Analysis of LDPC and Repeat-Accumulate Codes

Summarization: Information Theory was created in 1948, by Claude Shannon. Besides other contributions, Shannon defined the channel capacity and proved that it can be achieved arbitrarily well via channel coding. Since then, both theory and practice for point-to-point communications have been constantly developed, up to the point that, nowadays, techniques for practically attaining channel capacity exist. This has been made possible by the invention of powerful coding methods, such as turbo codes and low-density parity-check (LDPC) codes. In this thesis, we focus on LDPC codes, which were invented by Robert Gallager in the early Sixties. At that time, the limited available computational power made the use of LDPC codes impractical and prevented scientists from fully understanding their potential. After the introduction of irregular LDPC codes and of practical performance analysis tools in the late nineties, LDPC codes became the most powerful error correcting codes, enabling reliable transmissions at rates close to the channel capacity for a number of communication channels