Journal of Advanced Navigation Technology (한국항행학회논문지)

The Korean Navigation Institute (한국항행학회)
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Syntheses and realization of Quaternary Galois Field Sum-Of-Product(QGFSOP) expressed 1-variable functions Permutational Literals

치환리터럴에 의한 Quaternary Galois Field Sum-Of-Product(QGFSOP)형 1-변수 함수의 합성과 실현

  • Park, Dong-Young (Dept. of Information & Telecommunication Eng., Gangneung-Wonju National University) ;
  • Kim, Baek-Ki (Dept. of Information & Telecommunication Eng., Gangneung-Wonju National University) ;
  • Seong, Hyeun-Kyeong (School of Computer, Information and Communication, Sang-Ji University)
  • 박동영 (강릉원주대학교 정보통신공학과) ;
  • 김백기 (강릉원주대학교 정보통신공학과) ;
  • 성현경 (상지대학교 컴퓨터정보공학부)
  • Received : 2010.08.16
  • Accepted : 2010.10.30
  • Published : 2010.10.31
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Abstract

Even though there are 256 possible 1-qudit(1-variable quantum digit) functions in quaternary logic, the most useful functions are 4!=24 ones capable of representing in QGFSOP expressions by possible permuting of 0,1,2, and 3. In this paper, we propose a permutational literal(PL) representation and a QPL(Quaternary PL) gate which use the operands of a multiplicand A and an augend D in $Ax^C$+D(GF4) operation as a control variable of multi-cascaded PLs. And we also present new PL synthesis algorithms to synthesize QGFSOP expressed 24 (1-qudit) functions by applying three PL operators as ab(mutual permutation), + D(addition), and XA (multiplication). Finally architectures, circuits, and a CMOS implementation to realize proposed PL synthesis algorithms for $Ax^C$+D(GF4) functions are presented.

Quaternary 논리에서 생성 가능한 1-qudit(1-variable quantum digit) 함수는 총 256개가 존재하지만 이들 중에서 가장 유용한 것은 "0,1,2,3"의 치환에 의해 $Ax^C$+D(GF4)형의 QGFSOP 표현이 가능한 24개이다. 본 논문에서는 24개 1-qudit 함수들의 $Ax^C$+D(GF4) 연산에서 피연산자인 피승수 A와 피기수 D를 다단 종속된 치환리터럴의 제어인자로 사용하는 치환리터럴(Permutational Literals, PL) 표현과 QPL(Quaternary PL) gate를 제안하였다. 그리고 상호치환 'ab', 가산 '+D', 그리고 승산 'xA'과 같은 세 개의 PL 연산자를 사용하여 QGFSOP 표현된 24개 (1-qudit) 함수를 합성하기 위한 PL 합성법을 제안하였다. 끝으로 PL 합성법을 실현하기 위한 $Ax^C$+D(GF4) 구조와 연산회로 및 CMOS 실현 방법을 제시하였다.

Keywords

References

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