103 research outputs found
Exact Random Coding Secrecy Exponents for the Wiretap Channel
We analyze the exact exponential decay rate of the expected amount of
information leaked to the wiretapper in Wyner's wiretap channel setting using
wiretap channel codes constructed from both i.i.d. and constant-composition
random codes. Our analysis for those sampled from i.i.d. random coding ensemble
shows that the previously-known achievable secrecy exponent using this ensemble
is indeed the exact exponent for an average code in the ensemble. Furthermore,
our analysis on wiretap channel codes constructed from the ensemble of
constant-composition random codes leads to an exponent which, in addition to
being the exact exponent for an average code, is larger than the achievable
secrecy exponent that has been established so far in the literature for this
ensemble (which in turn was known to be smaller than that achievable by wiretap
channel codes sampled from i.i.d. random coding ensemble). We show examples
where the exact secrecy exponent for the wiretap channel codes constructed from
random constant-composition codes is larger than that of those constructed from
i.i.d. random codes and examples where the exact secrecy exponent for the
wiretap channel codes constructed from i.i.d. random codes is larger than that
of those constructed from constant-composition random codes. We, hence,
conclude that, unlike the error correction problem, there is no general
ordering between the two random coding ensembles in terms of their secrecy
exponent.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
Coding Schemes for Achieving Strong Secrecy at Negligible Cost
We study the problem of achieving strong secrecy over wiretap channels at
negligible cost, in the sense of maintaining the overall communication rate of
the same channel without secrecy constraints. Specifically, we propose and
analyze two source-channel coding architectures, in which secrecy is achieved
by multiplexing public and confidential messages. In both cases, our main
contribution is to show that secrecy can be achieved without compromising
communication rate and by requiring only randomness of asymptotically vanishing
rate. Our first source-channel coding architecture relies on a modified wiretap
channel code, in which randomization is performed using the output of a source
code. In contrast, our second architecture relies on a standard wiretap code
combined with a modified source code termed uniform compression code, in which
a small shared secret seed is used to enhance the uniformity of the source code
output. We carry out a detailed analysis of uniform compression codes and
characterize the optimal size of the shared seed.Comment: 15 pages, two-column, 5 figures, accepted to IEEE Transactions on
Information Theor
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