Browse Prior Art Database

Contracted Reed Solomon Codes with Combinational Decoding

IP.com Disclosure Number: IPCOM000082222D
Original Publication Date: 1974-Oct-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 2 page(s) / 13K

Publishing Venue

IBM

Related People

Carter, WC: AUTHOR [+2]

Abstract

The codes described herein and their encoding/decoding scheme allow b-adjacent error correction/detection codes to be used for a wider set of word lengths for smaller b-adjacency, making the designs more useful in practical cases.

This text was extracted from a PDF file.
This is the abbreviated version, containing approximately 68% of the total text.

Page 1 of 2

Contracted Reed Solomon Codes with Combinational Decoding

The codes described herein and their encoding/decoding scheme allow b- adjacent error correction/detection codes to be used for a wider set of word lengths for smaller b-adjacency, making the designs more useful in practical cases.

If t bursts of b-adjacent errors are to be corrected and t + d bursts detected, then a Reed-Solomon (R-S) code has the limitation that the length of the code (data and check bits) must be less than or equal to n = b(2/b/+1) [if t = d = 1, then n = b(2/b/+r2)], and thus the length of the data must be k = n - b(2t + d). For small values of b, such as occur in fast storage module design, this is a severe limitation, as shown in the following table. b t d n k

2 1 0 10 6

3 1 0 27 21

1 1 30 31

2 27 15

4 1 0 68 60

1 1 72 60

2 68 52

b t d n k

5 1 0 165 155

1 1 170 155

2 0 164 145

2 1 165 140.

Thus, standard 64-data bit words cannot be handled until the width of the burst is 5. Most current packages have a width of 2, 3 and 4, although 1 is popular so that standard Hamming codes may be used.

If t = 1, then generalized Hamming codes (Peterson) have lengths n = 2/mb/-1/2/b/-1, where m is the number of rows, and k = T = mb. If m = 2, these codes are isomorphic with the Reed-Solomon codes with t = 1, d = 0. However, if t = 1 only, the number of check bits increases by b as each row is added, and the multiple error detecting capabilities for shortened codes are not as good or predictable as for Reed-Solomon codes. Values of n and k are given in the following table. b m n k

2 3 42 36

4 170 162

3 3 219 210.

A new code is proposed which uses b-bit...