Polar Coding Schemes For Cooperative Transmission Systems

With the rapid development of wireless communications, people require much higher data-rate transmission for wireless services. However, due to the rareness of radio spectrum, people have to use the limited radio resources sufficiently and effectively to support high-rate transmission for wireless systems, which is an emergency problem to be solved for future wireless communications. Cooperative communications have become a key technology in recent years to solve the high-rate transmission and broad-range wireless coverage, because of its ability to provide the spatial diversity and increase the efficiency of radio spectrum and the system capacity. The relay channel model, as an important component of cooperative communications, has been paid much attention. For the requirements of cooperative communications, the practical distributed channel coding schemes come out recently. A good distributed channel coding scheme can obtain extra coding gain and further increase the system performance by using the spatial diversity sufficiently. Therefore, the distributed channel coding scheme with better performance and lower complexity is a core problem that needs to be studied much deeper for cooperative communication systems.Polar codes have been proved to be the first family of codes that can achieve the symmetric capacity of binary-input discrete memoryless channels (B-DMC) based on a phenomenon called channel polarization. Polar codes are constructive channel coding scheme with the advantages of a low encoding and decoding complexity and a non-existent error floor problem. Therefore, from the theoretical and practical point of view, it is of importance to study low-complexity polar coding and decoding schemes and transmission protocols based on polar codes to acheive the capacities of relay systems.Considering polar codes as powerful channel coding schemes, this paper studies the performance of concatenated polar codes and the key techniques of polar codes in the application of relay systems from the theoretical and practical aspects. The main contributions are as follows:Firstly, a serially-concatenated coding scheme, with a polar code as the outer code and a low density generator matrix (LDGM) code as the inner code based on the idea of the traditional concatenated codes, is proposed. First, theoretical study shows that, by concatenation, the proposed scheme, referred to as serially-concatenated Polar-LDGM (SCPL) codes, provides a method to improve significantly the low convergence speed problem of the former and the high error floor problem of the latter, while keeping the advantages of both such as the low encoding/decoding complexity. Then, we describe the encoding scheme and derive the message iterative decoding algorithm based on tanner graph. Finally, the appropriate combination of the inner and outer coding rates and the appropriate weight of the inner LDGM code are investigated by simulations. As an advantage with respect to the low-density parity-check (LDPC) codes, the encoding complexity of SCPL codes is as low as O(N1logN1)+O(N), where N1and N are the block lengths of the outer code and the inner code, respectively. Simulation results show that the resulting bit error rate (BER) performance of SCPL codes approaches the Shannon capacity limit very closely while avoiding error floor until the BER falls down to10-10.Secondly, according to the degraded half-duplex single-relay channel model, a novel transmission protocol based on polar codes is proposed. In the proposed scheme, referred to as the partial message relaying (CPMR) protocol, we theoretically prove that the proposed scheme can asymptotically achieve the capacity of the channel model and we also derive the upper bound of the block error probability under the successive cancellation (SC) decoding. To the choice of receiving time fraction and distance between the relay and the source, we investigate the sensitivity of capacities for the half-duplex additive Gaussian noise (AWGN) relay channel with BPSK modulation. In addition to the asymptotic analysis, we also develop a practical joint iterative soft parallel interference cancellation (JISPIC) receiver structure that is suitable to the proposed scheme. Finally, we testify the CPMR scheme with finite block lengths by simulations. Compared with the LDPC codes in single-relay systems, the proposed scheme inherits the advantage of low encoding and decoding complexity of polar codes and outperforms the conventional LDPC coding scheme.Thirdly, we extend our low-complexity CPMR scheme to multiple-relay networks, since nonconstructive random coding schemes have high complexity in multiple-relay networks. For a given network, different CPMR protocols are possible, depending on the relation between the partial messages forwarded and the partial information sets. Therefore, a relay can flexibly forward the partial messages of the decoded messages the following relay or the destination needs. According to two degraded multiple-relay networks with orthogonal receiver components (MRN-ORCs), we study the constructive solutions for the polar codes and propose the corresponding algorithms for calculating the partial message sets. We prove that the proposed schemes can achieve the capacities of the above degraded MRN-ORCs with the average block error probability being upper bounded by O(2N), where N is the block length and (0,12). Finally, we confirm that the CPMR scheme can be applied to the multiple-relay networks effectively by simulations.