Improved error probability bounds for a block-coded signal with a bounded decision region in the presence of AWGN

Bounding techniques for the error probability in detecting a transmitted signal in the presence of AWGN are considered. The error probability, P_e(i), is the conditional probability that the received signal is incorrectly detected assuming that the ith signal was transmitted. Tight upper and lower bounds on P_e(i) in the low SNR region are useful for the performance analysis of some concatenated multilevel block coded modulation schemes which can achieve a high coding gain. We propose a new lower bound which is always tighter than the bounds of Shannon (1949) and Swaszek (see IEEE Trans. Inform. Theory, vol.41, p.837-41, 1995) so that the bound is tight at both high and low SNRs. This so-called improved cone lower bound was derived by combining the bounding techniques of Shannon and Swaszek