An efficient approach to verifying galois-field arithmetic circuits of higher degrees and its application to ECC decoders

Rei Ueno, Kotaro Okamoto, Naofumi Hommam, Takafumi Aoki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

This paper presents an efficient approach to verifying higher-degree Galois-Field(GF) arithmetic circuits. The proposed method describes GF arithmetic circuits by graph-based representation, and verifies them by a combination of algebraic method with a new verification method based on natural deduction for the first-order predicate logic with equal sign. The natural deduction method can verify kind of higher-degree GF arithmetic circuits efficiently while the conventional methods requires enormous time to verify them or sometimes cannot verify them. In this paper, we apply the proposed method to the design and verifications of various Reed-Solomon (RS) code decoders. We confirm that the proposed method can verify RS code decoders with higher-degree functions while the conventional method fails. In particular, we show that the proposed method can be applied to practical decoders with 8-bit symbols.

Original languageEnglish
Title of host publicationProceedings - 2014 IEEE 44th International Symposium on Multiple-Valued Logic, ISMVL 2014
PublisherIEEE Computer Society
Pages144-149
Number of pages6
ISBN (Print)9781479935345
DOIs
Publication statusPublished - 2014
Event44th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2014 - Bremen, Germany
Duration: 2014 May 192014 May 21

Publication series

NameProceedings of The International Symposium on Multiple-Valued Logic
ISSN (Print)0195-623X

Other

Other44th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2014
CountryGermany
CityBremen
Period14/5/1914/5/21

Keywords

  • Galois field
  • Reed-Solomon code
  • arithmetic circuits
  • computer algebra
  • formal verification
  • predicate logic

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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