《信息論》(電子科大)第七章 信息率失真理論

1、 )X(HlbmLKR)X(H一、離散信源的信息率失真函數(shù)一、離散信源的信息率失真函數(shù) )x(p)x(p)x(pxxx)X(PXn21n211、平均失真度、平均失真度 )y,x(d.)y,x(d)y,x(d.)y,x(d.)y,x(d)y,x(d)y,x(d.)y,x(d)y,x(dDmn2n1nm22212m12111 jiji0)y,x(dji 0.0.0D2ijji)xy()y,x(d n1im1jjiiiiji)y,x(d)x/y(p)x(p)y,x(dEDDD DD: )x/y(pPijD DD )Y;X( IminRmin)D(RDijDijP)x/y(pP)x/y(p 2、信息率

2、失真函數(shù)的定義、信息率失真函數(shù)的定義3、信息率失真函數(shù)的性質(zhì)和、信息率失真函數(shù)的性質(zhì)和具有非負(fù)性具有非負(fù)性因此，可知信息率失真函數(shù)因此，可知信息率失真函數(shù)的大致的大致曲線為：曲線為：maxDminD信息信息DD)y,x(dmin)x(p)y,x(d)x/y(p)x(pDjin1ijin1im1jjiiji )y,x(dmin)x(pDjin1ijimin n, 2 , 1i)y(p)x/y(p0)D(Rjij n1im1jjiji)y(pmax)y,x(d)y(p)x(pminDj m1jjj)y(pn1ijiim1jj)y(pD)y(pmin)y,x(d)x(p)y(pminjj n1iji

3、ij)y,x(d)x(pD其其中中jjm1jjjDminD)y(p jjm1jjj)y(pmaxDminD)y(pminDj 2 , 1j , 0021021)y,x(dmin)x(pDji21ijimin 0440D2DDDminmax 2421021)y,x(d)x(pD1i21ii1 2021421)y,x(d)x(pD2i21ii2 2 , 1j , 2DminDjjmax 2D0 q1qp1p)X/Y(P設(shè)設(shè))y,x(d)x/y(p )x(pD1i21iij21ji 21p21qp 解解得得 p2321pp1p)X/Y(P故故實(shí)實(shí)驗(yàn)驗(yàn)信信道道) qp( 220) q1 (214q21

4、4) p1 (210p21 12022DDminmax 信息信息n, 2 , 1i1)x/y(pm1jij 4、信息率失真函數(shù)的參量表達(dá)式、信息率失真函數(shù)的參量表達(dá)式 n1im1jjiiii)y,x(d)x/y(p)x(pDD)y,x(d)x/y(p)x(p S)Y;X( In1km1llkklki n, 2 , 1i 1)x/y(pm1lili m, 2 , 1j ,n, 2 , 1i0)x/y(piji 令令)x( p )x/y( p)x( p)x/y( p)y( p)x/y( pin1kkjkijjij )x(p)y(pln)x(p)y(pln)y(p)x/y(pijilm1llij )

5、x(p)x/y(pln)x(p )x/y(pln)x/y(p)x(p)x/y(piijin1kklm1lklkij )y,x(d)x(SpD)y,x(d)x/y(p)x(pS)x/y(pjiin1km1llkklkij m, 2 , 1j ,n, 2 , 1i0)y,x(d)x(Sp)y(p)x/y(pln)x(p)x/y(pijiijijiiji m, 2 , 1j ,n, 2 , 1i0)x(p)y,x(Sd)y(p)x/y(plniijijij )x(plniii 令令m, 2 , 1j ,n, 2 , 1i0lneln)y(p)x/y(plni)y,x(Sdjijji m, 2 , 1

6、j , n, 2 , 1ie )y(p)x/y(p)y ,x(Sdjiijji n, 2 , 1ie )y(p1m1j)y,x(Sdjiji m, 2 , 1je )x(p1n1i)y,x(Sdiiji m, 2 , 1j ,Se )x(p1) 1 (in1i)y,x(Sdiiji 的的求求含含由由n, 2 , 1i),y(pSe )y(p1)2(jm1j)y ,x(Sdjiji 的的求求含含由由m, 2 , 1j , n, 2 , 1ie )y(p)x/y(pS)3()y,x(Sdjiijji 的的求求含含 n1im1jjiiii)y,x(d)x/y(p)x(pDSSD)4(的的即即含含求求

7、 n1ijijm1jiji)y(p)x/y(pln)x/y(p)x(p)D(RSSR)5(的的即即含含求求)y,x(de )y(p)x(pjijijiin1im1j)y,x(Sd )y(pe )y(plne )y(p)x(pjjijijijii)y,x(Sdn1im1j)y,x(Sd n1iiiln)x(pSSDdDdRdDdSSRDRdDdRin1ii dDdSdSd)x(pDSiiin1i m, 2 , 1je )y,x(d)x(pe )x(pdSd0)y,x(Sdjiii)y,x(Sdin1iijiji dDd)x(pdDdSDSin1iii n1im1j)y,x(Sdijijin1im

