TABLE OF CONTENTS In traditional transmission systems, information symbols are protected by coding and then a carrier intervenes to modulate. The functions of modulation and coding, and, consequently, of demodulation and decoding, are treated independently. The first examples of codes that combine modulation and coding and demodulation and decoding and which have led to the concept of coded modulation are the "Trellis Codes" introduced by Gottfried Ungerboeck in 1976. To transmit n bit/symbol with a 2-dimensional modulation, the trellis-coded modulations (TCM) use a constellation with 2 n+1 points. The redundancy does not cause an expansion of band occupancy, but merely an increase in the size of the constellation. This chapter deals with the most important aspects of coded modulation.
Binary codes presented in the preceding chapters had been selected for their properties of minimum Hamming distance. However, it is known that for a transmission on a Gaussian channel, the criterion of choosing a modulation scheme is that of Euclidean distance. Indeed, if the signal-to-noise ratio in the channel is sufficiently high, the modulation diagram whose minimum Euclidean distance is the largest will have the weakest probability of error. That leads to the decoding being "with soft decisions", i.e., that the "demodulator" calculates the Euclidean distance (metric) for each decision, while the decoder looks for the codeword with the best metric.
We can see that if the modulation is binary, the criterion of Hamming distance is equivalent to that of Euclidean distance.
