On the exact bit error probability for Viterbi decoding of convolutional codes
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1766856
- author
- Bocharova, Irina LU ; Hug, Florian LU ; Johannesson, Rolf LU and Kudryashov, Boris LU
- organization
- publishing date
- 2011
- type
- Contribution to conference
- publication status
- published
- subject
- conference name
- Information Theory and Applications Workshop (ITA), 2011
- conference location
- San Diego, CA, United Kingdom
- conference dates
- 2011-02-06 - 2011-02-11
- 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
- date added to LUP
- 2016-04-04 13:52:57
- date last changed
- 2022-01-30 01:02:01
@misc{692e63b4-c8ab-4edd-a24d-46c4d04b68e0,
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.<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.}},
author = {{Bocharova, Irina and Hug, Florian and Johannesson, Rolf and Kudryashov, Boris}},
language = {{eng}},
title = {{On the exact bit error probability for Viterbi decoding of convolutional codes}},
url = {{http://ita.ucsd.edu/workshop/11/files/paper/paper_1887.pdf}},
year = {{2011}},
}