3,093 research outputs found
Successive Refinement with Decoder Cooperation and its Channel Coding Duals
We study cooperation in multi terminal source coding models involving
successive refinement. Specifically, we study the case of a single encoder and
two decoders, where the encoder provides a common description to both the
decoders and a private description to only one of the decoders. The decoders
cooperate via cribbing, i.e., the decoder with access only to the common
description is allowed to observe, in addition, a deterministic function of the
reconstruction symbols produced by the other. We characterize the fundamental
performance limits in the respective settings of non-causal, strictly-causal
and causal cribbing. We use a new coding scheme, referred to as Forward
Encoding and Block Markov Decoding, which is a variant of one recently used by
Cuff and Zhao for coordination via implicit communication. Finally, we use the
insight gained to introduce and solve some dual channel coding scenarios
involving Multiple Access Channels with cribbing.Comment: 55 pages, 15 figures, 8 tables, submitted to IEEE Transactions on
Information Theory. A shorter version submitted to ISIT 201
Information Nonanticipative Rate Distortion Function and Its Applications
This paper investigates applications of nonanticipative Rate Distortion
Function (RDF) in a) zero-delay Joint Source-Channel Coding (JSCC) design based
on average and excess distortion probability, b) in bounding the Optimal
Performance Theoretically Attainable (OPTA) by noncausal and causal codes, and
computing the Rate Loss (RL) of zero-delay and causal codes with respect to
noncausal codes. These applications are described using two running examples,
the Binary Symmetric Markov Source with parameter p, (BSMS(p)) and the
multidimensional partially observed Gaussian-Markov source. For the
multidimensional Gaussian-Markov source with square error distortion, the
solution of the nonanticipative RDF is derived, its operational meaning using
JSCC design via a noisy coding theorem is shown by providing the optimal
encoding-decoding scheme over a vector Gaussian channel, and the RL of causal
and zero-delay codes with respect to noncausal codes is computed.
For the BSMS(p) with Hamming distortion, the solution of the nonanticipative
RDF is derived, the RL of causal codes with respect to noncausal codes is
computed, and an uncoded noisy coding theorem based on excess distortion
probability is shown. The information nonanticipative RDF is shown to be
equivalent to the nonanticipatory epsilon-entropy, which corresponds to the
classical RDF with an additional causality or nonanticipative condition imposed
on the optimal reproduction conditional distribution.Comment: 34 pages, 12 figures, part of this paper was accepted for publication
in IEEE International Symposium on Information Theory (ISIT), 2014 and in
book Coordination Control of Distributed Systems of series Lecture Notes in
Control and Information Sciences, 201
Multiple Access Channels with Combined Cooperation and Partial Cribbing
In this paper we study the multiple access channel (MAC) with combined
cooperation and partial cribbing and characterize its capacity region.
Cooperation means that the two encoders send a message to one another via a
rate-limited link prior to transmission, while partial cribbing means that each
of the two encoders obtains a deterministic function of the other encoder's
output with or without delay. Prior work in this field dealt separately with
cooperation and partial cribbing. However, by combining these two methods we
can achieve significantly higher rates. Remarkably, the capacity region does
not require an additional auxiliary random variable (RV) since the purpose of
both cooperation and partial cribbing is to generate a common message between
the encoders. In the proof we combine methods of block Markov coding, backward
decoding, double rate-splitting, and joint typicality decoding. Furthermore, we
present the Gaussian MAC with combined one-sided cooperation and quantized
cribbing. For this model, we give an achievability scheme that shows how many
cooperation or quantization bits are required in order to achieve a Gaussian
MAC with full cooperation/cribbing capacity region. After establishing our main
results, we consider two cases where only one auxiliary RV is needed. The first
is a rate distortion dual setting for the MAC with a common message, a private
message and combined cooperation and cribbing. The second is a state-dependent
MAC with cooperation, where the state is known at a partially cribbing encoder
and at the decoder. However, there are cases where more than one auxiliary RV
is needed, e.g., when the cooperation and cribbing are not used for the same
purposes. We present a MAC with an action-dependent state, where the action is
based on the cooperation but not on the cribbing. Therefore, in this case more
than one auxiliary RV is needed
Control-theoretic Approach to Communication with Feedback: Fundamental Limits and Code Design
Feedback communication is studied from a control-theoretic perspective,
mapping the communication problem to a control problem in which the control
signal is received through the same noisy channel as in the communication
problem, and the (nonlinear and time-varying) dynamics of the system determine
a subclass of encoders available at the transmitter. The MMSE capacity is
defined to be the supremum exponential decay rate of the mean square decoding
error. This is upper bounded by the information-theoretic feedback capacity,
which is the supremum of the achievable rates. A sufficient condition is
provided under which the upper bound holds with equality. For the special class
of stationary Gaussian channels, a simple application of Bode's integral
formula shows that the feedback capacity, recently characterized by Kim, is
equal to the maximum instability that can be tolerated by the controller under
a given power constraint. Finally, the control mapping is generalized to the
N-sender AWGN multiple access channel. It is shown that Kramer's code for this
channel, which is known to be sum rate optimal in the class of generalized
linear feedback codes, can be obtained by solving a linear quadratic Gaussian
control problem.Comment: Submitted to IEEE Transactions on Automatic Contro
Channels with Cooperation Links that May Be Absent
It is well known that cooperation between users in a communication network
can lead to significant performance gains. A common assumption in past works is
that all the users are aware of the resources available for cooperation, and
know exactly to what extent these resources can be used. Unfortunately, in many
modern communication networks the availability of cooperation links cannot be
guaranteed a priori, due to the dynamic nature of the network. In this work a
family of models is suggested where the cooperation links may or may not be
present. Coding schemes are devised that exploit the cooperation links if they
are present, and can still operate (although at reduced rates) if cooperation
is not possible.Comment: Accepted for publication in the IEEE transaction on Information
Theory, June 201
Rate-Distortion Theory for Secrecy Systems
Secrecy in communication systems is measured herein by the distortion that an
adversary incurs. The transmitter and receiver share secret key, which they use
to encrypt communication and ensure distortion at an adversary. A model is
considered in which an adversary not only intercepts the communication from the
transmitter to the receiver, but also potentially has side information.
