It is well known that an interleaver with random properties, quite often generated by pseudo-random algorithms, is one of the essential building blocks of turbo codes. However, randomly generated interleavers have two major drawbacks: lack of an adequate analysis that guarantees their performance and lack of a compact representation that leads to a simple implementation. In this paper we present several new classes of deterministic interleavers of length , with construction complexity ( ), that permute a sequence of bits with nearly the same statistical distribution as a random interleaver and perform as well as or better than the average of a set of random interleavers. The new classes of deterministic interleavers have a very simple representation based on quadratic congruences and hence have a structure that allows the possibility of analysis as well as a straightforward implementation. Using the new interleavers, a turbo code of length 16384 that is only 0.7 dB away from capacy at a bit-error rate (BER) of 10 5 is constructed. We also generalize the theory of previously known deterministic interleavers that are based on block interleavers, and we apply this theory to the construction of a nonrandom turbo code of length 16384 with a very regular structure whose performance is only 1.1 dB away from capacity at a BER of 10 5 .

This paper describes an application of turbo codes in conjunction with 16QAM in high speed mobile satellite communications. The channel characteristics, the architecture of the modem and the performance curves for the selected turbo codes are presented. 1 INTRODUCTION The Institute for Telecommunications Research (ITR) from the University of South Australia investigated suitable modulation and error correction schemes for 2 bit/symbol bandwidth efficiency. A feasibility study was done for data rates between 4.8 kbit/s and 128 kbit/s. Rate half turbo codes obtained from puncturing a rate third turbo code [1, 2] and Gray mapping into a 16 Quadrature Amplitude Modulation (16QAM) scheme [3] is the preferred solution and some of the results are presented in this paper. Following the feasibility study, a proof of concept study which includes building a modem/codec is under way. This will allow optimisation of system parameters and the performance of field trials. The most important factors ...

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/cellular communications, microwave links, paging, etc., are some of the possible applications of this revolutionary coding technique. Part I of the paper discussed the history of turbo codes, why they are different from traditional convolutional/block codes, the turbo encoder structures and issues related to the interleaver design. Part II addresses the decoder architecture, the achievable performance for turbo codes for a wide range of coding rates and modulation techniques and discusses delay and implementation issues. 2 1 Introduction The optimum decoding of turbo codes is the maximum likeli...

This paper discusses a realistic turbo coding system when the signal phase has not been perfectly estimated. We propose improved decoding algorithms for the situations when the residual phase error can be modelled by the Gaussian probability distribution and a Markov chain, a model which can be used in many actual phase estimators. It is shown that increasing the state space of the decoders can dramatically improve the bit error probability without the need of increasing transmitted power.

In this paper we present a modification of a typical turbo code to allow for the header bits to be decoded much faster than the other bits. This gives the decoder a possibility to discard data packets not addressed to it, and saves time and power since fewer iterations need to be performed to reliably decode the header.

In this paper we present an extended version of a turbo decoder which can cope with occasional phase shifts of the received signal. Such shifts are usually caused by noise bursts which prevent a proper synchronization of the incoming signal. To model such a channel we propose a concatenation of the BSC and the AWGN channel which can easily be incorporated into the classical turbo decoding algorithm by extending the state space. The proposed algorithm improves the performance by 0.2-0.6 dB as compared to the classical turbo decoder. A simplified version of the algorithm is also presented and shown to perform as good as the full version. 1.

#A method of efficiently implementing a continuous MAP decoding algorithm is presented. A sliding window technique is used to reduce the block size at the expense of extra computations. The smaller block size results in a large reduction in memory storage requirements, reduced delay, and the ability to implement a continuous MAP decoder. A technique for reducing the synchronisation time for a turbo decoder without the use of synchronisation words is also presented. This technique artificially forces the low delay inner decoder to synchronise to a large number of states so that the large delay outer decoder (due to the interleaver between the inner and outer decoder) has fewer states to synchronise to. The overall synchronisation time is thus reduced. Index Terms#MAP decoding, continuous decoding, turbo codes, synchronisation I. INTRODUCTION Turbo codes [1] combined with iterative decoding are currently the most powerful form of error control known. The first results from [1] showed t...

Terminating the trellis was considered essential to lower the bit error probability in a turbo coded system [1]. When a sliding window algorithm is used, this issue becomes even more important. This letter shows that one can completely ignore the trellis termination by using an interleaver that takes into account the particular window size of the sliding window algorithm.

The Turbo code interleaver design problem is considered for large block sizes, where the eect of trellis termination is less marked. The performance of various interleavers with a similar block size are compared, including an implementation of the uniform interleaver. An optimised interleaver design technique based on simulated annealing is proposed { the results obtained show that the error performance may be signi cantly improved without increasing the delay. Finally, interleaver design for small Turbo codes is considered. In this case it is shown that while correct termination improves the performance for an average interleaver, its eect on Turbo codes with optimised interleavers is negligible.

Turbo coding is a powerful class of error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its application to the reconciliation problem occuring in a continuous-variable quantum key distribution protocol. 1.