single errors or a class of paired errors can be corrected using a class of specially constructed single error correcting majority decodable codes. This class of codes has (m-1) m information bits and 2m checkbits where m is an integer. For a word of n information bits, b(i), double errors in the information part of the message can be categorized with classes of paired errors (b(i), b(i) + tau), where i = 0, 1, 2,....., n-1. tau is a member of the set of integers from 1 to n-
1. Obviously, double adjacent errors (DAE's) is a class of paired errors denoted by (b(i), b(i) + 1). The addition (i + tau) is done in Mod n arithmetic.

The class of codes used is constructed in such a way that if (b(i), b(i) + tau) is the class of paired errors to be corrected then the pair b(i) and b(i) + tau is permitted to appear in at most one set of voting equations; furthermore, b(i) and b(i) + tau should not be involved in the same parity check equation. With these two properties fulfilled, to correct a class of paired errors is simply a two-step decoding procedure; the first decoding step transforms a paired error into a single error and the second decoding step corrects this error. Thus, by decoding a received word twice, paired errors can always be corrected. In addition to this simplicity in decoding, three-way voting gates rather than five-way gates usually required for double error correction are used, thus a reduction in hardware is achieved.

The...