systematic information component on The decoder2 operates according to the same message-passing principle as above Figure 5.of the TTCM decoder. 5.9.2.3 Numerical results Coucatenated Two-State TCM (CT-TCM)Schemes The component encoder of a CT-TCM code consists of a binary two-state trellis encode followed by a multi-ary signal mapper,see Fig.5.9.7.Let a binary n-tuple d=(dod)be an information symbol.Let d=dk be an input sequence to the binary encoder,producing a coded symbol sequenceEach ccontains a parity check bit(d)and is mapped to a appropriate ary signal constellation. producing a modulated symbol x.In the following,c andx=x are also referred to as unmodulated and modulated codewords,respectively. information coded modulated symbols binary symbols signal symbols d=(d.d)encoder c=(d,94) mapper Fig.5.9.7.The component encoder structure for the CT-TCM scheme. We assume that the binary encoder in Fig.5.9.7 is characterized by the two-state trellis in Fig.5.98(similar to the tree encoder in [Liping20011).The parity check bit is generated by =9+d8-48, mod 2,k>0 (5.9.7)8 systematic information component on uk. The decoder 2 operates according to the same message-passing principle as above. (1) La Figure 5.9.6 Structure of the TTCM decoder. 5.9.2.3 Numerical results 5.9.3 Concatenated Two-State TCM (CT-TCM) Schemes 5.9.3.1 Encoder The component encoder of a CT-TCM code consists of a binary two-state trellis encoder followed by a multi-ary signal mapper, see Fig. 5.9.7. Let a binary n-tuple ( , , ) dk = dk ,0 " dk ,n−1 be an information symbol. Let } d = {dk , k ≥ 0 be an input sequence to the binary encoder, producing a coded symbol sequence c={ck}. Each ck contains a parity check bit qk, i.e., ck = (dk, qk), and is mapped to an appropriate 2n+1 -ary signal constellation, producing a modulated symbol xk. In the following, c and x={xk} are also referred to as unmodulated and modulated codewords, respectively. signal mapper coded symbols modulated symbols ( ) k k k c = d ,q k x binary encoder information symbols ( , , ) dk = dk ,0 " dk ,n−1 Fig. 5.9.7. The component encoder structure for the CT-TCM scheme. We assume that the binary encoder in Fig. 5.9.7 is characterized by the two-state trellis in Fig. 5.9.8 (similar to the tree encoder in [Liping2001]). The parity check bit qk is generated by qk qk dk gk = + ⋅ −1 ∑= = ⋅ k i i i 0 d g mod 2, k > 0 (5.9.7)