Majority Logic Decoding under Data-Dependent Logic Gate Failures

摘要

A majority logic decoder made of unreliable logic gates, whose failures aretransient and datadependent, is analyzed. Based on a combinatorialrepresentation of fault configurations a closed-form expression for the averagebit error rate for an one-step majority logic decoder is derived, for a regularlow-density parity-check (LDPC) code ensemble and the proposed failure model.The presented analysis framework is then used to establish bounds on theone-step majority logic decoder performance under the simplified probabilisticgate-output switching model. Based on the expander property of Tanner graphs ofLDPC codes, it is proven that a version of the faulty parallel bit flippingdecoder can correct a fixed fraction of channel errors in the presence ofdata-dependent gate failures. The results are illustrated with numericalexamples of finite geometry codes.