17 research outputs found
Empirical and Strong Coordination via Soft Covering with Polar Codes
We design polar codes for empirical coordination and strong coordination in
two-node networks. Our constructions hinge on the fact that polar codes enable
explicit low-complexity schemes for soft covering. We leverage this property to
propose explicit and low-complexity coding schemes that achieve the capacity
regions of both empirical coordination and strong coordination for sequences of
actions taking value in an alphabet of prime cardinality. Our results improve
previously known polar coding schemes, which (i) were restricted to uniform
distributions and to actions obtained via binary symmetric channels for strong
coordination, (ii) required a non-negligible amount of common randomness for
empirical coordination, and (iii) assumed that the simulation of discrete
memoryless channels could be perfectly implemented. As a by-product of our
results, we obtain a polar coding scheme that achieves channel resolvability
for an arbitrary discrete memoryless channel whose input alphabet has prime
cardinality.Comment: 14 pages, two-column, 5 figures, accepted to IEEE Transactions on
Information Theor
Polar Coding for Secret-Key Generation
Practical implementations of secret-key generation are often based on
sequential strategies, which handle reliability and secrecy in two successive
steps, called reconciliation and privacy amplification. In this paper, we
propose an alternative approach based on polar codes that jointly deals with
reliability and secrecy. Specifically, we propose secret-key capacity-achieving
polar coding schemes for the following models: (i) the degraded binary
memoryless source (DBMS) model with rate-unlimited public communication, (ii)
the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m
broadcast model and (iv) the Markov tree model with uniform marginals. For
models (i) and (ii) our coding schemes remain valid for non-degraded sources,
although they may not achieve the secret-key capacity. For models (i), (ii) and
(iii), our schemes rely on pre-shared secret seed of negligible rate; however,
we provide special cases of these models for which no seed is required.
Finally, we show an application of our results to secrecy and privacy for
biometric systems. We thus provide the first examples of low-complexity
secret-key capacity-achieving schemes that are able to handle vector
quantization for model (ii), or multiterminal communication for models (iii)
and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information
Theory; parts of the results were presented at the 2013 IEEE Information
Theory Worksho
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
Private Information Retrieval with Private Noisy Side Information
Consider Private Information Retrieval (PIR), where a client wants to
retrieve one file out of files that are replicated in different servers
and the client selection must remain private when up to servers may
collude. Additionally, suppose that the client has noisy side information about
each of the files, and the side information about a specific file is
obtained by passing this file through one of possible discrete memoryless
test channels, where . While the statistics of the test channels are
known by the client and by all the servers, the specific mapping
between the files and the test channels is unknown
to the servers. We study this problem under two different privacy metrics.
Under the first privacy metric, the client wants to preserve the privacy of its
desired file selection and the mapping . Under the
second privacy metric, the client wants to preserve the privacy of its desired
file and the mapping , but is willing to reveal the
index of the test channel that is associated to its desired file. For both of
these two privacy metrics, we derive the optimal normalized download cost. Our
problem setup generalizes PIR with colluding servers, PIR with private
noiseless side information, and PIR with private side information under storage
constraints
Explicit Wiretap Channel Codes via Source Coding, Universal Hashing, and Distribution Approximation, When the Channels' Statistics are Uncertain
We consider wiretap channels with uncertainty on the eavesdropper channel
under (i) noisy blockwise type II, (ii) compound, or (iii) arbitrarily varying
models. We present explicit wiretap codes that can handle these models in a
unified manner and only rely on three primitives, namely source coding with
side information, universal hashing, and distribution approximation. Our
explicit wiretap codes achieve the best known single-letter achievable rates,
previously obtained non-constructively, for the models considered. Our results
are obtained for strong secrecy, do not require a pre-shared secret between the
legitimate users, and do not require any symmetry properties on the channel. An
extension of our results to compound main channels is also derived via new
capacity-achieving polar coding schemes for compound settings.Comment: 16 pages, two-column, 3 figures, accepted to IEEE Transactions on
Information Forensics and Securit