# Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes

@article{Subramanian2011StrongSO, title={Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes}, author={A Subramanian and Andrew Thangaraj and Matthieu R. Bloch and Steven W. McLaughlin}, journal={IEEE Transactions on Information Forensics and Security}, year={2011}, volume={6}, pages={585-594} }

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 <i>O</i>(exp(-(<i>c</i><sub>1</sub>)<i>n(c</i><sub>2</sub…

## 83 Citations

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- Mathematics, Computer Science2013 IEEE International Symposium on Information Theory
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This paper analyzes density evolution for protograph LDPC codes over the binary erasure channel and shows that their bit-error probability decreases double exponentially with the number of iterations when the erasure probability is below the bit- Error threshold, resulting in an exponential fall in bit- error probability below the threshold.

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An efficient and feasible authentication scheme based on low-density parity-check (LDPC) codes andinline-formula and lightweight hash functions over binary-input wiretap channel is proposed and theoretically proves that, the proposed schemes are perfect secure if the number of attacks from Eve is upper bounded by a polynomial times.

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This chapter analyzes the performance of practical codes over the Gaussian wiretap channel by using suitable metrics which take into account the codeword length and even the specific code structure, and focuses on low-density parity-check codes as they are among the most viable candidates for the use in this setting.

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- Mathematics, Computer Science2014 Twentieth National Conference on Communications (NCC)
- 2014

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Efficient encoding and decoding algorithms are proposed for multilevel binary low-density parity-check (LDPC) lattices constructed via Construction, which relaxes some of the nesting constraints on the parity- check matrices of the component codes, leading to a simpler and improved design.

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- Computer Science, MathematicsEURASIP J. Wirel. Commun. Netw.
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In this paper, we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models and analyze their secrecy performance…

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- Computer Science2021 55th Annual Conference on Information Sciences and Systems (CISS)
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The Gaussian wiretap channel (WTC), where two legitimate users communicate in the presence of a passive eavesdropper, is considered and the nested structure that exhibit and a coding scheme which achieves a level of information-theoretic security and reliability simultaneously is proposed.

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- Mathematics, Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
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## References

SHOWING 1-10 OF 47 REFERENCES

Strong secrecy for erasure wiretap channels

- Mathematics, Computer Science2010 IEEE Information Theory Workshop
- 2010

It is shown that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC) of erasure probability greater than 1–∊<inf>ef</inf>.

Stopping set distribution of LDPC code ensembles

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2005

Several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles are derived, including an expression for the normalized average stopping set distribution, yielding a critical fraction of the block length above which codes have exponentially many stopping sets of that size.

Exchange of Limits: Why Iterative Decoding Works

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2011

It is shown that as long as the message reliabilities are bounded and other technical conditions are met, the bit error probability vanishes up to a nontrivial threshold regardless of how the limit is taken.

Applications of LDPC Codes to the Wiretap Channel

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2007

This correspondence provides an alternative view of the proof for secrecy capacity of wire tap channels and shows how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel, and shows that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check codes that achieve secrecy.

Explicit construction of families of LDPC codes with no 4-cycles

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2004

It is proved that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/Sup 3/-2p/ Sup 2/+3p-2)/2, and it is shown that the minimum weight and the weight of the minimum stopping set of LU (3,q) are at least 2q and they are exactly 2q for many LU( 3,q).

Performance Analysis and Design of Two Edge-Type LDPC Codes for the BEC Wiretap Channel

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2013

A code construction method using two edge-type low-density parity-check (LDPC) codes based on the coset encoding scheme is proposed, and it is found that relatively simple constructions give very good secrecy performance.

Capacity-achieving sequences for the erasure channel

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 2002

It turns out that the right-regular sequence is c.a. in a much stronger sense than, e.g., the Tornado sequence, which explains why numerical optimization techniques tend to favor graphs with only one degree of check nodes.

Low-density parity-check codes

- Mathematics, Computer ScienceIRE Trans. Inf. Theory
- 1962

A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.

An analysis of the block error probability performance of iterative decoding

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2005

It is proved that there exist codes in Gallager's regular low-density parity-check codes, Tanner's generalized LDPC codes, and the turbo codes due to Berrou et al. for which the block length of the codes N and the number of iterations I go to infinity goes to zero.

A Combinatorial Family of Near Regular LDPC Codes

- Mathematics, Computer Science2007 IEEE International Symposium on Information Theory
- 2007

An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check (LDPC) codes achieving high girth is presented and it is demonstrated that these codes perform better than regular PEG codes and MacKay codes of similar length for all values of Signal to noise ratio.