The Combinatorics of Dom de Caen
Designs, Codes and Cryptography
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NETWORKING'08 Proceedings of the 7th international IFIP-TC6 networking conference on AdHoc and sensor networks, wireless networks, next generation internet
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In this correspondence we apply a recent inequality by de Caen (1997) to derive a lower bound on the probability of error for M-ary signals derived from a binary linear code and used on the additive white Gaussian noise channel with a maximum-likelihood decoder. This bound depends only on the weight enumerator of the code and the signal-to-noise ratio Eb/N0. We show that this bound converges to the union upper bound as Eb/N0 goes to infinity. Finally, by means of examples, we compare our lower bound with those of Shannon and Swaszek and with Poltyrev's upper bound