Applications of LDPC Codes to the Wiretap Channel

@article{Thangaraj2007ApplicationsOL,
  title={Applications of LDPC Codes to the Wiretap Channel},
  author={Andrew Thangaraj and Souvik Dihidar and A. Robert Calderbank and Steven W. McLaughlin and Jean-Marc Merolla},
  journal={IEEE Transactions on Information Theory},
  year={2007},
  volume={53},
  pages={2933-2945}
}
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. [...] Key Method 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…Expand
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References

SHOWING 1-10 OF 41 REFERENCES
The wire-tap channel
  • A. Wyner
  • Computer Science
    The Bell System Technical Journal
  • 1975
TLDR
This paper finds the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission, and implies that there exists a Cs > 0, such that reliable transmission at rates up to Cs is possible in approximately perfect secrecy.
Theory of Error-correcting Codes
The field of channel coding started with Claude Shannon's 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon's channel
Unconditionally Secure Key Agreement and the Intrinsic Conditional Information
TLDR
A new conditional mutual information measure is defined, the intrinsic conditional Mutual information between S and Y when given Z, denoted by I(X;Y/spl darr/Z), which is an upper bound on S(X, Y/spl par/Z).
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.
On a special class of broadcast channels with confidential messages
It is shown that Csiszar and Korner's (1978) characterization of a discrete memoryless channel (DMC)X/spl rarr/Y as being less noisy than the DMC X/spl rarr/Z is equivalent to the condition that the
Wire-tap channel II
TLDR
The optimal trade-offs among the parameters K, N, and μ and the intruder's uncertainty H (H is the "conditional entropy" of the data given the μ intercepted channel bits) were found and a system exists with H ≈ K − l.
Generalized privacy amplification
TLDR
This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard, and Robert for a special scenario, and yields results on wiretap and broadcast channels for a considerably strengthened definition of secrecy capacity.
Efficient encoding of low-density parity-check codes
TLDR
It is shown how to exploit the sparseness of the parity-check matrix to obtain efficient encoders and it is shown that "optimized" codes actually admit linear time encoding.
Secret Key Agreement by Public Discussion from Common Information
The problem of generating a shared secret key S by two parties knowing dependent random variables X and I’, respectively, but not sharing a secret key initially, is considered. An enemy who knows the
Broadcast channels with confidential messages
TLDR
Given two discrete memoryless channels (DMC's) with a common input, a single-letter characterization is given of the achievable triples where R_{e} is the equivocation rate and the related source-channel matching problem is settled.
...
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