Date post: | 11-Jun-2015 |
Category: |
Technology |
Upload: | nestor-barraza |
View: | 373 times |
Download: | 5 times |
A new Algorithm to construct LDPC codes with large stopping sets
A new Algorithm to construct LDPC codes withlarge stopping sets
Juan Camilo Salazar Ripoll† and Nestor R. Barraza‡
Septiembre - 2013
†Universidad de los Andes.‡Universidad Nacional de Tres de Febrero y Facultad de Ingenierıa, UBA
A new Algorithm to construct LDPC codes with large stopping sets
Indice
1 IntroductionLDPC codesBipartite Tanner graph - Stopping setVertex Edge Incidence MatrixProperties of Graphs - Girth
2 The AlgorithmThe aimThe methodGetting the LDPC code
3 Simulation
4 Conclusions
A new Algorithm to construct LDPC codes with large stopping sets
Indice
1 IntroductionLDPC codesBipartite Tanner graph - Stopping setVertex Edge Incidence MatrixProperties of Graphs - Girth
2 The AlgorithmThe aimThe methodGetting the LDPC code
3 Simulation
4 Conclusions
A new Algorithm to construct LDPC codes with large stopping sets
Indice
1 IntroductionLDPC codesBipartite Tanner graph - Stopping setVertex Edge Incidence MatrixProperties of Graphs - Girth
2 The AlgorithmThe aimThe methodGetting the LDPC code
3 Simulation
4 Conclusions
A new Algorithm to construct LDPC codes with large stopping sets
Indice
1 IntroductionLDPC codesBipartite Tanner graph - Stopping setVertex Edge Incidence MatrixProperties of Graphs - Girth
2 The AlgorithmThe aimThe methodGetting the LDPC code
3 Simulation
4 Conclusions
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
LDPC codes
H =
1 0 1 0 1 0 00 1 0 1 0 1 00 0 0 1 0 1 11 0 1 0 0 1 00 1 0 0 1 0 1
x1 + x3 + x5 = 0
x2 + x4 + x6 = 0
x4 + x6 + x7 = 0
x1 + x3 + x6 = 0
x2 + x5 + x7 = 0 (1)
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
x1 + x3 + x5 = 0
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
x1 + x3 + x5 = 0
x2 + x4 + x6 = 0
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
x1 + x3 + x5 = 0
x2 + x4 + x6 = 0
x4 + x6 + x7 = 0
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
x1 + x3 + x5 = 0
x2 + x4 + x6 = 0
x4 + x6 + x7 = 0
x1 + x3 + x6 = 0
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
x1 + x3 + x5 = 0
x2 + x4 + x6 = 0
x4 + x6 + x7 = 0
x1 + x3 + x6 = 0
x2 + x5 + x7 = 0
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
Stopping Set
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
Stopping Set
Message Passing
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Bipartite Tanner graph - Stopping set
1
2
3
4
5
6
7
8
9
10
11
12
Stopping Set
Message Passing
Variable nodes
Check nodes
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Vertex Edge Incidence Matrix
1 2 4
3
6
5a c
b
e
d
VE =
a b c d e
1 1 0 0 0 02 1 1 1 0 03 0 1 0 0 04 0 0 1 1 15 0 0 0 1 06 0 0 0 0 1
H?= VE (T )
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Vertex Edge Incidence Matrix
1 2 4
3
6
5a c
b
e
d
VE =
a b c d e
1 1 0 0 0 02 1 1 1 0 03 0 1 0 0 04 0 0 1 1 15 0 0 0 1 06 0 0 0 0 1
H
?= VE (T )
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Properties of Graphs - Girth
36
2
4
15
9
7
10
8
Petersen Graph. Girth = 5
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Properties of Graphs - Girth
36
2
4
15
9
7
10
8
Petersen Graph. Girth = 5
VE =
a b c d e e f g h i j k l m n o
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 02 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 03 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 04 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 05 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 06 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 07 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 08 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 09 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1
10 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Properties of Graphs - Girth
36
2
4
15
9
7
10
8
Petersen Graph. Girth = 5
Tanner Graph. H = VET .
a b c d e f g h i j k l m n o
1 2 3 4 5 6 7 8 9 10
A new Algorithm to construct LDPC codes with large stopping sets
Introduction
Properties of Graphs - Girth
36
2
4
15
9
7
10
8
Petersen Graph. Girth = 5
Tanner Graph. H = VET . Cycles in graph → Stopping sets.
a b c d e f g h i j k l m n o
1 2 3 4 5 6 7 8 9 10
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The aim
Construct a big graph with a big girth
Generate the LDPC code from the transpose of the vertex-edgeincidence matrix
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
The aim is to get a graph which determines the minimumstopping set of the obtained code.
The parity check matrix of the code is obtained as thetranspose of the vertex-edge incidence matrix of the graph.
