微分熵與平均互信息-閱讀頁
2025-06-04 08:22本頁面
【正文】 信宿 —— 連續(xù)型隨機變量序列 Y1Y2…Y n 微分熵與平均互信息 )xxx(p)xxxXXX(pXXdX)xxxXXX(dPn,2,1k]b,a[xxxxXXXn21n21n21n21n21n21kn21n21???????????????? ，為信源發(fā)出的消息的取值隨機變量序列 n21n21 xxxXXX ??)yyy(p)yyyYYY(pYYdY)yyyYYY(dP]b,a[]d,c[n,2,1k]d,c[yyyyYYYn21n21n21n21n21n21kn21n21????????????????? 通常，微分熵與平均互信息 為信宿收到的消息的取值隨機變量序列 n21n21 yyyYYY ??X1X2…X n p(y1y2…y n/x1x2…x n) Y1Y2…Y n p(y1y2…y n/x1x2…x n)為信道轉移概率密度函數 1dydydy)xxx/yyy(pdc n21n21n21dc dc ??? ? ????其中微分熵與平均互信息 聯合平均互信息與條件平均互信息 定義 表示負值的數學期望，用之比對數數的聯合轉移概率密度函信宿消息與信源消息函數的聯合概率密度—信宿消息—聯合平均互信息)YYY。XXX(I????????????? ? ?? ??? ? ?? ????dc n21n21n21n21n21n21badcdcbabadc n21n21n21n21n21badcdcbabadydydydxdxdx)xxx/yyy(pl o g)yyyxxx(pdydydydxdxdx)yyy(pl o g)yyyxxx(p???????????????)XXX/YYY(h)YYY(hdydydydxdxdx)xxx/yyy(pl og)yyyxxx(pdydydy)yyy(pl og)yyy(pn21n21n21dc n21n21n21n21n21n21badcdcbabadc n21n21n21dcdc?????????????????????? ? ?? ??? ?微分熵與平均互信息 定義 nLk1)YYXX/Y。X(I11212badcdc211112211badcdc21112211121?????? ? ?? ? ?)YYX/Y(h)YY/Y(hdydydydx)yyx/y(pl o g)yyyx(pdydydydx)yy/y(pl o g)yyyx(p)YY/Y。X(I1212112babadcdc212112122121babadcdc212111221211122?????? ? ? ?? ? ? ?)YYXX/Y(h)YYX/Y(hdydydydxdx)yyxx/y(pl o g)yyyxx(pdydydydxdx)yyx/y(pl o g)yyyxx(p)YYX/Y。X(I1n1n1n1n1n11n1ndcn21n211n1n1n1nn21n21badcdcbabadcn21n211n11n1nn21n21badcdcbaba1n11n1nn????????????????? ? ?? ??? ? ?? ????????????????????????微分熵與平均互信息 平均互信息的鏈式法則 )YYXX/Y。X(I)YX/Y。X(I)Y/Y。X(I)YYY。XXX(In21n21n21n21n21???????)YYXX/Y(h)YXX/Y(h)X/Y(h)YY/Y(h)Y/Y(h)Y(h1n1n1n1212111n1n121???????????????)YYXX/Y(h)YXX/Y(h)YX/Y(h)X/Y(h)YY/Y(h)YX/Y(h)Y/Y(h)Y(h1n1n1n1212112111n1n112121?????????????????)YYXX/Y。X(I)YX/Y。X(I)Y/Y。X(I1n11n1nn1n11n211221n1n112111????????????????????微分熵與平均互信息 平均互信息的界 )YYXX/Y。X(I)YX/Y。X(I)Y/Y。X(I)YYY。X
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