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A random coding theorem for nonlinear additive Gaussian channels is presented. Modeling the channel's nonlinear behavior as a causal, stationary Volterra system and under maximum likelihood decoding, an upper bound on the average error probability is obtained. The proposed bound is deduced by deploying exponential martingale inequalities. Cubic nonlinearities are used as example to illustrate the...
A new tight upper bound on the maximum-likelihood (ML) word and bit-error decoding probabilities for specific codes over discrete channels is presented. It constitutes an enhanced version of the Gallager upper bound and its variations resulting from the Duman-Salehi second bounding technique. An efficient technique is developed that, in the case of symmetric channels, overcomes the difficulties associated...
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