Single- and multiple-burst-correcting properties of a class of cyclic product codes

Author

Bahl, Lalit R. ; Chien, Robert T.

Volume

Issue

fYear

1971

fDate

9/1/1971 12:00:00 AM

Firstpage

594

Lastpage

600

Abstract

The direct product of $p$ single parity-check codes of block lengths $n_1,n_2, \\cdots ,n_p$ is a cyclic code of block length $n_1 \\times n_2 \\times \\cdots \\times n_p$ with $(n_1 - 1) \\times (n_2 - 1) \\times \\cdots \\times (n_p - 1)$ information symbols per block, if the integers $n_1,n_2 \\cdots ,n_p$ are relatively prime in pairs. A lower bound for the single-burst-correction (SBC) capability of these codes is obtained. Then, a detailed analysis is made for $p = 3$ , and it is shown that the codes can correct one long burst or two short bursts of errors. A lower bound for the double-burst-correction (DBC) capability is derived, and a simple decoding algorithm is obtained. The generalization to correcting an arbitrary number of bursts is discussed.

Keywords

Burst-correcting codes; Cyclic codes; Product codes; Contracts; Convolutional codes; Decoding; Information theory; Magnetic recording; NASA; Parity check codes; Product codes; State estimation; Viterbi algorithm;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1971.1054690

Filename

1054690

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=916244