Overlapped LT codes over the binary erasure channel: analysis and design

Fountain codes are promising forward error correction codes suitable for broadcast and multicast applications where many users with different capabilities are involved in the system. Fixed-rate codes need a priori information about each channel to decide the best code rate and the code rate is usually chosen according to the worst channel to avoid an outage. Fountain codes are agnostic to the channel conditions and rateless. The rate is realised based on the channel conditions for users separately. Overlapped fountain codes were previously invented over the binary erasure channel to provide more degrees of freedom and better trade-offs for the rateless-coded system parameters. In this study, the authors show via analysis and simulations that overlapped fountain codes need fewer decoding steps in comparison with the conventional fountain codes. For example, overlapped fountain codes reduce the number of decoding steps/iterations of belief propagation decoder by 29% even at a source length k=256. They optimise the overlap selection probability of the overlapped fountain codes to maximise the code rate and/or minimise the complexity. At source length, k=256, the proposed analytical and simulation studies show that the highest code rate and lowest average complexity are achieved at an overlap selection probability p=0.6.