A lower bound on the error probability for signals in white Gaussian noise
Copyright policy )A lower bound on the error probability for signals in white Gaussian noise
Summary: The author applies a recent inequality by \textit{D. de Caen} [Discrete Math. 169, 217-220 (1997; Zbl 0874.60001)] 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 \(E_b/N_0\). He shows that this bound converges to the union upper bound as \(E_b/N_0\) goes to infinity. Finally, by means of examples, he compares his lower bound with those of \textit{C. E. Shannon} [Probability of error for optimal codes in a Gaussian channel, Bell Syst. Tech. J. 38, No. 3, 611-656 (1959)] and \textit{P. F. Swaszek} [IEEE Trans. Inf. Theory 41, 837-841 (1995; Zbl 0820.94007)] and with \textit{G. Poltyrev}'s [IEEE Trans. Inf. Theory 40, 1284-1292 (1994; Zbl 0821.94035)] upper bound.
Signal theory (characterization, reconstruction, filtering, etc.), Bounds on codes, Modulation and demodulation in information and communication theory, linear code, signal-to-noise ratio, Error probability in coding theory, additive Gaussian noise, weight enumerator
Signal theory (characterization, reconstruction, filtering, etc.), Bounds on codes, Modulation and demodulation in information and communication theory, linear code, signal-to-noise ratio, Error probability in coding theory, additive Gaussian noise, weight enumerator
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