# Lund University Publications

## LUND UNIVERSITY LIBRARIES

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

; Hug, Florian LU and Kudryashov, Boris LU (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
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)
2011-06-17 08:48:16
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},
location     = {Moscow, Russian Federation},
title        = {Another look at the exact bit error probability for Viterbi decoding of convolutional codes},
year         = {2011},
}

```