In this dissertation, we investigate the theory and applications of the novel class of FEC codes called rateless or fountain codes in video transmission and wireless sensor networks (WSN). First, we investigate the rateless codes in intermediate region where the number of received encoded symbols is less that minimum required for full datablock decoding. We devise techniques to improve the input symbol recovery rate when the erasure rate is unknown, and also for the case where an estimate of the channel erasure rate is available. Further, we design unequal error protection (UEP) rateless codes for distributed data collection of data blocks of unequal lengths, where two encoders send their rateless coded output symbols to a destination through a common relay. We design such distributed rateless codes, and jointly optimize rateless coding parameters at each nodes and relaying parameters. Moreover, we investigate the performance of rateless codes with finite block length in the presence of feedback channel. We propose a smart feedback generation technique that greatly improves the performance of rateless codes when data block is finite. Moreover, we investigate the applications of UEP-rateless codes in video transmission systems. Next, we study the optimal cross-layer design of a video transmission system with rateless coding at application layer and fixed-rate coding (RCPC coding) at physical layer. Finally, we review the emerging compressive sensing (CS) techniques that have close connections to FEC coding theory, and designed an efficient data storage algorithm for WSNs employing CS referred to by CStorage. First, we propose to employ probabilistic broadcasting (PB) to form one CS measurement at each node and design CStorage- P. Later, we can query any arbitrary small subset of nodes and recover all sensors reading. Next, we design a novel parameterless and more efficient data dissemination algorithm that uses two-hop neighbor information referred to alternating branches (AB).We replace PB with AB and design CStorage-B, which results in a lower number of transmissions compared to CStorage-P.Electrical Engineerin
