Low-Complexity Distributed Set-Theoretic Decoders For Analog Fountain Codes

Analog fotuitain codes (AFCs) have been recently proposed as a capacity-approaching coding scheme for Gaussian channels. In AFCs, coded symbols are real valued, and the number of generated codes can grow unboundedly. In this work, we exploit these characteristics of AFCs to pose the decoding process as an adaptive filtering problem. This formulation opens up the possibility of deriving a large family of online decoding algorithms that process coded symbols as they arrive, in a truly online fashion. In particular, we present two algorithms based on the adaptive projected subgradient method, and we further improve the performance of these algorithms by using heuristics inspired by recent results on superiorization. We also show that the proposed techniques can be trivially extended to distributed settings where receivers can exchange information locally. Simulations show that the proposed techniques can outperform state-of-the-art batch methods in some scenarios.