8、1ji)y,x(Sdjijijie)y,x(d)y(p)x(pdSde )y(p)x(p0DdSd)x(pDdSd)x(pe )y(pn1iiiin1im1jiii)y,x(Sdjiji 0dDdS SdDdR p1pxx)X(PX2121p 其其中中 00D0 其其中中00)p1 (0p)y,x(dmin)x(pDjin1ijimin 5、二元信源的信息率失真函數(shù)、二元信源的信息率失真函數(shù) pDDminD2jjmax )p1()p1(0pD1 p0)p1(pD21e )p1 (pS21 1)p1 (pe2S1 )e1(p1S1 )e1)(p1 (1S2 m, 2 , 1j ,Se )x(p1

9、) 1 (in1i)y,x(Sdiiji 的的求求含含由由)e1 (pe )y(p)y(pSS21 )e1)(p1()y(pe )y(pSS21 SS1e1e )p1 (p)y(p SS2e1pe)p1 ()y(pn, 2 , 1i),y(pSe )y(p1)2(jm1j)y ,x(Sdjiji 的的求求含含由由)e1 (pe )p1 (p)x/y(pS2S11 )e1)(p1 (e )p1 (p)x/y(pS2S12 )e1 (ppe)p1 ()x/y(pS2S21 )e1)(p1 (pe)p1 ()x/y( pS2S22 m, 2 , 1j , n, 2 , 1ie )y(p)x/y(pS

10、)3()y,x(Sdjiijji 的的求求含含 SSe1e n1im1jjiiii)y,x(d)x/y(p)x(pDSSD)4(的的即即含含求求)y,x(de )y(p)x(pjijijiin1im1j)y,x(Sd n1ijijm1jiji)y(p)x/y(pln)x/y(p)x(p)D(RSSR)5(的的即即含含求求 n1iiiln)x(pSSD)e1ln()p1ln()p1 (plnpe1eS)e1ln()p1 ()p1ln()p1 ()e1ln(pplnpe1eSSSSSSSS D1Dln1S D1DeS D11e1S)p1ln()p1 (plnp)D1ln(D1DlnD)D(R )D

11、(H)p(H )p1ln()p1 (plnp)D1ln(D1DlnD ）（)D(H)p(H)D(R D1Dln)D(S )p(H) 0(R)D(Rmin )0(S)D(Smin0)D(Rmax p1pln)D(Smax )D(H2ln)D(H) 5 . 0(H)D(R )D1ln()D1 (1nDlnDnln)D(R )D(H) 1nln(Dnln )D(H) 1nln(Dnln)D(R m, 2 , 1j00n1)y ,x( dmin)x( pDn1ijin1ijimin m, 2 , 1jn1n)y ,x ( dn1)y ,x ( d )x ( pDn1ijin1ijiij m, 2 ,

12、1jn1nDminDjjmax n1nD0 43,41)X(P 0110D)D(H)p(H)D(R )D1ln()D1 (DlnD43ln4341ln41 2 , 1j , 0043041)y ,x(dmin)x(pDji21ijimin )symbol/nat()D1ln()D1 (DlnD563. 0 43143041)y,x(d)x(pD1i21ii1 41043141)y,x(d)x(pD2i21ii2 2 , 1j ,4141,43minDminDjjmax 41D0 )symbol/nat(186. 087ln8781ln81563. 0)81(R 011101110D)symbo

13、l/nat()D1ln()D1 (DlnDD693. 0099. 1 )D1ln()D1 (DlnD2lnD3ln 3 , 2 , 1j0)y ,x ( dmin31)y ,x ( dmin)x ( pDji31ijji31ijimin )D(H) 1nln(Dnln)D(R 3 , 2 , 1j32)y,x(d31)y,x(d)x(pD3i31i3i31iij 3 , 2 , 1j32DminDjjmax 32D0 32ln3231ln3131693. 0099. 1)31(R )symbol/nat(231. 0637. 0231. 0099. 1 dxdy)y, x(d)xy(pDDD:

14、 )x/y(pPD )Y;X(Iinf)D(RcP)x/y(pD dxdye )y, x(d)y(p)x()x(pSD)y, x(Sd dx)x(ln)x(pSSDSRdDdRS 1、信息率失真函數(shù)的參量表達(dá)式、信息率失真函數(shù)的參量表達(dá)式222)mx(2e21)x(p dx)x(xpm其其中中 dx)x(p)mx(222)yx()y, x(d 2、高斯信源的信息率失真函數(shù)、高斯信源的信息率失真函數(shù) dxdy)y, x(d)x/y(p)x(pD dx)yx)(y/x(p)y(D2 dy)y(D)y(pD dx)yx)(y/x(pdy)y(pdxdy)yx)(y/x(p)y(p22 dxdy)yx

15、)(x/y(p)x(p2)y(eD2ln21dx)y/x(pln)y/x(p)y/X(Hc dy)y/X(H)y(pdxdy)y/x(pln)y/x(p)y(p)Y/X(Hccdy)y(Dln)y(p21dy)y(p) e2ln(21dy)y(eD2ln)y(p21 dy)y(D)y(plndy)y(Dln)y(p )De2ln(21Dln21) e2ln(21dy)y(D)y(pln21) e2ln(21)Y/X(Hc DD )eD2ln(21)Y/X(Hc )e2ln(21)X(H2c )Dln(21)eD2ln(21)e2ln(21)Y/X(H)X(H)Y;X(I22ccc )Y;X(Iin