Soft N-modular redundancy

Eric P. Kim, Naresh R. Shanbhag

Research output: Contribution to journalArticlepeer-review


Achieving robustness and energy efficiency in nanoscale CMOS process technologies is made challenging due to the presence of process, temperature, and voltage variations. Traditional fault-tolerance techniques such as N-modular redundancy (NMR) employ deterministic error detection and correction, e.g., majority voter, and tend to be power hungry. This paper proposes soft NMR that nontrivially extends NMR by consciously exploiting error statistics caused by nanoscale artifacts in order to design robust and energy-efficient systems. In contrast to conventional NMR, soft NMR employs Bayesian detection techniques in the voter. Soft voter algorithms are obtained through optimization of appropriate application aware cost functions. Analysis indicates that, on average, soft NMR outperforms conventional NMR. Furthermore, unlike NMR, in many cases, soft NMR is able to generate a correct output even when all N replicas are in error. This increase in robustness is then traded-off through voltage scaling to achieve energy efficiency. The design of a discrete cosine transform (DCT) image coder is employed to demonstrate the benefits of the proposed technique. Simulations in a commercial 45 nm, 1.2 V, CMOS process show that soft NMR provides up to 10× improvement in robustness, and 35 percent power savings over conventional NMR.

Original languageEnglish (US)
Article number5669275
Pages (from-to)323-336
Number of pages14
JournalIEEE Transactions on Computers
Issue number3
StatePublished - 2012


  • Low-power design
  • redundant design
  • signal processing systems

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


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