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… 
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References

SHOWING 1-10 OF 47 REFERENCES
Strong secrecy for erasure wiretap channels
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
  • R. Gallager
  • Mathematics, Computer Science
    IRE Trans. Inf. Theory
  • 1962
TLDR
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
TLDR
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
TLDR
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.
...
1
2
3
4
5
...