Turbo Codes

Decoding Algorithm

The choice of decoding algorithm and number of decoder iterations also influences performance. Performance improves as the number of iterations increases. This improvement follows a law of diminishing returns. Also, the number of iterations required is a function of the interleaver’s size – bigger interleavers require more iteration. For example, a turbo code with an interleaver size of 16,384 bits only needs about 9 iterations of decoding in practice.

 Inmarsat

                Inmarsat's multimedia service, is a new service based on turbo codes and 16QAM that allows the user to communicate with existing Inmarsat-3 spot-beam satellites from a laptop-sized terminal at 64 kbit/s. The Narrowband Technology based on 16QAM and turbo-coding provides significant reduction (> 50%) in the required bandwidth for mobile satellite channels improving at the same time the satellite power efficiency.

UMTS

The advantage of turbo codes over conventional codes was thoroughly demonstrated one year after the invention of turbo codes in joint detection code division multiple access (JD-CDMA) mobile radio and GSM/DCS 1800 systems. Recently, the technical specification for the Universal Mobile Telecommunications System (UMTS) has been a Third Generation Partnership Project (3GPP) proposal that included turbo codes in the multiplexing and channel coding specification.

Introduction

The transfer of information from the source to its destination has to be done in such a way that the quality of the received information should be as close as possible to the quality of the transmitted information.

The information to be transmitted can be machine generated (e.g., images, computer data) or human generated (e.g., speech). Regardless of its source, the information must be translated into a set of signals optimized for the channel over which we want to send it. The first step is to eliminate the redundant part in order to maximize the information transmission rate. This is achieved by the source encoder block in Figure 1-1. In order to ensure the secrecy of the transmitted information, an encryption scheme must be used. The data must also be protected against perturbations introduced by the communication channel which could lead to misinterpretation of the transmitted message at the receiving end. This protection can be achieved through error control strategies: forward error correction (FEC), i.e., using error correcting codes that are able to correct errors at the receiving end, or automatic repeat request (ARQ) systems.

The modulator block generates a signal suitable for the transmission channel. In the traditional approach, the demodulator block from Figure 1-1 makes a "hard" decision for the received symbol and passes it to the error control decoder block. This is equivalent, in the case of a two level modulation scheme, to decide which of two logical values, say -1 and +1, was transmitted. No information is passed on about how reliable the hard decision is. For example, when a +1 is output by the demodulator, it is impossible to say if it was received as a 0.2 or a 0.99 or a 1.56 value at the input to the demodulator block. Therefore, the information concerning the confidence into the demodulated output is lost in the case of a "hard" decision demodulator.

Channel Capacity

The capacity of a channel, which was first introduced 50 years ago by Claude Shannon, is the theoretical maximum data rate that can be supported by the channel with vanishing error probability. In this discussion, we restrict our attention to the additive white Gaussian noise (AWGN) channel.Here, x is modulated symbol modelled by arandom process with zero mean and variance Es (Es is the energy per symbol). For the specific case of antipodal signalling 2 , x = + Es 1/2 . z is sample from an additive white Gaussian noise process with zero mean and variance N0/2.