In 1993 a major approvement in coding theory was achieved by the development of iterative decoding, also known as Turbo Decoding. For the first time it was possible to approach the Shannon limit by efficiently decoding of so-called Parallel Concatenated Convolutional Codes (PCCC), which were already known to be very powerful while missing an efficient algorithm for decoding.
Today, turbo codes have commenced their service in a variety of applications, but there are still unanswered fundamental questions concerning an in-depth understanding of iterative decoding, such as: Under which conditions does the algorithm admit a unique fixed-point? When are there multiple fixed-points?
In order to get answers to these questions we analyze the mechanisms of iterative decoding by means of linear algebraic methods.
