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( ) 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。 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。 42 Fano算法 開 始向 前 窺 探 最 佳 節(jié) 點大 于 門 限 ?向 前 移 動樹 的 終 點 ?首 次 訪 問 ?提 高 門 限降 低 門 限停 機向 后 觀 測大 于 門 限 ?向 后 移 動來 自 最 壞 節(jié) 點 ?向 前 觀 察 下 一 個 最 佳節(jié) 點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,但每次只對當時認為的最佳路徑進行延伸,然后再重新排序。 35 Fano度量 ? ?? a r g m a x P? ??? ??CC R CC? ?0 1 1Lc c c?C? ?1L10 RRR ??R? ? ? ? ? ??? ??????1010LniiiLiii0crPPP CRCR最大似然譯碼: ?接收序列: ?碼字序列: ?ML判決序列: ?對離散無記憶信道: 36 Fano度量 ? ? ? ? ? ?? ?R CRCRC P PPP ?? ? ? ?m a x P m a x P? ? ? ??? ? ? ?R C C R? ?? ?? ?????????1010002LniiLniiiLRnrPcrPPC0RC? ? C0