The advent of turbo codes has sparked tremendous research activities around the theoretical and practical aspects of turbo codes and turbo-like codes. The crucial novelty in these codes is the iterative decoding.

Turbo-like Codes introduces turbo error correcting concept in a simple language, including a general theory and the algorithms for decoding turbo-like code. It presents a unified framework for the design and analysis of turbo codes and LDPC codes and their decoding algorithms.

A major focus of Turbo-like Codes is on high speed turbo decoding, which targets applications with data rates of several hundred million bits per second (Mbps). In this book a novel high-speed turbo decoder is presented that exploits parallelization. Parallelism is achieved very efficiently by exploiting the flexibility of message-passing algorithm. It has been shown that very large speed gains can be achieved by this scheme while the efficiency is maintained reasonably high. Memory access, which poses a practical problem for the proposed parallel turbo decoder, is solved by introducing the conflict-free interleaver. The latency is further improved by designing a special kind of conflict-free interleaver. Furthermore, an algorithm to design such interleaver is presented. It is shown that the performance of turbo code is not sacrificed by using the interleaver with the proposed structure.

Although turbo code has near Shannon-capacity performance and the proposed architecture for parallel turbo decoder provides a very efficient and highly regular hardware, the circuit is still very complex and demanding for very high-speed decoding. Therefore, the next step would be finding turbo-like codes that not only achieve excellent error correction capability, but also are very simple. As a result, a class of new Low-Density Parity-Check (LDPC) codes for different rates and block-sizes, called Accumulate-Repeat-Accumulate (ARA) codes,is presented. The performance of ARA codes is analyzed and shown that some ARA codes perform very close to random codes, which achieve Shannon limit.

Zusammenfassung
The common property among turbo-like code is that they consist of very simple constituent codes that are connected to each other with random or pseudorandom interleavers. The crucial novelty in these codes is the iterative decoding. This means that the constituent codes are decoded separately, which is ef?cient and practically feasible since they are very simple codes. Then, they pass new information to each other in a course of a few iterations. It has been shown that iterative decoding is a generalization of the well-known probability or belief propagation algorithm. The belief propagation algorithm that has been essential for development of new ideas throughout this work is described in the context of coding. The basic theorems for this algorithm are explained and proven in the following paragraphs. Thisis then followed by a description of the computational algorithm. The probability propagation algorithm is proven in c- junctionwithatree-structuredgraphgraphswithoutanycycle.Infact,thegraphical representation of any problem solved by this algorithm is the centerpiece of the algorithm. The generalization of the algorithm for graphs with cycles is presented later on. Representation of codes on graph is the next step towards characterization of the iterative decoding as an example of the probability propagation algorithm. The graph representations are presented for a few codes that are commonly used in turbo-like codes.

Inhalt
Turbo Concept.- High-speed Turbo Decoders.- Very Simple Turbo-like Codes.- High Speed Turbo-like Decoders.