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Channel Coding Theory
Term: Fall 2005
This is an advanced course on channel coding techniques.
In the first part of the course, we will study some basic results from information and coding theory in order to see what is the best one should expect from a good code..
The study of channel codes is initiated with a review of linear codes, with emphasis on their algebraic structure (this complements the viewpoint taken in EECS 554, where the focus was on practical implementation of encoders and decoders). Next, the theory of finite fields is presented in some detail, as this is the basic tool for the study of non-binary linear codes. These results will be utilized for the construction of cyclic codes, and their significant subclass, namely BCH codes and Reed-Solomon (RS)codes. This will conclude the study of ``classical coding theory''.
Classical coding theory (which was founded almost 50 years ago) studies codes from their algebraic viewpoint. It served communication theorists and practitioners well, but essentially failed to reach the goal set by information theory, i.e., to provide codes that come close to channel capacity. However, 10 years ago, channel coding theory was revolutionized by the invention of ``turbo codes'' and the re-invention of ``low-density parity-check codes''. This revolution led to the birth of the new subfield of ``modern coding theory''.
In the second part of the course, we will study families of good codes, collectively referred to as turbo-like codes. Their asymptotic performance, and their encoding and decoding complexity will be studied. This investigation will conclude by asking the question of whether everything that Shannon predicted 50 years ago has been achieved.
The last part of the course deals with the multi-antenna wireless fading channel, which promises bandwidth efficiencies on the order of tens of bits per second per Hertz. Its capacity will be investigated and families of ``space-time codes'' will be introduced and analyzed.