北工大信息论第七章限失真信源编码14

1、信道信道XYX=x1 x2 xnjijijiyxyxyxd 0, 0),(111212122212( , ) ( ,) ( ,)( , ) ( ,) ( ,) ( , ) ( ,) ( ,)mmnnnmd x yd x yd x yd x yd x yd x ydd x yd x yd x y2( ,)()( ,) |( ,) |/|0( ,)()1ijijijijijijiijijijijd x yxyd x yxyd x yxyxxyd x yxyxy均方失真：绝对失真：相对失真：，误码失真：，信道信道XY.21212121jNjjjmiNiiinyyyYYYYYxxxXXXXX，的取值为

2、，的取值为，NiiiNYXdNYXd1),(1),(),(),(),(31),(1),(3322111YXdYXdYXdYXdNYXdNiiiN000031)0 , 0()0 , 0()0 , 0(31)000,000(ddddN3/1 10031)1 , 0()0 , 0()0 , 0(31)001,000(ddddN3/101031)0 , 0() 1 , 0()0 , 0(31)010,000(ddddN111 110 101 100 011 010 001 00003/13/13/23/13/23/213/103/23/13/23/113/23/13/203/13/213/13/23/

3、23/13/1013/23/23/13/13/23/2103/13/13/23/23/113/23/103/23/13/213/13/23/13/203/113/23/23/13/23/13/10111110101100011010001000NdXXYjiijiYjijiyxdxypxpyxdyxpdED),()|()(),()(NiiNiiiNNDNYXdENdED111),(1iD1012)()(),(iqiiQilsfilsfWCLSFLSFd10 , 4 . 09 , 8 . 081 , 0 . 1iiiCi)(ilsfPWi15. 0 )(ilsfP DD DD D: )|(DDa

4、bpBijD );(min)(YXIDRDB,.,221naaaA jijiaadji, 0, 1),(2/1D符号比特/2log)21,21(nnnH符号比特/2log)(nXHR0Dn2log 符号比特/1) 12log(212log)21(nnR21D21D nnnnnnnnaaaaaaaaaaaa2212211,.,.,nnnaaaaa2121naaa21 ),()|()(2121jininjijiaadaapapDnninniniininnnaadaapap21212/121 . 1 .21),()|()()()|()();(YHXYHYHYXI0)|(XYHnapapapn2/1)

5、()()(121nnapn21)() 1log(212log)(log)()(21nnnnapapYHjnjj) 1log(212log)();(nnnnYHYXI) 1log(212lognnnnR )1log(21) 12log(211)21(nnnnRR1n1n 。)(DR)(DR)(RD)(RD )0()(minRDRDDDR0)(maxminmin)(minDRD和0min D)()0(min)(XHRDR max)(maxDRD和0)(DR)(DRmax0DD maxD0)(DR)()|(jijypxyp ),()()( min),()|()(min1111maxjinimjjij

6、inimjijiyxdypxpyxdxypxpD ijiiyxdxp),()(1)(jyp ijiiyxdxp),()(0)(jyp ijiijyxdxpD),()(minmax1 , 0 YXminDmaxD3/2 , 3/1)(xp0110d minDsymbolbitXHRDR/91.0)()0(min)(1001P0)(maxDRmaxD3131,32min 032131, 132031min ),()(),()(),()(),()(min ),()(min222211122111maxjjjijiijyxdxpyxdxpyxdxpyxdxpyxdxpD1010P1)(, 0)(21y

7、pyp。)(DRmax0DD )(DR10max21DDD)()1 ()()1 (2121DRDRDDR)(DR max0DD21DD )()(21DRDR )(DR0)(DRmax0DD )()(0XHDRmaxDD0)(DR)(DR)(DR0D1DmaxD)()()(2121nnxpxpxpxxxPX)()()(2121mmypypypyyyPY ),(jiyxd)(DRmjijnimjjiijinixypDyxdxypxp, 2 , 1 1)|(),()|()( nimjjijijiypxypxypxpYXI11)()|(log)|()();( ), 2 , 1(niinixypsDYX

8、Ixypmjijiij, 2 , 1, 0 )|();()|(1)|(ijxyp)(DRimjexpniyxsdiiji, 2 , 1, 1)(1),(（1 1）计算）计算（i=1,2,.,n) )(jypmjyxsdjijieyp1),()(1（2 2）计算）计算 )(sDnimjyxsdjijiijieyxdypxpsD11),(),()()()(（3 3）计算）计算 )(DR)(log)()(1ssDxpsRniii（4 4）计算）计算 1 1）率失真函数的参量算法）率失真函数的参量算法pppp1) 1 ( ,) 0 (1)0 , 1 () 1 , 0( dd0) 1 , 1 ()0 ,

9、 0( ddmjexpniyxsdiiji, 2 , 1, 1)(1),(121)1()0(1)1()0()1 ,1(2)1 ,0(1)0,1(2)0,0(1sdsdsdsdepepepep1)1 (1 1 121ssepepmjyxsdjijieyp1),()(1)(1yp)(2yp2)1 , 1(2)0, 1(11)1 , 0(2)0, 0(11)()(1)()(sdsdsdsdeypeypeypeypsssseeppypeeppyp1)1 ()(1)1 ()(1112、)(1yp)(2yp、nimjyxsdjijiijieyxdypxpsD11),(),()()()(sseesD1)(D

10、Ds1log),(),( )1log()1 (log)1log()1 (log)(DDHppHDDDDppppDR)(log)()(1ssDxpsRniii),(ppH),(DDH 2 2）率失真函数的迭代算法）率失真函数的迭代算法A：迭代计算公式：迭代计算公式sjjijjijijyxsdypyxsdypxyp1*),(exp)(),(exp)()|(sjijijxypxpyp1*)|()()(nimjiijijixypypxypypxpxypxypxpYXIDRijjijj11)|()()|()()()|(log)|()(minmin);(minmin)(B：迭代计算步骤：迭代计算步骤),.

11、,2 , 1;,.,2 , 1( ,)|() 1 (mjnixypijsxypij1)|()1()1()|(ijxypsjijijxypxpyp1*)|()()()1()(jyp假定假定S1S1为以相当大的负值，选定起始传递概率为以相当大的负值，选定起始传递概率可取可取。将选定的。将选定的代入代入得到得到。)1 ()(jypsjjijjijijyxsdypyxsdypxyp1*),(exp)(),(exp)()|()2()|(ijxyp将将代入代入，得到，得到) 2()|(ijxypsjjijjijijyxsdypyxsdypxyp1*),(exp)(),(exp)()|()2()(jyp再将

12、再将代入代入，得到，得到 )()(DRk)()1(DRk)()(DRk)()1(DRk) 1(sR当当和和的差别小于预先给定的值，取的差别小于预先给定的值，取或或作为作为的近似值的近似值 选略小一些的负数选略小一些的负数s2s2，重复上述迭代过程，得到对应于，重复上述迭代过程，得到对应于s2s2的的)2(sR 重复上述过程，直到重复上述过程，直到)(maxsR逼近零逼近零 )()(DRk)()1(DRk重复前面的步骤，计算出第重复前面的步骤，计算出第k k次和第次和第k+1k+1次的次的和和)()|(log)|()()()()(11)()(jkijknimjijkikypxypxypxpDR)()|(log)|()()()()(11)1()1(jkijknimjijkikypxypxypxpDR ),(),(xxp,.,21qbbbyqqTTTTT1210.1,.,3 , 2, )(1