Turbo code concepts made easy, or how I learned to concatenate and reiterate

The goal of this paper is to describe the main ideas behind the new class of codes called turbo codes, whose performance in terms of bit-error-probability has been shown to be very close to the Shannon limit. The benefits of these concatenated codes are illustrated in the context of likelihood functions and a posteriori probabilities. Since the algorithms needed to implement the decoders have been well documented by others, they are only referenced here, but not described in detail. A numerical example, using a simple concatenated coding scheme, provides a vehicle for explaining how error performance can be improved when soft outputs from the decoders are used in an iterative decoding process