Information Theory in Modem Practice

1 Introduction The design of voiceband modems is an extremely intriguing area in which many related but different disciplines have converged to yield on of the most successful hi-tech consumer products. A first point of interest, for instance, is how previously existing communication techniques like Quadrature-Amplitude Modulation have been adapted to this particular problem. Another captivating aspect is represented by the remarkable improvements in data throughput which were made possible by the adoption of sophisticated information theoretical ideas. And, last but not least, the signal processing techniques which allow the entire machinery to run full-duplex, real time, and above all, robustly over a wide variety of telephone connections are simply fascinating. In these notes we will try to look at the interesting interplay between information theory and electrical communication practice which takes place inside modern modems, and which is arguably the fundamental reason behind their impressive performance. We will first examine the features of the telephone channel, and review some intuitive ideas in data transmission. We will then deal in some more detail with three fundamental modulation techniques which are used in practice, namely PAM, PSK, and QAM. QAM, in particular, is the cornerstone of data transmission in modern modems, and we will thus study it in greater detail, taking into account the differences between possible constellations and constellation-shaping schemes. We will finally reach trellis coded modulation, the heart of modem design: this is a modulation technique in which error control codes and constellation design mix together to yield remarkable transmission gains. Experience has shown that it is always risky to speak of " conclusions " when it comes to modems; we will however try in the end to at least sum up what we have learnt. Enjoy! Modem Design and the Telephone Channel 2 2 Modem Design and the Telephone Channel The history of modem design has been characterized by repeated and embarassingly wrong attempts to define the " ultimate " performance allowed for data transmission over the telephone channel. This upper limit has been again and again pushed forward by the newer modem standards defined over the years, and its current de facto value is set by the V.34bis specifications at a data rate of 33,600 bps (bits per second). It is interesting to note that in [1], a paper which does not fail to point out the hastiness of those who considered 4800 bps as an unsurpassable …