Open AccessAnalysis and design of a new fountain codec under belief propagation
Author(s) -
Mirrezaei Seyed Masoud,
Faez Karim,
Yousefi Shahram
Publication year - 2014
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2012.0737
Subject(s) - fountain code , codec , decoding methods , computer science , encoder , belief propagation , raptor code , coding gain , algorithm , coding (social sciences) , low density parity check code , theoretical computer science , luby transform code , telecommunications , mathematics , error floor , statistics , operating system
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.