# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Another look at the exact bit error probability for Viterbi decoding of convolutional codes

; ; and (2011) International Mathematical Conference '50 Years Of IPPI'
Abstract
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 (2-state) 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 (4-state) 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... (More)
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 (2-state) 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 (4-state) 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. The exact bit error probability for the binary symmetric channel is determined for various 8 and 16 states encoders including both polynomial and rational generator matrices for rates R=1/2 and R=2/3. Finally, the exact bit error probability is calculated for communication over the quantized additive white Gaussian noise channel. (Less)
author
; ; and
organization
publishing date
type
Contribution to conference
publication status
published
subject
conference name
International Mathematical Conference '50 Years Of IPPI'
conference location
Moscow, Russian Federation
conference dates
2011-07-25 - 2011-07-29
language
English
LU publication?
yes
id
20ebf7ab-4230-45e0-b606-14d1bfb1ceb0 (old id 1978581)
2016-04-04 14:10:29
date last changed
2018-11-21 21:18:43
```@misc{20ebf7ab-4230-45e0-b606-14d1bfb1ceb0,
abstract     = {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 (2-state) 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 (4-state) generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al.<br/><br>
<br/><br>
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. The exact bit error probability for the binary symmetric channel is determined for various 8 and 16 states encoders including both polynomial and rational generator matrices for rates R=1/2 and R=2/3. Finally, the exact bit error probability is calculated for communication over the quantized additive white Gaussian noise channel.},
author       = {Bocharova, Irina and Hug, Florian and Johannesson, Rolf and Kudryashov, Boris},
language     = {eng},
title        = {Another look at the exact bit error probability for Viterbi decoding of convolutional codes},
url          = {https://lup.lub.lu.se/search/files/6298098/1978600.pdf},
year         = {2011},
}

```