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Convolutional Code for Correcting Random and Burst Errors

IP.com Disclosure Number: IPCOM000084097D
Original Publication Date: 1975-Sep-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 2 page(s) / 46K

Publishing Venue

IBM

Related People

Chen, CL: AUTHOR

Abstract

To accommodate a data rate of 7200 BPS within 32000 BPS of bandwidth, a convolutional code of a rate 7200/32000 = 9/40 may be used for forward error correction. The code would require a basic block length of 40 resulting in a long constraint length. Alternatively, a code of slightly higher rate but shorter basic block length may be used. Redundant bits are then stuffed to reduce the overall data rate.

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Convolutional Code for Correcting Random and Burst Errors

To accommodate a data rate of 7200 BPS within 32000 BPS of bandwidth, a convolutional code of a rate 7200/32000 = 9/40 may be used for forward error correction. The code would require a basic block length of 40 resulting in a long constraint length. Alternatively, a code of slightly higher rate but shorter basic block length may be used. Redundant bits are then stuffed to reduce the overall data rate.

The convolutional code proposed here is a rate 1/4 code with a constraint length of 36. It is capable of correcting 3 random errors in an encoded sequence of 36 bits. It also corrects a single burst of 11 bits within 36 bits.

The encoded sequence of bits is arranged as shown in Fig. 1. The original information bits are represented by A(i). The check bits are B(i), C(i), and D(i). Extra redundant bits, denoted by S, are stuffed at the end of 36 encoded bits. Thus, the overall rate of the encoded sequence is 9/40.

The encoder shown in Fig. 2 generates check bits according to the following rules: B(9) = A(9) + A(6) C(9) = A(9) + A(9) (1) D(9) = A(6) + A(1). where the addition of two bits is a modulo 2 sum or exclusive OR sum. The 9-stage shift register is set to zero before the encoding.

Let EA(i), EB(i), EC(i), and ED(i) denote the channel errors at positions A(i), B(i), C(i), and D(i), respectively. The received code sequence is denoted by RA(i), RB(i), RC(i), and RD(i), where RA(i) = A(i) + EA(i) RB(i) = B(i)...