efficient modulation," IEEE Trans. Commun. Tech., COM-14 (3), pp. 283-297, June 1966. [29] J.M. Wozencraft and R. S. Kennedy, "Modulation and demodulation for prob- abilistic decoding," IEEE Trans. Inform. Theory, IT-12, pp. 291-297, July 1966. [30] M.A. Creighton, "Analysis of List Decoding Metrics for Jamming and Multiple Access Channels," Ph.D. Dissertation, University of California, Los Angeles, 1985. [31] P.J. Crepeau, M. A. Creighton, and .K. Omura, "Performance of FH/MFSK with list metric detection against partial band noise and random tone jam- ming," MILCOM '83, October 31-November 2, 1983. Non-Coherent Frequency-Hopped Systems [32] P.J. Crepeau, "Generalized list detection for coded FH/MFSK signaling on fad- ing and jamming channels," NRL Report 8708, Naval Research Laboratory, Washington, DC, June 1983. [33] P. J. Lee, "Decomposition of 2L ~ ary Input Channel into L Parallel Binary Input Component Channels and Independent Binary Coding," Ph.D. Dissertation, University of California, Los Angeles, 1985. APPENDIX 2A. JUSTIFICATION OF FACTOR OF ONE-HALF FOR FH/MFSK SIGNALS WITH DIVERSITY IN PARTIAL-BAND NOISE Chapter 2 employed a factor of 1/2 in the Chernoff performance bounds for FH/MFSK signals with diversity in partial-band noise. This factor was orig- inally introduced by Viterbi and Jacobs [2] based on an earlier existence proof by Jacobs [10]. However, some analysts were left with the erroneous belief that the result was valid only for maximum-likelihood metrics, which would disqualify the suboptimum linear combination metric of (2.57). Furthermore, Jacobs did not stress that his result does not usually apply to discrete-valued metrics such as those we encountered in the multitone jam- ming scenarios neglecting thermal noise. Appendix 4B in Part 1 derived many general conditions under which the factor of 1/2 is valid. In particular, using (4B.31), (4B.38), (4B.39b), and (4B.43), we conclude that (2A.1) provided that p(x) < pl-x); (2A.2) where p(x) is the probability density function of the random va