This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block co...This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.展开更多
The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs...The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi. The above paper is a copy of Dr. Rabindra Nath Das’s former article, entitled '“Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we solemnly withdrawn?the paper from the journal OJS. This paper published in OJS Vol.2 No.1, 39-47, 2012, has been retracted.展开更多
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical ind...The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).展开更多
This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will sho...This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will show that the above necessary conditions are also sufficient for k =3 with the definite exception( v,λ )=(10,1) and with several possible exceptions.展开更多
Some new construction methods of the optimum chemical balance weighing designs and pairwise efficiency and variance balanced designs are proposed, which are based on the incidence matrices of the known symmetric balan...Some new construction methods of the optimum chemical balance weighing designs and pairwise efficiency and variance balanced designs are proposed, which are based on the incidence matrices of the known symmetric balanced incomplete block designs. Also the conditions under which the constructed chemical balance weighing designs become A-optimal are also been given.展开更多
Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, ...Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.展开更多
The necessary conditions for the existence of weak designs are given in the form of two inequalities in this paper. The relations among weak block designs (WBDs) , Balanced incomplete block designs ( BIBDs) and differ...The necessary conditions for the existence of weak designs are given in the form of two inequalities in this paper. The relations among weak block designs (WBDs) , Balanced incomplete block designs ( BIBDs) and differential balanced block designs (DBBDs) are researched.展开更多
Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs ...Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.展开更多
General solution of normal equations in the general intra-block analysis of partially balanced incomplete block designs involving four associates is presented in this talk as they are quite useful in practice. Only in...General solution of normal equations in the general intra-block analysis of partially balanced incomplete block designs involving four associates is presented in this talk as they are quite useful in practice. Only intra-block estimates are given as the necessary formulae for inter-block estimates can be derived from them by changing the parameters as discussed in Rao[5]. We have obtained the general formulae for computation of four types of efficiencies, the average efficiency factor and the variance of the estimated elementary treatment contrast of the four types of comparisons irrespective of the type of association scheme a PBIB Design follows.展开更多
An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB ...An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.展开更多
基金the National Natural Science Foundation of China(No.60272009,No.60472045,and No.60496313).
文摘This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.
文摘The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi. The above paper is a copy of Dr. Rabindra Nath Das’s former article, entitled '“Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we solemnly withdrawn?the paper from the journal OJS. This paper published in OJS Vol.2 No.1, 39-47, 2012, has been retracted.
文摘The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).
基金National Natural Science Foundation ofChina(No.10 4710 93)
文摘This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will show that the above necessary conditions are also sufficient for k =3 with the definite exception( v,λ )=(10,1) and with several possible exceptions.
文摘Some new construction methods of the optimum chemical balance weighing designs and pairwise efficiency and variance balanced designs are proposed, which are based on the incidence matrices of the known symmetric balanced incomplete block designs. Also the conditions under which the constructed chemical balance weighing designs become A-optimal are also been given.
基金the National Natural Science Foundation of China (No. 10771193)the Starter Foundation for the Doctors of Zhejiang Gongshang University(No. 1020XJ030517)+1 种基金the Natural Science Foundationof Universities of Jiangsu Province (No. 07KJB110090)the Starter Foundation for the Doctors of Nantong University (No. 07B12)
文摘Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.
文摘The necessary conditions for the existence of weak designs are given in the form of two inequalities in this paper. The relations among weak block designs (WBDs) , Balanced incomplete block designs ( BIBDs) and differential balanced block designs (DBBDs) are researched.
文摘Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.
文摘General solution of normal equations in the general intra-block analysis of partially balanced incomplete block designs involving four associates is presented in this talk as they are quite useful in practice. Only intra-block estimates are given as the necessary formulae for inter-block estimates can be derived from them by changing the parameters as discussed in Rao[5]. We have obtained the general formulae for computation of four types of efficiencies, the average efficiency factor and the variance of the estimated elementary treatment contrast of the four types of comparisons irrespective of the type of association scheme a PBIB Design follows.
文摘An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.
