A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes
(2012) In IEEE Transactions on Information Theory 58(7). p.46354644 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 (2state) convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their formula was later extended to the rate R=1/2, memory m=2 (4state) convolutional encoder with generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al.
In this paper, a different approach to derive the exact bit error probability is described. A general recurrent matrix equation, connecting the average information weight at the current and previous states of a trellis section of the Viterbi decoder, is derived and solved. The general solution of this matrix... (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 (2state) convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their formula was later extended to the rate R=1/2, memory m=2 (4state) convolutional encoder with generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al.
In this paper, a different approach to derive the exact bit error probability is described. A general recurrent matrix equation, connecting the average information weight at the current and previous states of a trellis section of the Viterbi decoder, is derived and solved. The general solution of this matrix equation yields a closed form expression for the exact bit error probability. As special cases, the expressions obtained by Best et al. for the 2state encoder and by Lentmaier et al. for a 4state encoder are obtained. The closed form expression derived in this paper is evaluated for various realizations of encoders, including rate R=1/2 and R=2/3 encoders, of as many as 16 states.
Moreover, it is shown that it is straightforward to extend the approach to communication over the quantized additive white Gaussian noise channel. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2430435
 author
 Bocharova, Irina ^{LU} ; Hug, Florian ^{LU} ; Johannesson, Rolf ^{LU} and Kudryashov, Boris ^{LU}
 organization
 publishing date
 2012
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 additive white Gaussian noise channel, binary symmetric channel, bit error probability, convolutional code, convolutional encoder, exact bit error probability, Viterbi decoding
 in
 IEEE Transactions on Information Theory
 volume
 58
 issue
 7
 pages
 4635  4644
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 wos:000305575000033
 scopus:84862522819
 ISSN
 00189448
 DOI
 10.1109/TIT.2012.2193375
 language
 English
 LU publication?
 yes
 id
 efaebb6ad2a44b2694bc28d4db0fe842 (old id 2430435)
 date added to LUP
 20120403 10:34:30
 date last changed
 20180107 06:57:34
@article{efaebb6ad2a44b2694bc28d4db0fe842, 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 (2state) convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their formula was later extended to the rate R=1/2, memory m=2 (4state) convolutional encoder with generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al.<br/><br> <br/><br> In this paper, a different approach to derive the exact bit error probability is described. A general recurrent matrix equation, connecting the average information weight at the current and previous states of a trellis section of the Viterbi decoder, is derived and solved. The general solution of this matrix equation yields a closed form expression for the exact bit error probability. As special cases, the expressions obtained by Best et al. for the 2state encoder and by Lentmaier et al. for a 4state encoder are obtained. The closed form expression derived in this paper is evaluated for various realizations of encoders, including rate R=1/2 and R=2/3 encoders, of as many as 16 states.<br/><br> <br/><br> Moreover, it is shown that it is straightforward to extend the approach to communication over the quantized additive white Gaussian noise channel.}, author = {Bocharova, Irina and Hug, Florian and Johannesson, Rolf and Kudryashov, Boris}, issn = {00189448}, keyword = {additive white Gaussian noise channel,binary symmetric channel,bit error probability,convolutional code,convolutional encoder,exact bit error probability,Viterbi decoding}, language = {eng}, number = {7}, pages = {46354644}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Information Theory}, title = {A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes}, url = {http://dx.doi.org/10.1109/TIT.2012.2193375}, volume = {58}, year = {2012}, }