Specifically, the adversary may have causal or noncausal access to a signal
that is correlated with the source sequence or the receiver's reconstruction
sequence. The main contribution is the characterization of the optimal tradeoff
among communication rate, secret key rate, distortion at the adversary, and
distortion at the legitimate receiver. It is demonstrated that causal side
information at the adversary plays a pivotal role in this tradeoff. It is also
shown that measures of secrecy based on normalized equivocation are a special
case of the framework.Comment: Update version, to appear in IEEE Transactions on Information Theor
The benefit of a 1-bit jump-start, and the necessity of stochastic encoding, in jamming channels
We consider the problem of communicating a message in the presence of a
malicious jamming adversary (Calvin), who can erase an arbitrary set of up to
bits, out of transmitted bits . The capacity of such
a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or
not to erase bit depends on his observations was
recently characterized to be . In this work we show two (perhaps)
surprising phenomena. Firstly, we demonstrate via a novel code construction
that if Calvin is delayed by even a single bit, i.e. Calvin's decision of
whether or not to erase bit depends only on (and
is independent of the "current bit" ) then the capacity increases to
when the encoder is allowed to be stochastic. Secondly, we show via a novel
jamming strategy for Calvin that, in the single-bit-delay setting, if the
encoding is deterministic (i.e. the transmitted codeword is a deterministic
function of the message ) then no rate asymptotically larger than is
possible with vanishing probability of error, hence stochastic encoding (using
private randomness at the encoder) is essential to achieve the capacity of
against a one-bit-delayed Calvin.Comment: 21 pages, 4 figures, extended draft of submission to ISIT 201
Source-Channel Secrecy with Causal Disclosure
Imperfect secrecy in communication systems is investigated. Instead of using
equivocation as a measure of secrecy, the distortion that an eavesdropper
incurs in producing an estimate of the source sequence is examined. The
communication system consists of a source and a broadcast (wiretap) channel,
and lossless reproduction of the source sequence at the legitimate receiver is
required. A key aspect of this model is that the eavesdropper's actions are
allowed to depend on the past behavior of the system. Achievability results are
obtained by studying the performance of source and channel coding operations
separately, and then linking them together digitally. Although the problem
addressed here has been solved when the secrecy resource is shared secret key,
it is found that substituting secret key for a wiretap channel brings new
insights and challenges: the notion of weak secrecy provides just as much
distortion at the eavesdropper as strong secrecy, and revealing public messages
freely is detrimental.Comment: Allerton 2012, 6 pages. Updated version includes acknowledgement
Nested turbo codes for the costa problem
Driven by applications in data-hiding, MIMO broadcast channel coding, precoding for interference cancellation, and transmitter cooperation in wireless networks, Costa coding has lately become a very active research area. In this paper, we first offer code design guidelines in terms of source- channel coding for algebraic binning. We then address practical code design based on nested lattice codes and propose nested turbo codes using turbo-like trellis-coded quantization (TCQ) for source coding and turbo trellis-coded modulation (TTCM) for channel coding. Compared to TCQ, turbo-like TCQ offers structural similarity between the source and channel coding components, leading to more efficient nesting with TTCM and better source coding performance. Due to the difference in effective dimensionality between turbo-like TCQ and TTCM, there is a performance tradeoff between these two components when they are nested together, meaning that the performance of turbo-like TCQ worsens as the TTCM code becomes stronger and vice versa. Optimization of this performance tradeoff leads to our code design that outperforms existing TCQ/TCM and TCQ/TTCM constructions and exhibits a gap of 0.94, 1.42 and 2.65 dB to the Costa capacity at 2.0, 1.0, and 0.5 bits/sample, respectively
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