第6章信道編碼(3)

1、上次課內(nèi)容回顧：上次課內(nèi)容回顧：線性分組碼的譯碼線性分組碼的譯碼采用伴隨式糾錯譯碼采用伴隨式糾錯譯碼標(biāo)準(zhǔn)陣列譯碼標(biāo)準(zhǔn)陣列譯碼線性分組碼的結(jié)構(gòu)參數(shù)線性分組碼的結(jié)構(gòu)參數(shù)( (碼限碼限) )碼例與碼的重構(gòu)碼例與碼的重構(gòu)線性分組碼的結(jié)構(gòu)參數(shù)線性分組碼的結(jié)構(gòu)參數(shù)( (碼限碼限) )漢明碼漢明碼哈達(dá)瑪碼哈達(dá)瑪碼里德穆勒碼里德穆勒碼(RM(RM碼碼) )上次課內(nèi)容回顧：上次課內(nèi)容回顧：6.2.1 6.2.1 線性分組碼的譯碼線性分組碼的譯碼(9)rcecrem編碼器編碼器yTsrHTseH0(1)triinqqisscre由碼字組成c1為全零碼字e1(00)對越小的i，ei 選擇越容易出現(xiàn)的差錯圖案，對BS

2、C，ei滿足111()()()iiiikkw ew eeeC且BjAi11111111kkkrrrkrjqjqiijiiqjqqqqqcccecececeecececeececece,ijirycc若則B11,( , )ruijkikqkk urryccryr s 若，且則若則BAAciercier譯碼成功譯碼失敗ArBrCrDr 糾錯檢錯錯誤譯碼不可檢測錯誤Decrccc112()12()22ddRnnn14()2dRn12/(21)kkdn02tinkniC21()2dRHn2( )log(1)log(1)Hxxxxx 2102dinkniC21(2)2dRHn2dn好碼區(qū)好碼區(qū)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 線譯碼irie21111H 1/ 2/ 2/ 2/ 21NNNNNHHHHHH41111111111111111H10

4、,Nijikjkkijhhh hNijNNTNHHN INHNHNH122/ 22mmmnNMNkNmdN碼長 碼字?jǐn)?shù) 信息位長 log最不碼距 11222/ 22mmmnNMNdNNH1212/ 22mmmnNMNdN01rk nGGGG12 ,22mrimimrnmkC rmd1122,nnabab abab011111111G 12132312300000011000001010001000100000001ggggggggg1123000011110011001101010101gGgg12213312323,ggGggGggggg本次課內(nèi)容：本次課內(nèi)容：設(shè)計和構(gòu)造編碼方法：修正法。設(shè)

5、計和構(gòu)造編碼方法：修正法。循環(huán)碼循環(huán)碼循環(huán)碼的多項式描述循環(huán)碼的多項式描述循環(huán)碼的生成矩陣循環(huán)碼的生成矩陣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