Low Complexity Concurrent Error Detection for Complex Multiplication

This paper studies the problem of designing a low complexity Concurrent Error Detection (CED) circuit for the complex multiplication function commonly used in Digital Signal Processing circuits. Five novel CED architectures are proposed and their computational complexity, area, and delay evaluated in several circuit implementations. The most efficient architecture proposed reduces the number of gates required by up to 30 percent when compared with a conventional CED architecture based on Dual Modular Redundancy. Compared to a Residue Code CED scheme, the area of the proposed architectures is larger. However, for some of the proposed CEDs delay is significantly lower with reductions exceeding 30 percent in some configurations.

[1]  E. Swartzlander,et al.  Floating-point implementation of complex multiplication , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[2]  Naresh R. Shanbhag,et al.  Energy-efficient soft error-tolerant digital signal processing , 2006, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[3]  Michael Nicolaidis,et al.  A CAD framework for generating self-checking multipliers based on residue codes , 1999, Design, Automation and Test in Europe Conference and Exhibition, 1999. Proceedings (Cat. No. PR00078).

[4]  Mark G. Karpovsky,et al.  Design of Reliable and Secure Multipliers by Multilinear Arithmetic Codes , 2009, ICICS.

[5]  Salvatore Pontarelli,et al.  On the use of Karatsuba formula to detect errors in GF((2(sup)n(/sup))(sup)2(/sup)) multipliers , 2012, IET Circuits Devices Syst..

[6]  Thomas J. Brosnan,et al.  Modular Error Detection for Bit-Serial Multiplication , 1988, IEEE Trans. Computers.

[7]  BaumannRobert Soft Errors in Advanced Computer Systems , 2005 .

[8]  M. Nicolaidis,et al.  Design for soft error mitigation , 2005, IEEE Transactions on Device and Materials Reliability.

[9]  S. Pontarelli,et al.  On the use of Karatsuba formula to detect errors in GF ( ( 2 n ) 2 ) multipliers , 2011 .

[10]  Reto Zimmermann Datapath Synthesis for Standard-Cell Design , 2009, 2009 19th IEEE Symposium on Computer Arithmetic.

[11]  Paul D. Franzon,et al.  FreePDK: An Open-Source Variation-Aware Design Kit , 2007, 2007 IEEE International Conference on Microelectronic Systems Education (MSE'07).

[12]  Sudhakar M. Reddy,et al.  On the effectiveness of residue code checking for parallel two's complement multipliers , 1996, IEEE Trans. Very Large Scale Integr. Syst..

[13]  John W. Hartwell,et al.  A Procedure for Implementing the Fast Fourier Transform on Small Computers , 1971, IBM J. Res. Dev..

[14]  Alan V. Oppenheim,et al.  Discrete-time Signal Processing. Vol.2 , 2001 .

[15]  Karim Faez,et al.  A Fault Tolerant Method for Residue Arithmetic Circuits , 2009, 2009 International Conference on Information Management and Engineering.