A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes
Författare
Summary, in English
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.
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.
Publiceringsår
2012
Språk
Engelska
Sidor
4635-4644
Publikation/Tidskrift/Serie
IEEE Transactions on Information Theory
Volym
58
Issue
7
Fulltext
- Available as PDF - 367 kB
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Dokumenttyp
Artikel i tidskrift
Förlag
IEEE - Institute of Electrical and Electronics Engineers Inc.
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
Nyckelord
- additive white Gaussian noise channel
- binary symmetric channel
- bit error probability
- convolutional code
- convolutional encoder
- exact bit error probability
- Viterbi decoding
Status
Published
Forskningsgrupp
- Information Theory
ISBN/ISSN/Övrigt
- ISSN: 0018-9448