第6章 信道编码(3)

1、上次课内容回顾：上次课内容回顾：线性分组码的译码线性分组码的译码采用伴随式纠错译码采用伴随式纠错译码标准阵列译码标准阵列译码线性分组码的结构参数线性分组码的结构参数( (码限码限) )码例与码的重构码例与码的重构线性分组码的结构参数线性分组码的结构参数( (码限码限) )汉明码汉明码哈达玛码哈达玛码里德穆勒码里德穆勒码(RM(RM码码) )上次课内容回顾：上次课内容回顾：6.2.1 6.2.1 线性分组码的译码线性分组码的译码(9)rcecrem编码器编码器yTsrHTseH0(1)triinqqisscre由码字组成c1为全零码字e1(00)对越小的i，ei 选择越容易出现的差错图案，对BS

2、C，ei满足111()()()iiiikkw ew eeeC且BjAi11111111kkkrrrkrjqjqiijiiqjqqqqqcccecececeecececeececece,ijirycc若则B11,( , )ruijkikqkk urryccryr s 若，且则若则BAAciercier译码成功译码失败ArBrCrDr 纠错检错错误译码不可检测错误Decrccc112()12()22ddRnnn14()2dRn12/(21)kkdn02tinkniC21()2dRHn2( )log(1)log(1)Hxxxxx 2102dinkniC21(2)2dRHn2dn好码区好码区1221,

3、mh hh122121,321,3,mmmnmkmmHh hh1000101010011100101100001011G111010001110101101001H0123456(,)cc ccccc401251236013,0,1,2,3iicmicmmmcmmmcmmmm3m2m1m0c6c5c4t = 0,1,2,3t = 4,5,60123(,)mmmm0123456(,)cccccccr3r2r1r0016(,)r rrr6r5r4r3r2r1r0r6r5r43 7 线译码irie21111H 1/ 2/ 2/ 2/ 21NNNNNHHHHHH41111111111111111H10

4、,Nijikjkkijhhh hNijNNTNHHN INHNHNH122/ 22mmmnNMNkNmdN码长 码字数 信息位长 log最不码距 11222/ 22mmmnNMNdNNH1212/ 22mmmnNMNdN01rk nGGGG12 ,22mrimimrnmkC rmd1122,nnabab abab011111111G 12132312300000011000001010001000100000001ggggggggg1123000011110011001101010101gGgg12213312323,ggGggGggggg本次课内容：本次课内容：设计和构造编码方法：修正法。设

5、计和构造编码方法：修正法。循环码循环码循环码的多项式描述循环码的多项式描述循环码的生成矩阵循环码的生成矩阵0121(1)1012( )11011( )(,)(0,1)(,)(,)1,2,.,1nninnin in inninaaaaaaaaaaaaaaaaaainaa a0a3a1a2a6a5a4a7a8a9a10a1102134567891011a11a2a0a1a5a4a3a6a7a8a9a10i =1a10a1a11a0a4a3a2a5a6a7a8a9i =2( )()in ibaba0( )( )r xf x1011( )nnnnfxff xfxf x( )max |0,0,1, if

6、 xi fin0,1if ( )( )( ) mod1iinaxx a xx121210(1)12223101( )1211121011( )0,1( )( )nnnninnnnninniiinininn in ia xaxaxa xaaaxaxaxa xa xaaxaxaxa xa xaxaxa ( )( ) |,( ) ( )| ( )( ), ( )( )iiCc cbbCC xc xc xbx b xC x1011( )nnc xcc xcx11100( )0rrrg xxgxg xggrnk( ) ( )| ( )( ) ( ),( )C xc xc xa x g xa xk1nx

7、( )1 (1)( )( )( )( ) mod1knknx g xxr xr xnr xx g xx ( )( ) ( )( )r xb x g xb xk(1)( )( ) ( )( )( )( ) ( )nkkxx g xb x g xg x xb xg x f x1nx 1011( )( )( )( ) ( )kka g xa xg xaxg xa x g x( )( ) ( )xc xxa x g x1nx 10112111012(1)1(1)1( ) ( )()(1)()(1)( )( ) ( )( )nnnnnnnnnnxa x g xcc xcxxcxcc xc xcxcxcx

8、cf x g xcx(1)1( )( )( ) ( )ncxxa xcf x g x73231(1)(1)(1)xxxxxx 234501234523455001122334455( )()(1)()()()()()c xaa xa xa xa xa xxaaa xaa xaa xaa xaa xa x23320123( )()(1)c xaa xa xa xxx2330123( )()(1)c xaa xa xa xxx 2432012( )()(1)c xaa xa xxxx242012( )()(1)c xaa xa xxxx 654320( )(1)c xa xxxxxx (1)(1),kw ww1011( )( )( )kka g xa xg xaxg x1( ), ( ) ,( )kg x g x xx x，g0121(1)0121(1)011(,0,0)(0,0)(0,0 0,0,)rrrrrkrrwgggggwgggggwgggg，1( ), ( ) ,( )kg x g x xx x，g(1)(1),kw ww01201011000000rrrrrk ngggggggGgggg1011( )(1)/( )nkkkkh xxg xhh xhxh x101011000000000kkkkkr n