A useful tool in the design of reliable digital communication systems is channel coding. Turbo codes have been shown to yield an outstanding coding gain close to theoretical Shannon limit in the Additive White Gaussian Noise (AWGN) channel. This is due to relatively large coding gains that can be achieved. Over the past decade, turbo codes have been widely considered to be one of the most power...

Turbo-codes have attracted a great deal of interest since their discovery in 1993. This paper reviews the reasons for this, in particular their attainment of the ultimate limits of the capacity of a communication channel. The paper describes the two fundamental concepts on which they are based: concatenated coding and iterative decoding. This latter is the real ‘turbo-principle’, which is the r...

In this paper, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders. We developed new rate 1/3 and 2/3 constituent codes to be used in the turbo encoder structure. These codes, for 2 to 32 states, are designed by u...

This is a tutorial paper meant to introduce the reader to the new concept of turbo codes. This is a new and very powerful error correction technique which outperforms all previous known coding schemes. It can be used in any communication system where a significant power saving is required or the operating signal–to–noise ratio (SNR) is very low. Deep space communications, mobile satellite/cellu...

Requirement for efficient decoding techniques for Turbo & LDPC codes are in demand, many applications incorporates either LDPC or Turbo codes nowadays, due to their excellent performance which practically approaches Shannon’s limit. Although the theoretical performance of both codes is impressive, their practical implementation leads to problems like numerical inaccuracy, limited memory resourc...

Most of error correcting codes applying to DS/SS systems are such that information data is first (bit-bybit) encoded and then spread by pseudo noise (PN) sequence. Thus, coding gain achieved by such systems are mainly due to the error correcting codes and the redundancy produced by the spreading codes shows no effect on the coding gain. In this paper, a chip-by-chip Turbo coding for DS/SS syste...

An upper bound on the minimum distance of turbo codes is derived, which depends only on the interleaver length and the component scramblers employed. The derivation of this bound considers exclusively turbo encoder input words of weight 2. The bound does not only hold for a particular interleaver but for all possible interleavers including the best. It is shown that in contrast to general linea...

Turbo codes are a new class of forward error correcting codes that have proved to give a performance close to the channel capacity as proposed by C. Shannon. A turbo code encoder is formed by the parallel concatenation of two identical recursive convolutional encoders separated by an interleaver. The turbo code decoder utilizes two cascaded decoding blocks where each block in turn shares a prio...

Turbo codes, low-density parity-check (LDPC) codes and turbo product codes (TPCs) are high performance error-correction codes which employ iterative algorithms for decoding. Under different conditions, the behaviors of the decoders are different. While the nonlinear dynamical behaviors of turbo code decoders and LDPC decoders have been reported in the literature, the dynamical behavior of TPC d...

The paper starts with a short overview of channel coding and the reader is reminded the concept of convolutional encoding. Bottlenecks of the traditional approach are described and the motivation behind turbo codes is explained. After examining the turbo codes design more in detail, reasons behind their efficiency are brought out. Finally, a real-world example of the turbo code used in the thir...