[信息與通信]信道編碼理論-閱讀頁
2025-03-01 15:11本頁面
【正文】 限 ？向 后 移 動來 自 最 壞 節(jié) 點(diǎn) ？向 前 觀 察 下 一 個(gè) 最 佳節(jié) 點(diǎn)Y e sN oY e sN oY e sN oY e sN oY e sN o43 堆棧 (ST)算法 核心：存貯一組可能的路徑，但每次只對當(dāng)時(shí)認(rèn)為的最佳路徑進(jìn)行延伸，然后再重新排序。 44 ST算法的本質(zhì) 存貯一組可能路徑； 每次只有最可能的（度量最大的）路徑可以繁衍，同時(shí)刪去父路徑； 繁衍出的子路徑與其它未繁衍的路徑一起排序； 堆棧滿時(shí)最壞路徑被丟棄。 46 TCM encoder R a t e k /( k + r )C o n v o lu t io n a le n c o d e rS e le c t o n e o f2k + r s u b s e t sS e le c t o n e o f2m k s ig n a ls ins u b s e t S ( ci)m + r b i t sS i g n a l m a p p e rm b i t s p e rs y m b o lS u b s e t l a b e ls e q u e n c e { ci}( 1 )ia() kia( 1)kia?() mia( 1 )ic() kic()kric?( 1 )kric??S ( ci)()mric?( ) (1)( ... )mri i ix f c c??S i g n a ls e q u e n c e{ xi}47 TCM For a trellis code C (of length n), the minimum squared Euclidean distance between two different sequences of signal points is referred to as its free squared Euclidean distance。39。( ) m i n , , (o r )nnf r ee m m m mmmd ?? ? ? ?x x x x RCCC2free10 2 ( ) ( )m i n( ) /1 0 l o g/uudEdE????????C dB 2( )minud 48 TCM example The 4state TCM encoder for 8PSK T T8PSKSignalSet(1)ic( 2 )ic( 3 )ic(1)ia( 2 )iaxi( 3 ) ( 2 ) ( 1 )[]i i ic c c?c49 Set partition of 8PSK A : 8 P S K(1)0ic ?( 2 )0ic ?( 3 )0ic ?11111 1100 00(1)()iBc( 2 ) (1 )()iiC c c( 0 0 0 ) ( 1 0 0 ) ( 0 1 0 ) ( 1 1 0 ) ( 0 0 1 ) ( 1 0 1 ) ( 0 1 1 ) ( 1 1 1 )( 3 ) ( 2 ) (1)()i i ic c c0?1?2?sE50 Trellis diagram 40062 625104371573102C ( 0 0 ) = { 0 , 4 }C ( 1 0 ) = { 2 , 6 }C ( 0 1 ) = { 1 , 5 }C ( 1 1 ) = { 3 , 7 }S0S1S2S3The error event corresponding to 2free ()d S51 Coding gain The intrasubset minimum squared Euclidean distance is given by In this example, the parallel transitions are associated with signals from one of the four subsets, C(00), C(01), C(10), C(11), with minimum squared Euclidean distance In this example, the minimum squared Euclidean distance between any two different sequences of subsets 2 2 2 2f r e e ( ) ( 0 , 2 ) ( 0 ,1 ) ( 0 , 2 ) 4 . 5 8 6E E E sd d d d E? ? ? ?S22m i n ,39。 )}Essd d s s?? SSS 22 4 sE?? 52 Coding gain Thus, the free squared Euclidean distance of this TCM code is Compared with an uncoded QPSK scheme with the minimum squared Euclidean distance 2Es between signal points, this TCM scheme can provide an asymptotic coding gain of 2 2 2f r e e f r e e 2( ) m i n { ( ) , } = 4 sd d E??C S 41 0 l o g 32? ??(dB) 2 2 SE??SEQPSK constellation
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