For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability ε , decays as O(exp (-c 1nc2)) with the block-length n for positive constants c1 and c2 , as long as ε is less than the erasure threshold εth of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than 1-εth. © 2011 IEEE.

Andrew Edwin Thangaraj

Department of Electrical Engineering

Binary erasure channel

Density evolution

INFORMATION-THEORETIC SECURITY

LARGE GIRTH

LOW-DENSITY PARITY-CHECK CODES

SECRECY CAPACITY

STRONG SECRECY

WIRETAP CHANNEL

Coding errors

Error correction

Information theory

Probability

Channel coding

Fulltext

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IIT Madras

IEEE Transactions on Information Forensics and Security

The renewed interest for physical-layer security techniques has put forward a new role for error-control codes. In addition to ensuring reliability, carefully designed codes have been shown to provide a level of information-theoretic secrecy, by which the amount of information leaked to an adversary may be controlled. The ability to achieve information-theoretic secrecy relies on the study of alternative coding mechanisms, such as channel resolvability and privacy amplification, in which error-control codes are exploited as a means to shape the distribution of stochastic processes. This use of error-control codes, which goes much beyond that of correcting errors, creates numerous new design challenges. The objective of this paper is threefold. First, the paper aims at providing system engineers with explicit tools to build simple secrecy codes in order to stimulate interest and foster their integration in communication system prototypes. Second, it aims at providing coding and information theorists with a synthetic overview of the theoretical concepts and techniques for secrecy. Finally, it aims at highlighting the open challenges and opportunities faced for the integration of these codes in practical systems. © 2015 IEEE.

Proceedings of the IEEE

Error-Control Coding for Physical-Layer Secrecy

Wiretap channels form the most basic building block of physical-layer and information-theoretic security. Considerable research work has gone into the information-theoretic, cryptographic and coding aspects of wiretap channels in the last few years. The main goal of this tutorial article is to provide a self-contained presentation of two recent results - one is a new and simplified proof for secrecy capacity using channel resolvability, and the other is the connection between semantic security and information-theoretic strong secrecy. © 2014 IEEE.

2014 IEEE Information Theory Workshop, ITW 2014

Coding for wiretap channels: Channel resolvability and semantic security

Low Density Parity Check (LDPC) codes have capacity-approaching performance over several channels of interest. In practice, for good block-error rate performance, the girth of the Tanner graph of an LDPC code needs to be as high as possible. In theory, to show that block-error rate approaches zero for increasing block-lengths, the girth of the Tanner graph sequence needs to tend to infinity with block-length. To meet these requirements, we construct sequences of large-girth irregular LDPC codes for a given degree-distribution pair (DDP) by applying a general node splitting algorithm on large girth graphs. The obtained Tanner graph meets the required DDP up to a suitable approximation. By optimizing the node-splitting method and using suitable large-girth graphs, we show code constructions with smaller block length for the same girth, when compared to previous constructions. Similar gains in block length are observed in the construction of sequences of large-girth protograph LDPC codes. Simulations, over a binary erasure channel, confirm the gains in block-error rate obtained by the large girth construction. © 2014 IEEE.

2014 20th National Conference on Communications, NCC 2014

Node-splitting constructions for large girth irregular and protograph LDPC codes

For certain degree-distribution pairs with non-zero fraction of degree-two bit nodes, the bit-error threshold of the standard ensemble of Low Density Parity Check (LDPC) codes is known to be close to capacity. However, the degree-two bit nodes preclude the possibility of a block-error threshold. Interestingly, LDPC codes constructed using protographs allow the possibility of having both degree-two bit nodes and a block-error threshold. In this paper, we analyze density evolution for protograph LDPC codes over the binary erasure channel and show that their bit-error probability decreases double exponentially with the number of iterations when the erasure probability is below the bit-error threshold and long chain of degree-two variable nodes are avoided in the protograph. We present deterministic constructions of such protograph LDPC codes with girth logarithmic in blocklength, resulting in an exponential fall in bit-error probability below the threshold. We provide optimized protographs, whose block-error thresholds are better than that of the standard ensemble with minimum bit-node degree three. These protograph LDPC codes are theoretically of great interest, and have applications, for instance, in coding with strong secrecy over wiretap channels. © 2013 IEEE.

IEEE International Symposium on Information Theory - Proceedings

Deterministic constructions for large girth protograph LDPC codes

We show that duals of certain low-density paritycheck (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length n and girth ≥ 2k, for some k ≥ 2. We show that if the minimum left degree of the ensemble is lmin, the expected probability of block error is O(1/n[lmink/2]-k) when the erasure probability ε &lt; εef, where εef depends on the degree distribution of the ensemble. As long as lmin &gt; 2 and k &gt; 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1-εef. © 2010 IEEE.

2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

Strong secrecy for erasure wiretap channels

With the advent of quantum key distribution (QKD) systems, perfect (i.e., information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this correspondence, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check (LDPC) codes that achieve secrecy. © 2007 IEEE.

IEEE Transactions on Information Theory

Applications of LDPC codes to the wiretap channel

More sustainable constructions using limestone calcined clay cement (LC³)

Algorithmen - Eine Einführung

Bell System Technical Journal

Communication Theory of Secrecy Systems*

Strong secrecy on the binary erasure wiretap channel using large-girth LDPC codes

Journal	IEEE Transactions on Information Forensics and Security
ISSN	15566013
Open Access	Yes