Overlapped Fountain Coding: Design and Analysis

Abstract

The concept of fountain codes has gained considerable attention in the past few years due to its simplicity, reliability, and feasibility. Nowadays, fountain codes are used in many applications including, but not limited to, data storage, data broadcasting, and point-to-point communications. While traditional fountain codes achieve the channel capacity over the binary erasure channel universally and asymptotically, they offer much room for improvement over other channels, architectures, and regimes. With the development of new technologies for smart cities and the Internet-of-Things (IoT), data transmission methodologies with arguably the highest level of flexibility and adaptability are required. With these technologies, the end users have a very diverse set of capabilities in terms of memory, power, and processing. Besides, the end users are connected via a wide range of links with various qualities and capacities. As a result, the required methodologies must provide a comprehensive solution whereby voice, data, and streamed multimedia can be provided to users on an anytime-anywhere basis. Also, they must enable a dense network of nodes with very different capabilities to communicate with each other reliably and efficiently. This thesis focuses on the design of state-of-the-art data transmission methodology with one of the highest levels of flexibility and adaptability. We present a novel fountain-based encoding technique using overlapped generations of Luby-transform (LT) codes. The proposed overlapped LT (OLT) codes provide more degrees of freedom and better trade-offs for the rateless-coded system parameters. They are highly energy-efficient, scalable, and robust. First, we design new LT codes that are robust to the communication system's parameters such as erasure probability as well as the source length. Density evolution (DE), extrinsic information transfer (EXIT) chart, and code stability are used to design the parameters of fountain codes with different objectives. The main objectives are: maximizing the code rate, minimizing the bit erasure probability (BEP), and maximizing erasure threshold. Secondly, we propose OLT codes over the binary erasure channel (BEC) as well as additive white Gaussian noise (AWGN) channel to improve the performance in terms of error probability and code rate. Our analysis shows that by using OLT codes, significant gains in error probability and code rate are obtained. In addition, we show that OLT codes require a smaller number of operations to recover the source data compared with conventional LT codes.