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A Closed Form Expre...
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Bocharova, IrinaLund University,Lunds universitet,Institutionen för elektro- och informationsteknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Electrical and Information Technology,Departments at LTH,Faculty of Engineering, LTH
(författare)
A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes
- Artikel/kapitelEngelska2012
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2012
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electronicrdacarrier
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LIBRIS-ID:oai:lup.lub.lu.se:efaebb6a-d2a4-4b26-94bc-28d4db0fe842
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https://lup.lub.lu.se/record/2430435URI
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https://doi.org/10.1109/TIT.2012.2193375DOI
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Språk:engelska
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Sammanfattning på:engelska
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Ämneskategori:art swepub-publicationtype
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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 formula was later extended to the rate R=1/2, memory m=2 (4-state) 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 2-state encoder and by Lentmaier et al. for a 4-state 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.
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Hug, FlorianLund University,Lunds universitet,Institutionen för elektro- och informationsteknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Electrical and Information Technology,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)eit-foh
(författare)
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Johannesson, RolfLund University,Lunds universitet,Institutionen för elektro- och informationsteknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Electrical and Information Technology,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)it-rjo
(författare)
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Kudryashov, BorisLund University,Lunds universitet,Institutionen för elektro- och informationsteknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Electrical and Information Technology,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)eit-bko
(författare)
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Institutionen för elektro- och informationsteknikInstitutioner vid LTH
(creator_code:org_t)
Sammanhörande titlar
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Ingår i:IEEE Transactions on Information Theory58:7, s. 4635-46440018-9448
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