17 research outputs found
A Shannon Approach to Secure Multi-party Computations
In secure multi-party computations (SMC), parties wish to compute a function
on their private data without revealing more information about their data than
what the function reveals. In this paper, we investigate two Shannon-type
questions on this problem. We first consider the traditional one-shot model for
SMC which does not assume a probabilistic prior on the data. In this model,
private communication and randomness are the key enablers to secure computing,
and we investigate a notion of randomness cost and capacity. We then move to a
probabilistic model for the data, and propose a Shannon model for discrete
memoryless SMC. In this model, correlations among data are the key enablers for
secure computing, and we investigate a notion of dependency which permits the
secure computation of a function. While the models and questions are general,
this paper focuses on summation functions, and relies on polar code
constructions
Polynomial complexity of polar codes for non-binary alphabets, key agreement and Slepian-Wolf coding
We consider polar codes for memoryless sources with side information and show
that the blocklength, construction, encoding and decoding complexities are
bounded by a polynomial of the reciprocal of the gap between the compression
rate and the conditional entropy. This extends the recent results of Guruswami
and Xia to a slightly more general setting, which in turn can be applied to (1)
sources with non-binary alphabets, (2) key generation for discrete and Gaussian
sources, and (3) Slepian-Wolf coding and multiple accessing. In each of these
cases, the complexity scaling with respect to the number of users is also
controlled. In particular, we construct coding schemes for these multi-user
information theory problems which achieve optimal rates with an overall
polynomial complexity.Comment: 6 pages; presented at CISS 201
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
Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding
We consider the problem of polar coding for transmission over -user
multiple access channels. In the proposed scheme, all users encode their
messages using a polar encoder, while a multi-user successive cancellation
decoder is deployed at the receiver. The encoding is done separately across the
users and is independent of the target achievable rate. For the code
construction, the positions of information bits and frozen bits for each of the
users are decided jointly. This is done by treating the polar transformations
across all the users as a single polar transformation with a certain
\emph{polarization base}. We characterize the resolution of achievable rates on
the dominant face of the uniform rate region in terms of the number of users
and the length of the polarization base . In particular, we prove that
for any target rate on the dominant face, there exists an achievable rate, also
on the dominant face, within the distance at most
from the target rate. We then prove that the proposed MAC polar coding scheme
achieves the whole uniform rate region with fine enough resolution by changing
the decoding order in the multi-user successive cancellation decoder, as
and the code block length grow large. The encoding and decoding
complexities are and the asymptotic block error probability of
is guaranteed. Examples of achievable rates for
the -user multiple access channel are provided
Achieving the Capacity of any DMC using only Polar Codes
We construct a channel coding scheme to achieve the capacity of any discrete
memoryless channel based solely on the techniques of polar coding. In
particular, we show how source polarization and randomness extraction via
polarization can be employed to "shape" uniformly-distributed i.i.d. random
variables into approximate i.i.d. random variables distributed ac- cording to
the capacity-achieving distribution. We then combine this shaper with a variant
of polar channel coding, constructed by the duality with source coding, to
achieve the channel capacity. Our scheme inherits the low complexity encoder
and decoder of polar coding. It differs conceptually from Gallager's method for
achieving capacity, and we discuss the advantages and disadvantages of the two
schemes. An application to the AWGN channel is discussed.Comment: 9 pages, 7 figure