Signal Space Coding over Rings

Chapter 2: Combined coding and modulation techniques 10
2 Combined coding and modulation techniques
2.1 Introduction
The idea of combining coding and modulation suggested by Massey [43] is closely
related to the use of soft decision in the decoding procedure to provide an
improvement in performance over the communication system and also to the
properties of the transmission of signals in noisy channels deduced from the Shannon
theorem [2]. An increase in the dimensionality of the signal set used in the
transmission is equivalent to an increase of the length of the code, when coding and
modulation are combined in one entity.
The Shannon and Nyquist theorems state the more general bounds in the transmission
of information over a given channel. Combined coding and modulation techniques are
found as suitable methods for approaching the bounds stated in the above theorems.
One of the most relevant contributions to the design of combined coding and
modulation schemes has been the work of Ungerboeck [44, 45], who proposed a new
scheme combining convolutional coding with MPSK, to provide an improvement over
the corresponding uncoded system without sacrificing the transmission bandwidth.
This Chapter is concerned mainly with trellis-coded modulation (TCM). Discussion of
block-coded modulation (BCM) is deferred until Chapter 6, partly because the results
in Chapter 5 motivate and lead into those of Chapter 6, and partly to conveniently
group together in one Chapter both background and novel results.
2.2 Bounds on Communications. Shannon and Nyquist Theorems
2.2.1 Introduction
As is well known, the most relevant theorem regarding the problem of communication
in the presence of noise is due to Claude Shannon [2], who has derived his famous
theorem stating that the channel capacity, C ch under the effect of Additive White
Gaussian Noise (AWGN) is a function of the relationship between the average signal