This method allows to construct LDPC codes up to astopping set size of 12, and with a slight variation the girthcan be increased to 14.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
The aim is to get a graph which determines the minimumstopping set of the obtained code.
The parity check matrix of the code is obtained as thetranspose of the vertex-edge incidence matrix of the graph.
This method allows to construct LDPC codes up to astopping set size of 12, and with a slight variation the girthcan be increased to 14.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
The aim is to get a graph which determines the minimumstopping set of the obtained code.
The parity check matrix of the code is obtained as thetranspose of the vertex-edge incidence matrix of the graph.
This method allows to construct LDPC codes up to astopping set size of 12, and with a slight variation the girthcan be increased to 14.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.
Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.
Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
Take a core C which is a simple graph, its girth determinesthe stopping set size of the LDPC code.
Make 2|C |+ 1 copies of the core obtaining 2|C |+ 2 subgraphs.
Divide the subgraphs into two sets: a left set and a right set,each one of |C |+ 1 subgraphs. Lets name the subgraphs inthe left set 0, 1, · · · , |C | and the subgraphs in the right set0′, 1′, · · · , |C |′.Connecting the nodes
Take the node i from the graph j and connect it to the node jof the graph i ′ for i 6= j with 1 ≤ i , j ≤ |C |.Connect the node i from the graph i to the node i of thegraph 0′, in a similar way connect the node i from the graph i ′
to the node i of the graph 0.
A graph with 2|C |(|C |+ 1) nodes and girth(graph) =mın(girth(core),12) is obtained. The degree of each node isincreased by one.
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
k
i
j
i
k’k i
j
j
ki
j
j’
k
ji’
i
jk
The shortest cycle not involving0 and 0’ subgraphs
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
k
i
j
i
k’k i
j
j
ki
j
j’
k
ji’
i
jk
The shortest cycle not involving0 and 0’ subgraphs
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs afterpermutation in nodes in 0 and 0’
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs afterpermutation in nodes in 0 and 0’
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs afterpermutation in nodes in 0 and 0’
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
The method
j
i
j’
j
i
iji
0’
ij0
i
j
j
i
j
i’The shortest cycle involving 0and 0’ subgraphs afterpermutation in nodes in 0 and 0’
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
Getting the LDPC code
The parity check matrix H is obtained as the transpose of thevertex-edge incidence matrix of the graph.
The nodes of the graph are the check nodes of the code andthe edges of the graph are the variable nodes.
Cycles of length k give cycles of length 2k in the Tannergraph. Then, the size of the stopping set in the LDPC codewill not be less than the girth of the graph.
If a regular graph is chosen as the core, being dv the degree ofeach node, the number of nodes in the generated graph is(|C |) (2 |C |+ 2) and the number of edges is(dv + 1)(|C |)(|C |+ 1).
As a consequence, we get an LDPC code withn = (dv + 1)(|C |)(|C |+ 1) and rate R = dv−1
dv+1 .
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
Getting the LDPC code
The parity check matrix H is obtained as the transpose of thevertex-edge incidence matrix of the graph.
The nodes of the graph are the check nodes of the code andthe edges of the graph are the variable nodes.
Cycles of length k give cycles of length 2k in the Tannergraph. Then, the size of the stopping set in the LDPC codewill not be less than the girth of the graph.
If a regular graph is chosen as the core, being dv the degree ofeach node, the number of nodes in the generated graph is(|C |) (2 |C |+ 2) and the number of edges is(dv + 1)(|C |)(|C |+ 1).
As a consequence, we get an LDPC code withn = (dv + 1)(|C |)(|C |+ 1) and rate R = dv−1
dv+1 .
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
Getting the LDPC code
The parity check matrix H is obtained as the transpose of thevertex-edge incidence matrix of the graph.
The nodes of the graph are the check nodes of the code andthe edges of the graph are the variable nodes.
Cycles of length k give cycles of length 2k in the Tannergraph. Then, the size of the stopping set in the LDPC codewill not be less than the girth of the graph.
If a regular graph is chosen as the core, being dv the degree ofeach node, the number of nodes in the generated graph is(|C |) (2 |C |+ 2) and the number of edges is(dv + 1)(|C |)(|C |+ 1).
As a consequence, we get an LDPC code withn = (dv + 1)(|C |)(|C |+ 1) and rate R = dv−1
dv+1 .
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
Getting the LDPC code
The parity check matrix H is obtained as the transpose of thevertex-edge incidence matrix of the graph.
The nodes of the graph are the check nodes of the code andthe edges of the graph are the variable nodes.
Cycles of length k give cycles of length 2k in the Tannergraph. Then, the size of the stopping set in the LDPC codewill not be less than the girth of the graph.
If a regular graph is chosen as the core, being dv the degree ofeach node, the number of nodes in the generated graph is(|C |) (2 |C |+ 2) and the number of edges is(dv + 1)(|C |)(|C |+ 1).
