For the BPSK signaling over an AWGN channel 20 =1-log,(1+e6, Therefore,we have (4.41) R For R=1/3, E6 (-0.5dB,(correspondong to capacity) N2.03dB,(correspondong to cutoff rate) .4 BPSK soft-decision bound BSC bound Cutoff rate,RO 0.0 0.6 0.4 02 6 Eb/NO(dB) Figure 4.x C.Ro vs.Eb/NO 4+364-36 For the BPSK signaling over an AWGN channel, 2 2 0 2 2 2 1 ( )( ) 1 log 1 exp 2 2 s s yE yE R dy                       2 2 2 1 1 log 1 exp 2 2 s y E dy                      0 / 2 1 log (1 ) E N s e   Therefore, we have 0 1 0 0 ln(2 1) R Eb N R     (4.41) For Rc=1/3, 0 0.5dB, (correspondong to capacity) 2.03dB, (correspondong to cutoff rate) Eb N     -2 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Eb/N0 (dB) Capacity (bits/symbol) BPSK soft-decision bound BSC bound Cutoff rate, R0 Figure 4.x C, R0 vs. Eb/N0