Frederique Oggier, Emanuele Viterbo, «Algebraic Number Theory And Code Design For Rayleigh Fading Channels»

×

Frederique Oggier, Emanuele Viterbo, «Algebraic Number Theory And Code Design For Rayleigh Fading Channels»

Close

Elementary number theory was the basis of the development of error correcting codes in the early years of coding theory. Finite fields were the key tool in the design of powerful binary codes and gradually entered in the general mathematical background of communications engineers. Thanks to the technological developments and increased processing power available in digital receivers, attention moved to the design of signal space codes in the framework of coded modulation systems. Here, the theory of Euclidean lattices became of great interest for the design of dense signal constellations well suited for transmission over the Additive White Gaussian Noise (AWGN) channel.
More recently, the incredible boom of wireless communications forced coding theorists to deal with fading channels. New code design criteria had to be considered in order to improve the poor performance of wireless transmission systems. The need for bandwid the ?cient coded modulation became even more important due to scarce availability of radio bands. Algebraic number theory was shown to be a very useful mathematical tool that enables the design of good coding schemes for fading channels.