16:332:548 Error Control Coding Spring 2014 PRELIMINARY COURSE SYLLABUS

Error-control codes are essentially important in achieving the high degree of reliability required in modern data transmission and storage systems. Apart from the study of codes that efficiently achieve reliable transmission across channels corrupted by noise, the Error-Control Coding (ECC) Theory studies the design of encoding and decoding schemes which could be easily implemented. The course will begin with an introduction to the fundamental problems of the ECC Theory, and their mathematical formulations. This will include a review of the finite field arithmetic and vector space preliminaries. It continues with binary linear block codes (focus on Hamming codes), cyclic codes (focus on Reed-Solomon and BCH codes), and binary linear convolutional codes (focus on the Viterbi algorithm). We will also cover the basics of multivariate-polynomials based codes (Reed-Muller). Next, we will discuss codes on graphs, a more modern approach to encoding and decoding, which will include some of the following topics: the sum-product and min-sum algorithms; the BCJR algorithm; turbo codes; LDPC codes and RA codes; and iterative decoding of codes on graphs. To motivate students ’ interest in the ECC topics beyond this course, we will touch upon some advanced topics, such as code bounds based on the notion of minimum distance, and introduce the concept of Maximum Distance Separable (MDS) codes which offer maximum protection against symbol errors fo