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Analysis and design of a new fountain codec under belief propagation

Error-prone patterns have been extensively studied for low-density parity-check codes yet they have never been fully explored for generator-based ‘Fountain codes’. It is shown here that these phenomena are related to certain combinatorial structures within the Tanner graph (TG) representation of the code, previously termed absorbing sets. The authors systematically define the ‘absorbing sets’ in the generator-based TG of a code. They then demonstrate how these substructures are damaging to the ‘realised rate, delay’ and ‘decoding cost’ of Fountain codes particularly at low error rates. They further analyse the existence probability of certain absorbing sets and propose a new encoder/decoder pair forming a new family of Fountain codes. The authors experimental results show that these new codecs lead to improvements in all system features. Typical gains for Luby-transform codes include 20% reduction in the decoding complexity and simultaneous coding gains of 0.6 and 0.9 dB at bit error rates of 10 − 5 and 10 − 6, respectively. As such, this work takes a step towards better rateless code design and construction.