# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### On the exact bit error probability for Viterbi decoding of convolutional codes

; Hug, Florian LU and Kudryashov, Boris LU (2011) Information Theory and Applications Workshop (ITA), 2011
Abstract
Forty years ago, Viterbi published upper bounds on both the first error event (burst error) and bit error probabilities for Viterbi decoding of convolutional codes. These bounds were derived using a signal flow chart technique for convolutional encoders. In 1995, Best et al. published a formula for the exact bit error probability for Viterbi decoding of the rate R=1/2, memory m=1 convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their method was later extended to the rate R=1/2, memory m=2 generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al.

In this paper, we shall use a different approach to derive the exact bit error probability. We derive and solve a... (More)
Forty years ago, Viterbi published upper bounds on both the first error event (burst error) and bit error probabilities for Viterbi decoding of convolutional codes. These bounds were derived using a signal flow chart technique for convolutional encoders. In 1995, Best et al. published a formula for the exact bit error probability for Viterbi decoding of the rate R=1/2, memory m=1 convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their method was later extended to the rate R=1/2, memory m=2 generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al.

In this paper, we shall use a different approach to derive the exact bit error probability. We derive and solve a general matrix recurrent equation connecting the average information weights at the current and previous steps of the Viterbi decoding. A closed form expression for the exact bit error probability is given. Our general solution yields the expressions for the exact bit error probability obtained by Best et al. (m=1) and Lentmaier et al. (m=2) as special cases. (Less)
author
organization
publishing date
type
Contribution to conference
publication status
published
subject
conference name
Information Theory and Applications Workshop (ITA), 2011
external identifiers
• Scopus:79955757285
language
English
LU publication?
yes
id
692e63b4-c8ab-4edd-a24d-46c4d04b68e0 (old id 1766856)
alternative location
http://ita.ucsd.edu/workshop/11/files/paper/paper_1887.pdf
```@misc{692e63b4-c8ab-4edd-a24d-46c4d04b68e0,