第三章 信道容量-1,2,6,7習(xí)題答案

1、173.1設(shè)信源通過一干擾信道，接收符號(hào)為Y=y1y2，信道轉(zhuǎn)移矩?????????????4.06.0)(21xxXPX陣為，求：??????????43416165(1)信源X中事件x1和事件x2分別包含的自信息量；(2)收到消息yj(j=12)后，獲得的關(guān)于xi(i=12)的信息量；(3)信源X和信宿Y的信息熵；(4)信道疑義度H(XY)和噪聲熵H(YX)；(5)接收到信息Y后獲得的平均互信息量。解：1)bitxpxIbitxpx

2、I322.14.0log)(log)(737.06.0log)(log)(22222121??????????2)bitypxypyxIbitypxypyxIbitypxypyxIbitypxypyxIxypxpxypxpypxypxpxypxpyp907.04.043log)()(log)(263.16.041log)()(log)(263.14.061log)()(log)(474.06.065log)()(log)(4.0434.

3、0616.0)()()()()(6.0414.0656.0)()()()()(222222221212122212221211121122212122121111????????????????????????????3)symbolbitypypYHsymbolbitxpxpXHjjjiii971.010log)4.0log4.06.0log6.0()(log)()(971.010log)4.0log4.06.0log6.0()(lo

4、g)()(22??????????????4)symbolbitYHXYHXHYXHYXHYHXYHXHsymbolbitxypxypxpXYHijijiji715.0971.0715.0971.0)()()()()()()()(715.010log)43log434.041log414.061log616.065log656.0()(log)()()(2???????????????????????????19??????symbol

5、bitXYHYHXHYXIsymbolbityxpyxpXYHsymbolbitypYHsymbolbitxpXHyxpypyxpyxpyxpypyxpypyxpyxpyxpypxypxpyxpxypxpyxpijjijijjii186.0638.1943.0881.0)()()()(638.122.0log22.008.0log08.014.0log14.056.0log56.0)(log)()(943.036.0log36.064.

6、0log64.0)()(881.03.0log3.07.0log7.0)()(22.014.036.0)()()()()()(08.056.064.0)()()()()()(14.02.07.0)()()(56.08.07.0)()()(22222222212222221211112121111212111111???????????????????????????????????????????????????????????????

7、??3.4若XYZ是三個(gè)隨機(jī)變量，試證明(1)I(XYZ)=I(XY)I(XZY)=I(XZ)I(XYZ)；證明：)()()()(log)()()(log)()()()()(log)()()(log)()()()()()(log)()()(log)()()()()(log)()()(log)()(ZYXIZXIzxpzyxpzyxpxpzxpzyxpzxpxpzxpzyxpzyxpxpzyxpzyxpYZXIYZXIYXIyxpzyxp

8、zyxpxpyxpzyxpyxpxpyxpzyxpzyxpxpzyxpzyxpYZXIijkkikjikjiijkikikjiijkkiikikjikjiijkikjikjiijkjikjikjiijkijikjiijkjiijikjikjiijkikjikji????????????????????????????????????(2)I(XYZ)=I(YXZ)=H(XZ)–H(XYZ)；證明：????????ijkkjkikjkji