A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes

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

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

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

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

(creator_code:org_t)

2012
2012
Engelska.
Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 58:7, s. 4635-4644

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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.

Av författaren/redakt...: Bocharova, Irina; Hug, Florian; Johannesson, Rol ...; Kudryashov, Bori ...

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