| Polar codes were invented as the first error-correcting codes to achieve the capacity for the discrete channels with relatively low-complexity for encoding and decoding. However, this is only possible with significantly large code lengths which are not practical for many systems. Meanwhile, the performance of the finite-lengths polar codes is not competitive with other modern error-correcting codes. This can be attributed to the suboptimality of the decoding process and the relatively poor minimum Hamming distances. This thesis aims to improve the performance of polar codes. The contributions include improving the performance of the conventional successive cancellation decoder. This is based on a novel technique, namely one-step decision delay, which incorporates some extra computational nodes to the code tree. Also, this thesis presents two methods for increasing the Hamming distances of polar codes; in the first, the code rate remains unchanged, while in the second, that produces superior performance, a modest reduction in the code rate occurs. Both methods enhance the performance with using belief propagation decoder. In addition, the latency of the decoding process is reduced by applying the fast Hadamard transform decoder on polar codes for the first time. In this regard, a method to modify the encoder is presented for some lengths that are not normally compatible with the proposed decoder. Interestingly, this modification method has another advantage that in the sense that it increases the minimum Hamming distances of the codes. Furthermore, this thesis presents the utilisation of polar codes in some practical communication systems. Firstly, polar codes are examined over power line communication systems. In this respect, the construction of polar codes is analysed by using three different methods. Additionally, the practical performance of polar codes is illustrated for both single-carrier and multi-carrier channels. Secondly, this thesis explores polar codes for unequal error protection by partitioning the information sets into a number of subsets with different reliabilities. JPEG2000, which is an image compression method, is used for validating the advantages of the proposed technique. Moreover, a new joint source channel decoding is proposed from the combination of the polar decoder and JPEG2000 decoder in order to enhance the quality of the compressed images. Finally, polar codes are investigated for the energy transfer by presenting new subcodes that are chosen according to the weights of the produced codewords. In this context, two modes of energy transfer are presented. The proposed modes can successfully extend the lifetime of the receiver's battery. |
