Theory of Error - Correcting Codes

The field of channel coding started with Claude Shannon’s 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon’s channel capacity limit on AWGN channels, both power-limited and band-limited. Similar gains are being achieved in other important applications, such as wireless channels. This course is divided in two parts. In the first part, we remind students of the basics of the theory of linear codes for conventional memoryless ergodic channels. We then introduce more advanced notions so as to make comprehensible some of the most recent coding schemes proposed in the literature. In the second part, we expound the principles of coded modulations for the Gaussian channel and, if time permits, for Rician and Rayleigh fading channels (fully interleaved). We will conclude the course by evoking some aspects of code design for non-ergodic block-fading channels.