※ 引述《shiyoung (睽違已久的ID)》之銘言： : ※ 引述《supsymmetry (supsymmetry)》之銘言： : : A binary communication system transmits signals s_i(t)(i=1,2).The receiver t : : est statistic z(T)=a_i+n_0, where the signalcomponent a_i is either a_1=1 or : : a_2=-1 and the noise component n_0 is uniformly distributed, yielding the c : : onditional density functions p(z|s_i) given by : : p(z|s_1)=1/2 for -0.2<=z<=1.8 : : 0 otherwise : : and : : p(z|s_2)=1/2 for -1.8<=z<=0.2 : : 0 otherwise : : Find the probability of a bit error, P_B, for the case of equally likely sig : : naling and the use of an optimum decision threshold. : : 我才判決水平應該是\gamma=0,然后bit error probability 應該是 : : \int_{-0.2}^{0}1/2dz=0.1的. : : 但是怎么都不能從原來的題目的已知中推導出來. : : 求求解思路.謝謝. .... Should be Bayesian. choose S1 if P(s1 | Z ) > P(s2 | Z) , where Z is the observation. Assume S1, S2 are equally likely.. etc. Prob. of Error = 0.1 is a correct answer, However, you can choose arbitary decision boundary between [-0.2 , 0.2] and achieve the same prob of error. Or,in other words, what happens if the likelihood ration is equal to the threshold ? : From MAP criterion : 1 : > : p(z|s_1) p(z|s_2) : < : -1 : therefore P_B = Pr(s_1-s_2 < 0) what's your symbol Pr(s_1-s_2 < 0) here ? : s_1 : s_2 ┌─────┐ : ┌──┼──┐ │ : ─┴──┴──┴──┴── : -1.8 -0.2 0.2 1.8 : P_B = int_{-0.2}^{0.2} int_{x}^{0.2} 0.5 dydx : = int_{-0.2}^{0.2} 0.5(0.2-x) dx : = 0.1x - 0.25x^2 |_{-0.2}^{0.2} : = 0.01 - (-0.03) : = 0.04 No idea what's talk about. : 囧rz....跟你算的不一樣 : 我不保證我的就對 : 參考看看吧 : 有錯也指正一下 : 很久沒算這玩意兒了 -- 趙客縵胡纓，吾鉤霜雪明。銀鞍照白馬，颯沓如流星。 十步殺一人，千里不留行。是了拂衣去，深藏身與名。 閑過信陵飲，脫劍膝前橫。將炙啖朱亥，持觴勸侯贏。 三杯吐然諾，五嶽倒為輕。眼花耳熱後，意氣素霓生。 就趙揮金錘，邯鄲先震驚。千秋二壯士，烜赫大梁城。 --

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