\input zb-basic \input zb-ioport \iteman{io-port 00721904} \itemau{Honary, B.; Markarian, G.} \itemti{Minimisation of error multiplication for $M$-ary signals.} \itemso{Ganley, M. J. (ed.), Cryptography and coding III. Based on the proceedings of the 3rd conference organized by the Institute of Mathematics and its Applications on cryptography and coding, held at Cirencester, GB, on Dec. 16-18, 1991. Oxford: Clarendon Press. Inst. Math. Appl. Conf. Ser., New Ser. 45, 211-221 (1993).} \itemab Summary: A new adaptive technique which gives the optimum format for $M$-ary signals to minimize the error multiplication of binary errors in noisy channel conditions is given. The new adaptive technique is most applicable to time varying communication channels in which the signal-to- noise ratio is varying. In addition two examples (8-PSK and 8-FSK), for which the appropriate signalling formats have been calculated, are presented. A new parameter -- order of error $k$ -- is introduced and the relationship between signal energy-to-noise ratio $(E\sb s/ N\sb 0)$ and order of error $k$ is derived. \itemrv{~} \itemcc{} \itemut{8-PSK; error multiplication; noisy channel; signal-to-noise ratio; 8-FSK; signalling formats; order of error} \itemli{} \end