4 research outputs found
Quantifying Equivocation for Finite Blocklength Wiretap Codes
This paper presents a new technique for providing the analysis and comparison
of wiretap codes in the small blocklength regime over the binary erasure
wiretap channel. A major result is the development of Monte Carlo strategies
for quantifying a code's equivocation, which mirrors techniques used to analyze
normal error correcting codes. For this paper, we limit our analysis to
coset-based wiretap codes, and make several comparisons of different code
families at small and medium blocklengths. Our results indicate that there are
security advantages to using specific codes when using small to medium
blocklengths.Comment: Submitted to ICC 201
Secrecy Coding for the Binary Symmetric Wiretap Channel via Linear Programming
In this paper, we use a linear programming (LP) optimization approach to
evaluate the equivocation for a wiretap channel where the main channel is
noiseless, and the wiretap channel is a binary symmetric channel (BSC). Using
this technique, we present an analytical limit for the achievable secrecy rate
in the finite blocklength regime that is tighter than traditional fundamental
limits. We also propose a secrecy coding technique that outperforms random
binning codes. When there is one overhead bit, this coding technique is optimum
and achieves the analytical limit. For cases with additional bits of overhead,
our coding scheme can achieve equivocation rates close to the new limit.
Furthermore, we evaluate the patterns of the generator matrix and the
parity-check matrix for linear codes and we present binning techniques for both
linear and non-linear codes using two different approaches: recursive and
non-recursive. To our knowledge, this is the first optimization solution for
secrecy coding obtained through linear programming.Comment: Submitted for possible Journal publicatio
Subspace Decomposition of Coset Codes
A new method is explored for analyzing the performance of coset codes over
the binary erasure wiretap channel (BEWC) by decomposing the code over
subspaces of the code space. This technique leads to an improved algorithm for
calculating equivocation loss. It also provides a continuous-valued function
for equivocation loss, permitting proofs of local optimality for certain
finite-blocklength code constructions, including a code formed by excluding
from the generator matrix all columns which lie within a particular subspace.
Subspace decomposition is also used to explore the properties of an alternative
secrecy code metric, the chi squared divergence. The chi squared divergence is
shown to be far simpler to calculate than equivocation loss. Additionally, the
codes which are shown to be locally optimal in terms of equivocation are also
proved to be globally optimal in terms of chi squared divergence.Comment: 36 pages, 2 figures, submitted to Transactions on Information Theor