Research On Accumulate Repeat Tree Codes And Its Performance For OFDM Systems

To be the technology used for ensuring the reliability of the data transmission in communication systems, the channel coding technology plays an important role in both communication and coding fields, and it has become an indispensable standard technology for combating the channel noise and interfere of wireless communication systems. With the proposal of turbo codes and the refinding of low-density parity-check (LDPC) codes, turbo-like codes represented by repeat accumulate (RA) codes have become more and more attractive in the channel coding technologies. This class of turbo-like codes, combining the advantage of encoding simplicities of turbo codes and the advantage of low decoding costs of LDPC codes, can be viewed as a special subclass of both turbo codes and LDPC codes. Meanwhile, turbo-like codes have good decoding performance close to the Shannon limit. Based on the analysis of two typical turbo-like codes, i.e., RA codes and concatenated tree (CT) codes, in this dissertation, we propose a novel channel coding scheme with precoding performance, called accumulate repeat tree (ART) codes. The basic performance of this ART codes is studied, and the applications of ART codes in the orthogonal frequency division multiplexing (OFDM) systems are discussed.In recent years many researchers have paied attention to turbo-like coding schemes. The structure characteristic and the basic conception of turbo-like codes are summed up at first. The condition of generating the word error rate (WER) interleaver gains for classical parallel concatenated coding (PCC) is analyzed, i.e., only if the number of the constituent codes is more than 2, the overall code generates the WER interleaver gains, proving that turbo codes with two parallel constituent codes have no WER interleaver gains.The basic performance of turbo-like codes is analyzed. The dissertation proposes the novel ART coding schemes by focusing on RA codes and CT codes primarily, connecting serially concatenated constituent repetition codes of the RA codes with parallel concatenated constituent tree codes of the CT codes through an interleaver between them, and putting an accumulator before the repetition codes. The analysis shows that this structure of placing the accumulator ahead can bring some correlative coding gains, so it can be seen as a precoder. The serially decoding algorithm and the parallel belief-propagation (BP) iterative decoding algorithm is studied. The performance of ART codes in the additive white Gaussian noise (AWGN) channel and the Rayleigh fading channel is given by theoretical analysis and computer simulations. The results show better performance of ART codes than RA and CT codes under the same simulation condition in both AWGN channels and Rayleigh fading channels.The decoding performance of ART codes is discussed. Since there is no practical maximum likelihood decoding (MLD) algorithm available for real turbo-like coding systems, the discussion is mainly concerned with the MLD bounds for turbo-like codes to estimate the performance, including the union bounds based on the Bhattacharyya coefficient, and the tight bounds based on the uniform interleaver theory. Then we analyzed the issue of weight distribution (WD), having computed the input-output weight enumerator (IOWE) of the ensemble of ART codes, and then using this IOWE we could make the MLD decoding analysis of ART codes. Besides, the analysis methods for BP iterative decoding are discussed. The density evolution (DE) and the optimizing design for ART codes are discussed. The DE method for ART codes is mainly studied using two practical algorithms, i.e., the discrete density evolution (DDE) algorithm and the Gaussian density evolution (GDE) algorithm. According to the DE, the thresholds for the BP iterative decoding algorithm are computed. Theoretical analysis and computing results make us select two ART codes with good performance, i.e., ART(3,1) codes and ART(2,2) codes.The performance of ART codes in OFDM systems is studied. The OFDM systems are divided into two forms with different orthogonal bases, i.e., the discrete Fourier transform (DFT) based OFDM and the discrete wavelet transform (DWT) based OFDM, which is the WOFDM. The advantage and the disadvantage between the DFT-OFDM and the WOFDM is discussed. Compared with the DFT-OFDM systems, the frequency spectrum efficiency and the data transmitting velocity of the WOFDM can be improved, for it does not need the cyclic prefix (CP). The ART-OFDM channel coding schemes with two orthogonal bases are given, and the relative decoding is analyzed. Simulation results show that ART codes have good performance in OFDM systems with both orthogonal bases.