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Bounds on the a priori index crossover probabilities for trellis-based channel codes

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1 Author(s)
Belzer, B. ; Dept. of Electr. Eng. & Comput. Sci., Washington State Univ., Pullman, WA, USA

This paper derives truncated union bounds on the a priori index crossover probabilities p(j|i) that result when an n-bit data index i is convolutionally encoded, transmitted over a noisy channel, and decoded with the Viterbi algorithm, giving received index j. The bounds are derived with a modified transfer function technique, using n-stage state transition matrices with symbolic labels. The technique is easily automated with commercial symbolic algebra packages. Bounds are obtained for convolutional and trellis-coded modulation (TCM) codes, over binary symmetric and additive white Gaussian noise (AWGN) channels. A joint source channel coding example demonstrates that the bounds on p(j|i) developed in this paper can give a 13-dB accuracy improvement in end-to-end signal-to-noise ratio (SNR) predictions, when compared to predictions based on bounds on the delivered bit error probability Pb

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 4 )