### Abstract

This paper addresses the problem of constructing reliable memories from unreliable components. We consider the memory construction proposed by Taylor in which a codeword stored in a faulty memory is regularly updated by an LDPC decoder to overcome the memory degradation. We assume that the LDPC decoder used in the system is a faulty one-step majority logic decoder. Compared to [1], [2] which analyze only the faulty one-step majority logic decoder, we analyze here the reliability of the whole memory construction. We introduce a sequence of output errors probabilities at successive time instants and determine the properties and the fixed points of the sequence. From the fixed-point analysis, we define a threshold that predicts the noise level which can be tolerated for the memory to stay reliable. We finally represent the reliability regions of the Taylor-Kuznetsov memory with respect to the decoder noise parameters and validate the theoretical results with Monte-Carlo simulations.

Original language | English (US) |
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Title of host publication | 2015 Information Theory and Applications Workshop, ITA 2015 - Conference Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 46-53 |

Number of pages | 8 |

ISBN (Print) | 9781479971954 |

DOIs | |

State | Published - Oct 27 2015 |

Event | Information Theory and Applications Workshop, ITA 2015 - San Diego, United States Duration: Feb 1 2015 → Feb 6 2015 |

### Other

Other | Information Theory and Applications Workshop, ITA 2015 |
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Country | United States |

City | San Diego |

Period | 2/1/15 → 2/6/15 |

### Keywords

- Decoding
- Degradation
- Error probability
- Memory architecture
- Noise
- Parity check codes
- Reliability

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

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## Cite this

*2015 Information Theory and Applications Workshop, ITA 2015 - Conference Proceedings*(pp. 46-53). [7308965] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITA.2015.7308965