On The Efficient Map Decoding, Non-data-aided Snr Estimation And Polynomial Interleaver Design For Turbo Coding Systems

Turbo codes were proposed in 1993 for the coded channel transmission. Due to their excellent error correction performance which is near the Shannon limit, turbo codes have been rapidly applied for many practical communication systems. In the past 17 years, a lot of researches have been dedicated to the theory and application of turbo codes, including simplified decoding algorithms, analysis of decoding algorithm convergence, design of excellent component codes, analysis and estimation of the minimum code distance, design of interleavers, parallel implementation of decoding algorithms, etc. Based on existing researches, this thesis focuses mainly on the efficient maximum a posteriori probability (MAP) decoding algorithm in non-logarithm domain, numerical normalization techniques for Log-MAP algorithms in logarithm domain, non-data-aided signal to noise ratio (SNR) estimation, and permutation polynomial (PP) interleavers of turbo codes.To begin with, the principle of turbo encoding/decoding, in-depth survey of previous research work and outcome in turbo coding are firstly presented, followed by the research motivation, ideas, main contributions, and the organizations of this thesis. Then, an improved MAP decoding algorithm is derived from the original standard MAP algorithm. The proposed algorithm can avoid any logarithmic and exponential functions in the iterative decoding steps without involving logarithm domain. As a result, it can attain high decoding efficiency which is similar to the efficiency of Max-Log-MAP decoding in general-purpose computers. The proposed algorithm is optimal in terms of error correction performance, while the Max-Log-MAP, at a cost of error correction performance, is sub-optimal.Next, a linearly approximated Log-MAP decoding algorithm with two numerical normalization techniques and pure integer arithmetic is presented, where the two numerical normalization techniques, referred to as addition normalization and multiplication normalization, respectively, are proved to do not affect the decoding performance. The addition normalization can solve the overflow problem of turbo decoding with fixed-point number arithmetic and the multiplication normalization can be used to implement turbo decoding with pure integer arithmetic or the proof that Max-Log-MAP algorithm does not require any SNR estimation. In order to choose an appropriate multiplication normalization factor, two methods based on a probability analysis and the equivalent look-up table size, respectively, are proposed. It is shown, from the simulated frame error rate (FER) performance of the pure integer implementation of 3GPP standard turbo decoding, that the 9-bit wide integers can guarantee a comparable error correction performance to the optimal improved MAP algorithm.Based on previous SNR estimation techniques using moment estimations over the received binary shift key (BPSK) signals of a turbo code block, three non-data-aided SNR estimators for uncorrelated Rayleigh fading channels are compared in the thesis. These three SNR estimators are also based on moment estimations and the curve fit technique is used to compute SNR. It has been found that the curve fit bias can well compensate the SNR estimation errors for short code blocks. Turbo decoding simulation results have shown that two proposed SNR estimators can achieve lower SNR estimation errors and better bit error ratio (BER) performance than the result in previous literature, especially for short code blocks. Another advantage of the three SNR estimators is that they do not require any knowledge of SNR and Rayleigh fading parameter.Since 2005, quadratic permutation polynomials (QPPs) over integer rings have been proposed for turbo code interleavers. The QPP interleavers do not need the storage of interleaving tables in a turbo decoder, and have shown excellent performance which is significantly superior to uniform random interleavers. Moreover, all QPP interleavers have natural maximum-contention-free property which can avoid the memory access collision in parallel turbo decoding. Some new results for permutation polynomial (PP) interleavers are obtained in this thesis, including a simple method for generation of m-degree (m≥1) PPs over integer rings, a proof for the necessary and sufficient condition of quadratic null-polynomials (QNPs), the enumeration of QPP interleavers excluding their equivalence, and etc. A preliminary search of high order PP interleavers has been done in order to achieve excellent turbo decoding performance. A high order PP interleaver for frame size N=2048, code rate Rc=1/3 and 8-state turbo code has been found whose turbo decoding performance is comparable to the famous code matched interleaver (CMI) design and is better than QPP interleavers.