Analysis and Design of Rateless Codes

Abstract: The invention of turbo codes and the re-discovery of sparse graph codes constitute a milestone in error-correction codes designed for communication and storage systems. Sparse graph codes such as low-density parity-check codes can offer a performance that approaches the previously elusive Shannon capacity with reasonable practical computational complexity. Fountain codes have emerged in the realm of sparse graph codes, and  have shown excellent performance for multicast and broadcast transmission without channel state information at the transmitter. A fountain code is inherently rateless, and as a consequence, such codes may potentially generate an unlimited number of encoded symbols on the fly. Thus due to the rateless property, these codes are suitable for transmission over time varying channels. The results presented in this thesis aim at providing insight into the fundamental design of rateless codes, which could serve as a guideline for the optimal design of rateless codes in real-world applications.The thesis is divided into two parts. The first part considers the analysis and design of rateless codes for point-to-point communication. To this end, we commence by considering the concatenation of Luby transform (LT) codes, which were the first practical realization of rateless codes, with differential modulators to exploit the inherent coding gain of differential modulations. An algorithm is developed based on the extrinsic information transfer (EXIT) chart to obtain optimized degree distributions of LT coded differential modulator systems in terms of convergence performance. Then, we delve deeper into the characteristics of LT codes with the objective of improving the error floor performance over noisy channels. An encoding scheme is proposed, which is subsequently used to reduce the error floor. To observe the consequences of the modified encoding scheme, the convergence behavior of the proposed LT code is analyzed using EXIT charts, and shown to be similar to the convergence performance of conventional LT codes. This idea is then extended to LT codes for transmission over erasure channels and a design framework is developed to jointly improve the transmission efficiency and erasure floor performance. For complexity-constrained applications, we construct low-complexity LT codes and devise a reduced-complexity LT decoder for transmission over noisy channels.The second part of the thesis deals with the analysis and design of rateless codes for multi-point communication. To address the shortcomings of existing distributed LT (DLT) codes, we introduce buffer-based DLT codes for a multi-source and multi-relay network to virtually convert lossy source-relay links to corresponding lossless links. We optimize the proposed DLT codes in terms of transmission efficiency; thus exhibiting better performance as compared to their conventional counterparts at the expense of increased computational complexity. The idea is then extended to a multi-way relay network where a linear-programming design framework is outlined for optimizing degree distributions in terms of transmission efficiency. Finally, a design framework is provided for DLT coding schemes, to jointly improve the transmission efficiency and erasure floor performance.