Recommendation itu-r f. 1101 Characteristics of digital fixed wireless systems below about 17 ghz

2 Trellis coded modulation

To achieve this, a redundant signal alphabet is used. It is obtained by convolutionally encoding k out of n information bits to be transmitted at a certain time. The convolutional code has rate k/(k  1), and adds 1 bit redundancy. In the symbol-mapping procedure that follows the convolutional encoder, the encoder bits determine the sub-set (or “sub-modulation”) to which the transmitted symbol belongs, and the uncoded bits determine a particular signal point in that sub-set. The mapping procedure is also called “set-partitioning” and has the purpose of increasing the minimum distance d_E among the symbols.

The optimum receiver for the trellis coded sequence requires a maximum likelihood sequence estimation (MLSE) that can be implemented as a Viterbi algorithm.

Since the redundancy of coding in the time domain, as used in serial FEC, is replaced by a “spatial” redundancy, the cost of coding gain is not an increase of the necessary transmission bandwidth, but a higher modulation complexity.

Another advantage of TCMs is their higher flexibility with respect to serial coding, because of the possibility of increasing the constellation efficiency by 1 bit/symbol (in the case of 4-D codes). On an additive white Gaussian noise channel, the coding gain over an uncoded reference system is represented in Fig. 4, considering the case of a rate 2/3, 8 sub-set encoder and 3 bit soft decision Viterbi decoder.

The coding gain over the uncoded reference system (corresponding to the same number of net information bits per transmitted symbol) is about 2 dB at BER  10^3 and about 4 dB at BER  10^10, in the case of 2-D codes. In the case of 4-D codes, such gains are 1.8 dB and 3.5 dB, respectively. Some practical values have also been reported (see Fig. 4).

Moreover, it has also been shown that the coding gain of a TCM system on a non-linear channel is greater than on a linear one. This advantage of TCMs is of crucial importance to reduce residual BER in the case of high complexity modulation schemes.

An application of TCM has been proposed with the aim of not increasing the number of signal symbols, at the cost of a bandwidth expansion of about 14%. In this case, 8 bit baseband signal streams for uncoded 256-QAM are transformed into 7 bit baseband signal streams by a speed converter and then transmitted as 256‑TCM.