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

(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)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1978581

- 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
- 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)
- date added to LUP
- 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}, }