Performance Analysis Based on Density Evolution on Fault Erasure Belief Propagation Decoder

Hiroki MORI  Tadashi WADAYAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.12   pp.2155-2161
Publication Date: 2016/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.2155
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory and Techniques
Keyword: 
LDPC codes,  BP decoder,  fault,  density evolution,  

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Summary: 
In this paper, we will present analysis on the fault erasure BP decoders based on the density evolution. In the fault BP decoder, the messages exchanged in a BP process are stochastically corrupted due to unreliable logic gates and flip-flops; i.e., we assume circuit components with transient faults. We derived a set of the density evolution equations for the fault erasure BP processes. Our density evolution analysis reveals the asymptotic behaviors of the estimation error probability of the fault erasure BP decoders. In contrast to the fault free cases, it is observed that the error probabilities of the fault erasure BP decoder converge to positive values, and that there exists a discontinuity in an error curve corresponding to the fault BP threshold. It is also shown that an message encoding technique provides higher fault BP thresholds than those of the original decoders at the cost of increased circuit size.