scholarly journals LDPC Codes Based on α – Resolvable BIB and Group Divisible Designs

2021 ◽  
Author(s):  
Shyam Saurabh
Keyword(s):  
Block Design ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Finite Geometries ◽  
Group Divisible Designs ◽  
Tanner Graph ◽  
Group Divisible ◽  
Check Matrix ◽  
Balanced Incomplete Block ◽  
Resolvable Group

<p>Structured LDPC codes have been constructed using balanced incomplete block (BIB) designs, resolvable BIB designs, mutually orthogonal Latin rectangles, partial geometries, group divisible designs, resolvable group divisible designs and finite geometries. Here we have constructed LDPC codes from <i>α </i>–<b> </b>resolvable BIB and Group divisible designs. The sub–matrices of incidence matrix of such block design are used as a parity – check matrix of the code which satisfy row – column constraint. Here the girth of the proposed code is at least six and the corresponding LDPC code (or Tanner graph) is free of 4– cycles. </p>

scholarly journals LDPC Codes Based on α – Resolvable BIB and Group Divisible Designs

2021 ◽  
Author(s):  
Shyam Saurabh
Keyword(s):  
Block Design ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Finite Geometries ◽  
Group Divisible Designs ◽  
Tanner Graph ◽  
Group Divisible ◽  
Check Matrix ◽  
Balanced Incomplete Block ◽  
Resolvable Group

<p>Structured LDPC codes have been constructed using balanced incomplete block (BIB) designs, resolvable BIB designs, mutually orthogonal Latin rectangles, partial geometries, group divisible designs, resolvable group divisible designs and finite geometries. Here we have constructed LDPC codes from <i>α </i>–<b> </b>resolvable BIB and Group divisible designs. The sub–matrices of incidence matrix of such block design are used as a parity – check matrix of the code which satisfy row – column constraint. Here the girth of the proposed code is at least six and the corresponding LDPC code (or Tanner graph) is free of 4– cycles. </p>

A New Method of Construction of E-optimal Generalized Group Divisible Designs (GGDD)

2008 ◽  
Vol 1 (1) ◽  
pp. 38-42
Author(s):  
Alex Thannippara ◽  
Sreejith V ◽  
S. C. Bagui ◽  
D. K. Ghosh
Keyword(s):  
Block Design ◽  
Group Testing ◽  
New Method ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Group Divisible Designs ◽  
Group Divisible ◽  
Incomplete Block Design ◽  
Generalized Group Divisible Design ◽  
Balanced Incomplete Block

In this article, we develop a new method of construction of E-optimal generalized group divisible designs through group testing designs. Keywords: Balanced Incomplete Block Design (BIBD); Group Divisible (GD); Generalized Group Divisible Design (GDD); E-optimality. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i1.1697

scholarly journals Investigation of random-structure regular LDPC codes construction based on progressive edge-growth and algorithms for removal of short cycles

2021 ◽  
Vol 4 (9(112)) ◽  
pp. 46-53
Author(s):  
Viktor Durcek ◽  
Michal Kuba ◽  
Milan Dado
Keyword(s):  
Hamming Distance ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Error Correcting Codes ◽  
Random Structure ◽  
Parity Check ◽  
Parity Check Matrix ◽  
Tanner Graph ◽  
Check Matrix ◽  
Computer Based

This paper investigates the construction of random-structure LDPC (low-density parity-check) codes using Progressive Edge-Growth (PEG) algorithm and two proposed algorithms for removing short cycles (CB1 and CB2 algorithm; CB stands for Cycle Break). Progressive Edge-Growth is an algorithm for computer-based design of random-structure LDPC codes, the role of which is to generate a Tanner graph (a bipartite graph, which represents a parity-check matrix of an error-correcting channel code) with as few short cycles as possible. Short cycles, especially the shortest ones with a length of 4 edges, in Tanner graphs of LDPC codes can degrade the performance of their decoding algorithm, because after certain number of decoding iterations, the information sent through its edges is no longer independent. The main contribution of this paper is the unique approach to the process of removing short cycles in the form of CB2 algorithm, which erases edges from the code's parity-check matrix without decreasing the minimum Hamming distance of the code. The two cycle-removing algorithms can be used to improve the error-correcting performance of PEG-generated (or any other) LDPC codes and achieved results are provided. All these algorithms were used to create a PEG LDPC code which rivals the best-known PEG-generated LDPC code with similar parameters provided by one of the founders of LDPC codes. The methods for generating the mentioned error-correcting codes are described along with simulations which compare the error-correcting performance of the original codes generated by the PEG algorithm, the PEG codes processed by either CB1 or CB2 algorithm and also external PEG code published by one of the founders of LDPC codes

Generalized Hadamard Matrices and Orthogonal Arrays of Strength Two

1964 ◽  
Vol 16 ◽  
pp. 736-740 ◽  
Author(s):  
S. S. Shrikhande
Keyword(s):  
Block Design ◽  
Orthogonal Arrays ◽  
Hadamard Matrices ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

The purpose of this note is to point out some connexions between generalized Hadamard matrices (4, 5) and various tactical configurations such as group divisible designs (3), affine resolvable balanced incomplete block designs (1), and orthogonal arrays of strength two (2). Some constructions for these arrays are also indicated.A balanced incomplete block design (BIBD) with parameters v, b, r, k, λ is an arrangement of v symbols called treatments into b subsets called blocks of k < v distinct treatments such that each treatment occurs in r blocks and any pair of treatments occurs in λ blocks.

scholarly journals GD PBIBD(2)s in incomplete split-plot × split-block type experiments

2006 ◽  
Vol 3 (1) ◽  
Author(s):  
Katarzyna Ambroży ◽  
Iwona Mejza
Keyword(s):  
Block Structure ◽  
Block Design ◽  
Block Type ◽  
Block Designs ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Split Plot ◽  
Randomization Scheme ◽  
Balanced Incomplete Block ◽  
Modeling Data

In this paper we present a method of designing a three-factor experiment with crossed and nested treatment structures. The design considered is called a split-plot × split-block design. A kind of design incomplete with respect to all three factors is examined. Additionally, we consider the usefulness of group divisible partially balanced incomplete block designs with two associate classes in planning such experiments. In modeling data obtained from them, we take into account the structure of experimental material and a four-step randomization scheme for the different kind of units. As regards the analysis of the obtained randomization model with seven strata, we adapt an approach typical of multistratum experiments with orthogonal block structure.

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