The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Definition of Triangle Cell and Effective Generating methodology of Generalized Reed-Holler Coefficients

삼각 셀의 정의와 효율적인 GRM 계수 생성 기법

  • 나기수 (인하대학교 전자공학과 회로및시스템 연구실) ;
  • 윤병희 (인하대학교 전자공학과 회로및시스템 연구) ;
  • 변기영 (가톨릭대학교 정보통신 전자공학부)
  • Published : 2004.06.01
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Abstract

In this paper, we propose the method to derive new GRM(Generalized Reed-Muller) coefficients for each 2$^n$ polarities using Triangle cell. As the existing methods to generate GRM coefficients, there are Green's method to operate transform matrix with a given RM coefficient and Besslich's method to get other polarities using basic transfer matrices repeatedly. In this paper, Triangle cell is defined so as to obtain GRM coefficients efficiently. After arranging 2$^n$ given RM coefficients of a first row of Triangle cell, sequence modulo sum is peformed in parallel to low column by a fixed numerical formula. To prove the efficiency of proposed arithmetic method, it is compared with Besslich’s method. As the compared result, to calculate GRM coefficients of all polarities to n input variables, Besslich’s method needs 2$^n$$^{-1}$ ${\times}$(2$^n$-1) two-input Ex-ORs and the proposed method needs 2${\times}$(the number of Ex-ORs for n-1 variables)+3$^n$$^{-1}$ for the same system complexity - (lo $g_2$$^n$) $T_{X}$./.

본 논문에서는 삼각 셀을 이용하여 2$^n$개의 서로 다른 극수를 갖는 새로운 GRM 계수의 생성 기법을 제안한다. 기존의 GRM 계수 생성방법으로는 주어진 RM제수를 변환행렬과 연산하는 Green 등의 방법과 기본 전달행렬들을 만복 적용하여 다른 극수들을 구하는 Besslich 등의 방법이 대표적이다. 본 논문에서 효율적인 GRM 계수의 생성을 위하여 삼각 셀을 정의하였고, 삼각 셀의 첫 행에 2n개의 주어진 RM계수를 나열한 후 고정된 수식에 의해 하위 열에 순차적 모듈로 합을 행하는 병렬형 방법이다. 제안한 연산 기법의 효율성을 예증하기 위해 기존의 기법들과 비교하였고, 비교결과 n개의 입력 변수에서 모든 극수의 GRM 계수들을 구하는데 같은 시스템 복잡도 (log 2$^n$) $T_{X}$에 대하여 Besslich 등의 기법은 2$^n$$^{-1}$／${\times}$(2$^n$-1)개의 2입력 Ex-OR가 필요한 반면에 본 논문에서 제안한 기법은 2${\times}$(n-1변수의 Ex-OR 개수) + 3$^n$$^{-1}$ 개의 2입력 Ex-OR만을 필요로 한다.다..

Keywords

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