Quantifying the computational efficacy of nanocomputing channels

Information-theoretic computational efficacy measures are introduced and applied to the analysis of interacting effects of noise and structural randomness in nanocomputing channels. Two complementary measures–the computational fidelity and representational faithfulness–are shown together to quantify the efficacy with which a particular noisy computing channel implements a specified logical transformation. The statistics of these two measures, evaluated for an ensemble of nanocomputing channels with random sample-to-sample structural variations, allows quantitative characterization of the interacting effects of transient noise and structural randomness in the channel ensemble. Application of these efficacy measures is illustrated for artificial nanocomputing channels–noisy quantum-dot cellular automata arrays with random defects–although they can be used to quantify the computational efficacy of a wide variety of artificial or natural nanoscale networks with computational capabilities.

[1]  Teijo Lehtonen.  On Fault Tolerance Techniques towards Nanoscale Circuits and Systems , 2005 .

[2]  Lei Wang,et al.  Analysis of Defect Tolerance in Molecular Crossbar Electronics , 2009, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[3]  F. Jain,et al.  A Quantitative Approach for Analysis of Defect Tolerance in QCA , 2008, 2008 8th IEEE Conference on Nanotechnology.

[4]  T.J. Dysart,et al.  > Replace This Line with Your Paper Identification Number (double-click Here to Edit) < 1 , 2001 .

[5]  Neal G. Anderson,et al.  Heat dissipation bounds for nanocomputing: Theory and application to QCA , 2011, 2011 11th IEEE International Conference on Nanotechnology.

[6]  S. Bhanja,et al.  Probabilistic Modeling of QCA Circuits Using Bayesian Networks , 2006, IEEE Transactions on Nanotechnology.

[7]  Christof Teuscher,et al.  Adaptive learning in random linear nanoscale networks , 2011, 2011 11th IEEE International Conference on Nanotechnology.

[8]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[9]  Massoud Pedram,et al.  Architectures for silicon nanoelectronics and beyond , 2007, Computer.

[10]  Maya Gokhale,et al.  Nanocomputing in the presence of defects and faults: a survey , 2004 .

[11]  Lei Wang,et al.  Analysis of defect tolerance in molecular electronics using information-theoretic measures , 2007, 2007 IEEE International Symposium on Nanoscale Architectures.

[12]  P. D. Tougaw,et al.  Logical devices implemented using quantum cellular automata , 1994 .

[13]  Wolfgang Porod,et al.  Quantum cellular automata , 1994 .

[14]  Fabrizio Lombardi,et al.  An information-theoretic analysis of quantum-dot cellular automata for defect tolerance , 2010, JETC.

[15]  Teng Wang,et al.  Fault-Tolerant Nanoscale Processors on Semiconductor Nanowire Grids , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  P. D. Tougaw,et al.  Thermal effect in quantum-dot cellular automata , 2005 .

[17]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[18]  François Simon,et al.  On the capacity of noisy computations , 2011, 2011 IEEE Information Theory Workshop.

[19]  S. Winograd,et al.  Reliable Computation in the Presence of Noise , 1963 .

[20]  Massimo Macucci,et al.  Quantum Cellular Automata , 2006 .

[21]  Neal G. Anderson,et al.  An information-theoretic measure for the computational fidelity of physical processes , 2008, 2008 IEEE International Symposium on Information Theory.

[22]  C. Moritz,et al.  Towards Defect-Tolerant Nanoscale Architectures , 2006, 2006 Sixth IEEE Conference on Nanotechnology.

[23]  Naresh R. Shanbhag,et al.  Energy-efficiency bounds for deep submicron VLSI systems in the presence of noise , 2003, IEEE Trans. Very Large Scale Integr. Syst..

[24]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[25]  Amir Fijany,et al.  New Design for Quantum Dots Cellular Automata to obtain Fault Tolerant Logic Gates , 2001 .

[26]  Mahfuza Khatun,et al.  Fault-tolerance and thermal characteristics of quantum-dot cellular automata devices , 2010 .

[27]  Neal G. Anderson,et al.  On the physical implementation of logical transformations: Generalized L-machines , 2010, Theor. Comput. Sci..

[28]  Csaba Andras Moritz,et al.  Parameter Variability in Nanoscale Fabrics: Bottom-Up Integrated Exploration , 2010, 2010 IEEE 25th International Symposium on Defect and Fault Tolerance in VLSI Systems.

[29]  Naresh R. Shanbhag,et al.  Toward achieving energy efficiency in presence of deep submicron noise , 2000, IEEE Trans. Very Large Scale Integr. Syst..

[30]  Massimo Macucci.  Quantum Cellular Automata: Theory, Experimentation and Prospects , 2006 .

[31]  Jianbo Gao,et al.  Toward hardware-redundant, fault-tolerant logic for nanoelectronics , 2005, IEEE Design & Test of Computers.

[32]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[33]  Robert W. Keyes,et al.  Component variability as a limit in digital electronics , 2008 .