ct similar results to the ML metric since the two metrics are approx- imately equal. This follows from the approximation (2.350) for large values of signal-to-noise ratios and the optimized choice of v = v/NJ. The difficulty with the energy quantization presented here is that a good choice of V depends on channel measurement which may be difficult to accurately obtain in jamming and fading channels. Eb/N (dB) Figure 2.118. Energy quantizer parameters. Non-Coherent Frequency-Hopped Systems 2.7.2 Hard Decision with One Bit Quality Measure The demodulator-to-decoder interface is used to reduce the number of bits representing each channel output. The fewest bits correspond to the hard decision interface function (2.332). A practical compromise is to pass over this interface, a binary vector of low dimension. Viterbi [27] noted that the first (most significant) bits of this vector will correspond to the demodula- tor's hard decision while subsequent bits provide information on the qual- ity of the channel which require some modification in the conventional demodulator design. He concentrated on adding one quality bit to the mod- ulator's hard decision. This metric is presented here. Define a modified hard decision demodulator-to-decoder interface func- tion as follows: (2.351) for some parameter Y 1. This is the hard decision function with a quality bit where "1" indicates a "good" channel while a "0" indicates a "poor" chan- nel. For FH/MFSK this results in a coding channel with M inputs and 2M outputs. Figure 2.119 illustrates this for M = 4. Now what remains is to deter- mine the coding channel conditional probabilities. Note that output y = (1,1) is a correct decision if x = 1. This occurs when e1 = Yem m = 2, 3, , M. (2.352) (1,1) (1,0) (2,1) (2,0) (3, I) (3,0) (4, 1) (4, O) Figure 2.119. FH/4FSK coding channel. Other Coding Metrics The channel conditional probability is p((1,1)|1)=PrP{e1zymaxemx=1} = = (2.353) where 2 0 0 i = 0,1 (2.354) (2.355) Since (2.356) the conditional probability is p((1,1)|1) (2.357) Def