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Shortened Cyclic Code with Burst Error Detection and Synchronization Recovery Capability

IP.com Disclosure Number: IPCOM000080319D
Original Publication Date: 1973-Nov-01
Included in the Prior Art Database: 2005-Feb-27
Document File: 3 page(s) / 44K

Publishing Venue

IBM

Related People

Bahl, LR: AUTHOR [+2]

Abstract

Cyclic codes of shortened block lengths (e.g., 40 bits) which have good capability for correcting synchronization errors and detecting burst errors can be generated by unique polynomials, one example of which is described herein.

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Shortened Cyclic Code with Burst Error Detection and Synchronization Recovery Capability

Cyclic codes of shortened block lengths (e.g., 40 bits) which have good capability for correcting synchronization errors and detecting burst errors can be generated by unique polynomials, one example of which is described herein.

A polynomial-generated code, due to its inherent cyclic nature, is weak against synchronization errors (slips of code block boundaries in either direction). A coset code, obtained by adding a certain fixed vector to all code vectors, has been shown to have synchronization error control capability. For instance, a (n,k) cyclic code can be made invulnerable to synchronization errors of m positions for 1</- absolute value of m</-n-k-1, by adding some nonzero element of the code field to the first symbol of each code vector. However, when a (n,k) cyclic code is shortened by upsilon symbols to result in an (n-upsilon,k-upsilon) code, the largest m (number of positions which can be made invulnerable to synchronization error) is similarly reduced to 1</- absolute value of m </-n-k- upsilon-1. Clearly, if upsilon>/-n-k-1, other properties of a shortened cyclic code must be relied upon for synchronization error protection. Of particular practical importance, is the question of how a shortened burst error control code can be made to protect against synchronization errors.

Proposed herein is a simple scheme for detecting nonconcurrent burst and synchronization errors, based upon the following theorem:

A shortened (n-upsilon,k-upsilon) code obtained from a (n,k) cyclic burst-b correcting code can be made to detect synchronization errors up to position absolute value of m </-b-1, by adding a nonzero element of the code field to the first symbol of each code vector. An example of such a code follows:

In a 40-bit code, 8 bits are allowed for parity checks. lt is desired to have some burst error plus synchronization error detection. The cod...