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A Closed Form Expre...
A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes
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- Bocharova, Irina (författare)
- Lund 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
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- Hug, Florian (författare)
- Lund 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
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- Johannesson, Rolf (författare)
- Lund 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
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- Kudryashov, Boris (författare)
- Lund 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
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(creator_code:org_t)
- 2012
- 2012
- Engelska.
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 58:7, s. 4635-4644
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http://dx.doi.org/10...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)
Nyckelord
- additive white Gaussian noise channel
- binary symmetric channel
- bit error probability
- convolutional code
- convolutional encoder
- exact bit error probability
- Viterbi decoding
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- ref (ämneskategori)
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