EG-LDPC Codes for the Erasure Wiretap Channel
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EG-LDPC Codes for the Erasure Wiretap Channel


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Abstract

The wiretap channel model, proposed by Wyner,
has been studied by various authors from the perspectives of
security, reliability and cryptographic protocols. A basic theme
of these discussions has been information theoretically secure
communication whose degree of secrecy can be theoretically
proved. This paper explains a practical implementation of Euclidean
Geometry (EG) - Low Density Parity Check (LDPC)
codes for wiretap channels of type I and II.

INTRODUCTION

The wiretap channel, introduced by Wyner [1] and later
generalized by Csiszar and Korner [2], provides a good model
for developing schemes for information-theoretic security. In
a wiretap channel, the legitimate users (Alice and Bob) are
separated by a channel called the main channel, while an
adversary (Eve) listens to all of Alice’s transmissions through
another channel called the wiretapper’s channel. Under certain
conditions on the main and wiretapper’s channels, Alice can
achieve both error-free communication to Bob (reliability
objective) and information-theoretic security against Eve (security
objective). The maximum rate (bits per channel use)
at which both objectives are attainable is called the secrecy
capacity of the wiretap channel.

EUCLIDEAN GEOMETRY CODES

Finite Geometry codes are based on the lines and points of
Euclidean or Projective Geometries defined over finite fields.
Such codes not only have good minimum distance properties,
but are also cyclic or quasi-cyclic in nature. This makes them
amenable to simple linear time encoding using shift registers.

CONCLUSION

EG-LDPC codes hold a lot of promise in providing
information-theoretic security in the erasure wiretap channel
model. The existence of a LDPC matrix for these codes
enables analysis and use in the wiretap-I mode. The cyclic
structure enables study of security properties in the wiretap-
II model. In both models, encoding and decoding are of low
complexity and involve only shift register operations.
As future work, the generalized Hamming weights of these
codes can be bounded better. The analysis in wiretap-I channel
model for finite blocklength will provide better insight into the
working of these codes.
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