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

Content Provider	IEEE Xplore Digital Library
Author	Bocharova, I.E. Hug, F. Johannesson, R. Kudryashov, B.D.
Copyright Year	1963
Abstract	In 1995, Best etal. published a formula for the exact bit error probability for Viterbi decoding of the rate R =1/2, memory m = 1 (two-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 (four-state) convolutional encoder with generator matrix G(D) = (1 + D² 1 + D + D²) 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 two-state encoder and by Lentmaier et al. for a four-state encoder are used. 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.
Sponsorship	IEEE Information Theory Society
Starting Page	4635
Ending Page	4644
Page Count	10
File Size	2342685
File Format	PDF
ISSN	00189448
Volume Number	58
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Error probability Vectors Viterbi algorithm Measurement Decoding Convolutional codes Equations Viterbi decoding Additive white Gaussian noise (AWGN) channel binary symmetric channel (BSC) bit error probability convolutional code convolutional encoder exact bit error probability
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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