As a consequence, we get an LDPC code withn = (dv + 1)(|C |)(|C |+ 1) and rate R = dv−1
dv+1 .
A new Algorithm to construct LDPC codes with large stopping sets
The Algorithm
Getting the LDPC code
The parity check matrix H is obtained as the transpose of thevertex-edge incidence matrix of the graph.
The nodes of the graph are the check nodes of the code andthe edges of the graph are the variable nodes.
Cycles of length k give cycles of length 2k in the Tannergraph. Then, the size of the stopping set in the LDPC codewill not be less than the girth of the graph.
If a regular graph is chosen as the core, being dv the degree ofeach node, the number of nodes in the generated graph is(|C |) (2 |C |+ 2) and the number of edges is(dv + 1)(|C |)(|C |+ 1).
As a consequence, we get an LDPC code withn = (dv + 1)(|C |)(|C |+ 1) and rate R = dv−1
dv+1 .
A new Algorithm to construct LDPC codes with large stopping sets
Simulation
22
21
20
19
181716
15
14
13
12
11
10
9
8
76 5
4
3
2
1
Regular core |C | = 22, dv = 2
0 0
*
1 1
1− ε
ε
ε
1− ε
Binary erasure channel (BEC).
A new Algorithm to construct LDPC codes with large stopping sets
Simulation
Core Generated graph LDPC codeRegular Regular Regular, variable node
degree = 2
|C | = 22 |C |(2|C |+ 2) = 1012 no-des
1012 check nodes
dv = 2 node degree = dv +1 = 3 check nodes degree = 3dv+1
2 |C |(2|C | + 2) =1518 edges
1518 variable nodes
girth = 22 girth = 14 stopping set size = 14
R = dv−1dv+1 = 1
3
A new Algorithm to construct LDPC codes with large stopping sets
Simulation
0,10,20,30,40,50,6
10−5
10−4
10−3
10−2
10−1
100
ε
BE
R
Performance of the regular LDPC code in a BEC (R = 1/3, n =1518, girth = 28) with error probability ε.
A new Algorithm to construct LDPC codes with large stopping sets
Simulation
0,10,20,30,40,50,6
10−5
10−4
10−3
10−2
10−1
100
ε
BE
R
Performance of the regular LDPC code in a BEC (R = 1/3, n =1518, girth = 28) with error probability ε.
A new Algorithm to construct LDPC codes with large stopping sets
Conclusions
A new algorithm to construct an LDPC code from agenerated graph was presented
This graph is generated by making some connections betweenseveral copies of a given core
Since the stopping set of the LDPC code is related to thegirth of the graph, a large stopping set size is obtained
The parity check matrix is quite sparse, then, the generatedLDPC code converges in just a few iterations
It is possible to generate bigger codes using the obtainedgraph as the core. We are working now on this issue and itwill be shown in a future work
A new Algorithm to construct LDPC codes with large stopping sets
Conclusions
A new algorithm to construct an LDPC code from agenerated graph was presented
This graph is generated by making some connections betweenseveral copies of a given core
Since the stopping set of the LDPC code is related to thegirth of the graph, a large stopping set size is obtained
The parity check matrix is quite sparse, then, the generatedLDPC code converges in just a few iterations
It is possible to generate bigger codes using the obtainedgraph as the core. We are working now on this issue and itwill be shown in a future work
A new Algorithm to construct LDPC codes with large stopping sets
Conclusions
A new algorithm to construct an LDPC code from agenerated graph was presented
This graph is generated by making some connections betweenseveral copies of a given core
Since the stopping set of the LDPC code is related to thegirth of the graph, a large stopping set size is obtained
The parity check matrix is quite sparse, then, the generatedLDPC code converges in just a few iterations
It is possible to generate bigger codes using the obtainedgraph as the core. We are working now on this issue and itwill be shown in a future work
A new Algorithm to construct LDPC codes with large stopping sets
Conclusions
A new algorithm to construct an LDPC code from agenerated graph was presented
This graph is generated by making some connections betweenseveral copies of a given core
Since the stopping set of the LDPC code is related to thegirth of the graph, a large stopping set size is obtained
The parity check matrix is quite sparse, then, the generatedLDPC code converges in just a few iterations
It is possible to generate bigger codes using the obtainedgraph as the core. We are working now on this issue and itwill be shown in a future work
A new Algorithm to construct LDPC codes with large stopping sets
Conclusions
A new algorithm to construct an LDPC code from agenerated graph was presented
This graph is generated by making some connections betweenseveral copies of a given core
Since the stopping set of the LDPC code is related to thegirth of the graph, a large stopping set size is obtained
The parity check matrix is quite sparse, then, the generatedLDPC code converges in just a few iterations
It is possible to generate bigger codes using the obtainedgraph as the core. We are working now on this issue and itwill be shown in a future work