address bit of the signal point by an individual binary code C at level i.The individual codes were chosen in such a way that the minimum diatance of the Euclidean space code was maximized.This is now known as balanced distance rule.At the receiver side,each code C is decoded individually starting from the lowest level and taking into account decisions of prior decoding stages.This is known as multistage decoding. mpared ith TCM,the MLC approach provides rates anycode (e.g,block codes,convolutional codes,or concatenated codes)can be used as component code.TCM can be viewed as a special case of MLC using a single convolutional code with a nonbinary output alphabet while higher levels remain uncoded. 5.10.1 Block coded modulation(BCM) BCM is an ex ample of multilevel coded modulation.从TCM的set-partitioning可以看 出，信号label中的不同bit要求不同的保护能力。在BCM中，we provide this by用不 同纠错能力的码编不同bit具体地说，encode the LSB with a powerful code,and encode the MSB with the least powerful code(甚至不编码)。 将label排成一个阵列，forming columns with LSB at the top ccc.c- →x=[xx.x] Vectorsa,b,and e should form三个不同的长为n的码。 As an example,Fig.5.10.1 shows a 3-level BCM code over the 8-PSK signal set. Lo) c0) (8.1,8)repetition code 8-PSK/QPSK (8.7.2)SPC code QPSK/BPSK (8,8,1)trivial code Fig5.10.1 An I-level BCM code over a signal set(M-PSK or M-QAM)with 2 signal points is constructed in the same manner as a 3-level 8-PSK BCM code.For 0si<,let C,be a binary (n,k,d)linear block code of length n,dimension,and minimum Hamming distance di.Let12 address bit c (i) of the signal point by an individual binary code Ci at level i. The individual codes were chosen in such a way that the minimum diatance of the Euclidean space code was maximized. This is now known as balanced distance rule. At the receiver side, each code Cj is decoded individually starting from the lowest level and taking into account decisions of prior decoding stages. This is known as multistage decoding. Compared with TCM, the MLC approach provides flexible transmission rates; any code (e.g., block codes, convolutional codes, or concatenated codes) can be used as component code. TCM can be viewed as a special case of MLC using a single convolutional code with a nonbinary output alphabet while higher levels remain uncoded. 5.10.1 Block coded modulation (BCM) BCM is an example of multilevel coded modulation. 从 TCM 的 set-partitioning 可以看 出，信号 label 中的不同 bit 要求不同的保护能力。在 BCM 中，we provide this by 用不 同纠错能力的码编不同 bit.具体地说，encode the LSB with a powerful code, and encode the MSB with the least powerful code (甚至不编码)。 将 label 排成一个阵列，forming columns with LSB at the top. 01 1 01 1 01 1 n n n aa a bb b cc c − − − ⎡⎤ ⎡ ⎤ ⎢⎥ ⎢ ⎥ = ⎣⎦ ⎣ ⎦ a b c " " " ⇒ = x [ x01 1 x x " n− ] Vectors a, b, and c should form 三个不同的长为 n 的码。 As an example, Fig. 5.10.1 shows a 3-level BCM code over the 8-PSK signal set. Fig. 5.10.1 An l-level BCM code over a signal set (M-PSK or M-QAM) with 2l signal points is constructed in the same manner as a 3-level 8-PSK BCM code. For 0 ≤ <i l , let Ci be a binary (n, ki, di) linear block code of length n, dimension ki, and minimum Hamming distance di. Let