In this course, Professor Schlegel discusses the fundamental principles of modern error control coding, with particular emphasis on capacity-achieving graph-based codes such as turbo and low-density parity-check coding and their iterative decoding algorithms. The basic theory, code construction, iterative message-passing decoding algorithms and error performance analysis, implementation examples, and advanced simulation principles such as importance sampling are discussed.
In this lecture we discuss the information theoretic basics of error control coding from Shannon capacity formula, to the Shannon bound. We discuss fundamental transmission limits expressed by the channel coding theorem and highlight the accomplishments of error control coding over the last half century.
In this lecture we discuss some fundamental channel models we will be using in this course, in particular the ubiquitous additive white Gaussian noise (AWGN) channel. We then extend this basic model to the case of parallel channels, and finally to the correlated multiple-input multiple-output (MIMO) channel.
In this lecture we introduce the concept of error correction by discussing Hamming’s original [7,4] single error correction code from 1948. We then develop the Tanner graph of this code and illustrate how decoding can proceed by passing messages along the edges of this graphical representation of the code.
Here we discuss the basic principles of low-density parity-check (LDPC) codes, starting with their Tanner graph representation and rate definition. We introduce fundamental iterative message-passing decoding algorithms for binary erasure, binary symmetric, and the additive white Gaussian noise channel.