36 research outputs found
Strong secrecy on a class of degraded broadcast channels using polar codes
Two polar coding schemes are proposed for the degraded
broadcast channel under different reliability and secrecy
requirements. In these settings, the transmitter wishes to send
multiple messages to a set of legitimate receivers keeping them
masked from a set of eavesdroppers, and individual channels are
assumed to gradually degrade in such a way that each legitimate
receiver has a better channel than any eavesdropper. The layered
decoding structure requires receivers with better channel quality
to reliably decode more messages, while the layered secrecy
structure requires eavesdroppers with worse channel quality to
be kept ignorant of more messages.Postprint (author's final draft
Polar Coding for the General Wiretap Channel
Information-theoretic work for wiretap channels is mostly based on random
coding schemes. Designing practical coding schemes to achieve
information-theoretic security is an important problem. By applying the two
recently developed techniques for polar codes, we propose a polar coding scheme
to achieve the secrecy capacity of the general wiretap channel.Comment: Submitted to IEEE ITW 201
Polarization of the Renyi Information Dimension with Applications to Compressed Sensing
In this paper, we show that the Hadamard matrix acts as an extractor over the
reals of the Renyi information dimension (RID), in an analogous way to how it
acts as an extractor of the discrete entropy over finite fields. More
precisely, we prove that the RID of an i.i.d. sequence of mixture random
variables polarizes to the extremal values of 0 and 1 (corresponding to
discrete and continuous distributions) when transformed by a Hadamard matrix.
Further, we prove that the polarization pattern of the RID admits a closed form
expression and follows exactly the Binary Erasure Channel (BEC) polarization
pattern in the discrete setting. We also extend the results from the single- to
the multi-terminal setting, obtaining a Slepian-Wolf counterpart of the RID
polarization. We discuss applications of the RID polarization to Compressed
Sensing of i.i.d. sources. In particular, we use the RID polarization to
construct a family of deterministic -valued sensing matrices for
Compressed Sensing. We run numerical simulations to compare the performance of
the resulting matrices with that of random Gaussian and random Hadamard
matrices. The results indicate that the proposed matrices afford competitive
performances while being explicitly constructed.Comment: 12 pages, 2 figure
Polar Coding for the Cognitive Interference Channel with Confidential Messages
In this paper, we propose a low-complexity, secrecy capacity achieving polar
coding scheme for the cognitive interference channel with confidential messages
(CICC) under the strong secrecy criterion. Existing polar coding schemes for
interference channels rely on the use of polar codes for the multiple access
channel, the code construction problem of which can be complicated. We show
that the whole secrecy capacity region of the CICC can be achieved by simple
point-to-point polar codes due to the cognitivity, and our proposed scheme
requires the minimum rate of randomness at the encoder
A New Coding Paradigm for the Primitive Relay Channel
We consider the primitive relay channel, where the source sends a message to
the relay and to the destination, and the relay helps the communication by
transmitting an additional message to the destination via a separate channel.
Two well-known coding techniques have been introduced for this setting:
decode-and-forward and compress-and-forward. In decode-and-forward, the relay
completely decodes the message and sends some information to the destination;
in compress-and-forward, the relay does not decode, and it sends a compressed
version of the received signal to the destination using Wyner-Ziv coding. In
this paper, we present a novel coding paradigm that provides an improved
achievable rate for the primitive relay channel. The idea is to combine
compress-and-forward and decode-and-forward via a chaining construction. We
transmit over pairs of blocks: in the first block, we use compress-and-forward;
and in the second block, we use decode-and-forward. More specifically, in the
first block, the relay does not decode, it compresses the received signal via
Wyner-Ziv, and it sends only part of the compression to the destination. In the
second block, the relay completely decodes the message, it sends some
information to the destination, and it also sends the remaining part of the
compression coming from the first block. By doing so, we are able to strictly
outperform both compress-and-forward and decode-and-forward. Note that the
proposed coding scheme can be implemented with polar codes. As such, it has the
typical attractive properties of polar coding schemes, namely, quasi-linear
encoding and decoding complexity, and error probability that decays at
super-polynomial speed. As a running example, we take into account the special
case of the erasure relay channel, and we provide a comparison between the
rates achievable by our proposed scheme and the existing upper and lower
bounds.Comment: 10 pages, 4 figures, in Proc. of ISIT'18 (short version) and in
Algorithms (full version
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