2011/11/16 by Irina E. Bocharova, Florian Hug, Bocharova, Irina E. +5
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Energy Harvesting in Wireless Networks #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1111.3820
9 pages, 9 figures, submitted to IEEE Transactions on Information Theory in November 2011, revised version
openalex publication_date 2011/11/16 · arxiv created 2012/03/29 · arxiv updated 2015/03/19 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
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+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 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.