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<title><string language="fre"><![CDATA[2.7. Reducing the Key Size - LDPC codes]]></string></title>
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<string language="fre"><![CDATA[LDPC codes have an
interesting feature: they are free of algebraic structure. We will study in detail
this proposal for the McEliece cryptosystem in this
session. LDPC codes were originally introduced by Gallager, in
his doctoral thesis, in 1963. One of the characteristic of
LDPC codes is the existence of several iterative
decoding algorithms which achieve excellent performances.
Tanner, later, in the 1981, introduced a graphical
representation to these codes as bipartite graph. However, they remained
almost forgotten by the coding theory community until
1996 when MacKay and Neal re-discovered these codes,
promoting them to the select group of good linear codes for
telecommunication applications. LDPC codes admit two
different representations: on one hand, we have the
matrix representation. LDPC codes admit a sparse
parity-check matrix, that is, it contains few non-zero entries in
comparison to the amount of zeros. And we have also a
graphical representation. LDPC codes could be
represented with a graph which is also known as the Tanner
graph. First of all, recall the definition of a bipartite
graph which is a graph that we can partition the set of
vertices into two nonempty disjoint sets such that no two
vertices within the same set are adjacent. Now, let H be a sparse matrix. We will denote the
set of variable nodes
to the column of the
parity-check matrix and the check nodes to the rows of
the parity-check matrix. And we define an edge between
the j check nodes and the i variable nodes if the
entry (i,j) at the matrix H is non-zero. For
example, if we have a binary LDPC codes with this parity-check
matrix then we can associate the following Tanner graph. The first parity-check
equation gives us this relation. The second parity-check
equation gives us this other relation and the third one
gives us the complete graph. We explain here an iterative
decoding algorithm for LDPC codes which is called the
Bit-Flipping algorithm, which was already introduced by Gallager.]]></string></description>
<keyword><string language="fre"><![CDATA[algèbre linéaire]]></string></keyword><keyword><string language="fre"><![CDATA[chiffrement à clé publique]]></string></keyword><keyword><string language="fre"><![CDATA[cryptage des données]]></string></keyword><keyword><string language="fre"><![CDATA[cryptographie]]></string></keyword><keyword><string language="fre"><![CDATA[McEliece]]></string></keyword><keyword><string language="fre"><![CDATA[LDPC]]></string></keyword><keyword><string language="fre"><![CDATA[MDPC]]></string></keyword>
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<date><dateTime>2015-05-05</dateTime></date>
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