Rateless Coding for Single-Source Networks with Common Information

Abstract

In this thesis, we consider the communication problem of a single source simultaneously transmitting to multiple receivers whose sets of requested messages overlap. For decades, one of the challenges in this broadcast setting has been decreasing the number of transmissions from the source to the terminals without increasing the system complexity. The multicast and broadcast problems with ‘common’ information have been mostly studied ‘existentially’: information-theoretical bounds on rates and capacities have been discussed in a number of previous works. In this work, we take the contrasted ‘constructive’ viewpoint and attempt to design practical transmission protocols with low encoding and decoding complexities. Our approach is based on rateless fountain coding equipped with efficient belief propagation (BP) decoders. While previous network coding solutions require high-complexity Gaussian elimination decoding for optimality, fountain codes allow for much better performance-complexity trade-offs with BP decoders due to their sparse decoding Tanner graphs. We provide insights and solutions for the 2-terminal setting as an example that show the extraordinary power and flexibility of fountain codes to address the conflicting challenges in the design of efficient transmission protocols. Our ideas can be extended to larger number of receivers and though we have focused on Luby-Transform (LT) codes, other fountain coding distributions can be equally useful. The proposed coding methods in this thesis can be applied to many practical systems such as wireless sensor networks (WSN) that have limited power, memory, and processing capabilities.