[Show abstract][Hide abstract] ABSTRACT: In this paper, we consider communication on a two-hop channel, in which a
source wants to send information reliably and securely to the destination via a
relay. We consider both the untrusted relay case and the external eavesdropper
case. In the untrusted relay case, the relay behaves as an eavesdropper and
there is a cooperative node which sends a jamming signal to confuse the relay
when the it is receiving from the source. We propose two secure transmission
schemes using the scaled compute-and-forward technique. One of the schemes is
based on a random binning code and the other one is based on a lattice chain
code. It is proved that in either the high Signal-to-Noise-Ratio (SNR) scenario
and/or the restricted relay power scenario, if the destination is used as the
jammer, both schemes outperform all existing schemes and achieve the upper
bound. In particular, if the SNR is large and the source, the relay, and the
cooperative jammer have identical power and channels, both schemes achieve the
upper bound for secrecy rate, which is merely $1/2$ bit per channel use lower
than the channel capacity without secrecy constraints. We also prove that one
of our schemes achieves a positive secrecy rate in the external eavesdropper
case in which the relay is trusted and there exists an external eavesdropper.
[Show abstract][Hide abstract] ABSTRACT: Under the paradigm of caching, partial data is delivered before the actual
requests of the users are known. In this paper, this problem is modeled as a
canonical distributed source coding problem with side information, where the
side information represents the users' requests. For the single-user case, a
single-letter characterization of the optimal rate region is established, and
for several important special cases, closed-form solutions are given, including
the scenario of uniformly distributed user requests. In this case, it is shown
that the optimal caching strategy is closely related to total correlation and
Wyner's common information. For the two-user case, five representative
subproblems are considered, which draw connections to existing source coding
problems in the literature: the Gray--Wyner system, distributed successive
refinement, and the Kaspi/Heegard--Berger problem.
[Show abstract][Hide abstract] ABSTRACT: In this paper we study the data exchange problem where a set of users is
interested in gaining access to a common file, but where each has only partial
knowledge about it as side-information. Assuming that the file is broken into
packets, the side-information considered is in the form of linear combinations
of the file packets. Given that the collective information of all the users is
sufficient to allow recovery of the entire file, the goal is for each user to
gain access to the file while minimizing some communication cost. We assume
that users can communicate over a noiseless broadcast channel, and that the
communication cost is a sum of each user's cost function over the number of
bits it transmits. For instance, the communication cost could simply be the
total number of bits that needs to be transmitted. In the most general case
studied in this paper, each user can have any arbitrary convex cost function.
We provide deterministic, polynomial-time algorithms (in the number of users
and packets) which find an optimal communication scheme that minimizes the
communication cost. To further lower the complexity, we also propose a simple
randomized algorithm inspired by our deterministic algorithm which is based on
a random linear network coding scheme.
[Show abstract][Hide abstract] ABSTRACT: Compute-and-Forward is an emerging technique to deal with interference. It
allows the receiver to decode a suitably chosen integer linear combination of
the transmitted messages. The integer coefficients should be adapted to the
channel fading state. Optimizing these coefficients is a Shortest Lattice
Vector (SLV) problem. In general, the SLV problem is known to be prohibitively
complex. In this paper, we show that the particular SLV instance resulting from
the Compute-and-Forward problem can be solved in low polynomial complexity and
give an explicit deterministic algorithm that is guaranteed to find the optimal
solution.
[Show abstract][Hide abstract] ABSTRACT: Lattice codes used under the Compute-and-Forward paradigm suggest an
alternative strategy for the standard Gaussian multiple-access channel (MAC):
The receiver successively decodes integer linear combinations of the messages
until it can invert and recover all messages. In this paper, this strategy is
developed and analyzed. For the two-user MAC, it is shown that without
time-sharing, the entire capacity region can be attained with a single-user
decoder as soon as the signal-to-noise ratios are above $1+\sqrt{2}$. A partial
analysis is given for more than two users. Lastly the strategy is extended to
the so-called dirty MAC where two interfering signals are known non-causally to
the two transmitters in a distributed fashion. Our scheme extends the
previously known results and gives new achievable rate regions.
[Show abstract][Hide abstract] ABSTRACT: Compute-and-Forward (CF), also known as reliable physical layer network coding, is a technique that provides the possibility of exploiting the features of broadcast and superposition in wireless networks. It has been shown that the throughput for multiple unicast traffic can be significantly boosted by CF. In this letter, the limit of such improvement is investigated by comparing the performance of CF with the traditional routing-based transmission schemes. For networks characterized by local interference and half-duplex constraints, it is proven that the throughput gain of CF over traditional routing, expressed by an improvement factor, is upper bounded by $3K$, where $K$ is the number of unicast sessions. Furthermore, a class of networks is presented for which an improvement by a factor of $K/2$ is feasible by applying CF. Hence, the throughput gain of CF is at most on the order of $K$ for any network, and a gain in that order is indeed achievable for some networks.
[Show abstract][Hide abstract] ABSTRACT: The problem of successive refinement in distributed source coding and in joint source-channel coding is considered. The emphasis is placed on the case where the sources have to be recovered losslessly in the second stage. In distributed source coding, it is shown that all sources are successively refinable in sum rate, with respect to any (joint) distortion measure in the first stage. In joint source-channel coding, the sources are assumed independent and only a (per letter) function is to be recovered losslessly in the first stage. For a class of multiple access channels, it is shown that all sources are successively refinable with respect to a class of linear functions. Finally, when the sources have equal entropy, a simple sufficient condition of successive refinability is provided for partially invertible functions.
2014 IEEE International Symposium on Information Theory (ISIT); 06/2014
[Show abstract][Hide abstract] ABSTRACT: Lattice codes are applied to the two-user Gaussian multiple access channel (MAC) combined with a modified compute-and-forward transmitting scheme. It is shown that non-corner points on the boundary of the capacity region can be achieved by decoding two integer sums of the codewords, which can be viewed as a generalization of the well-known successive cancellation decoding. A similar idea is then applied to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme recovers previously known results and gives new achievable rate regions. The proposed scheme can be extended to the case with more than two users.
2014 IEEE International Symposium on Information Theory (ISIT); 06/2014
[Show abstract][Hide abstract] ABSTRACT: The Shortest Lattice Vector (SLV) problem is in general hard to solve, except
for special cases (such as root lattices and lattices for which an obtuse
superbase is known). In this paper, we present a new class of SLV problems that
can be solved efficiently. Specifically, if for an $n$-dimensional lattice, a
Gram matrix is known that can be written as the difference of a diagonal matrix
and a positive semidefinite matrix of rank $k$ (for some constant $k$), we show
that the SLV problem can be reduced to a $k$-dimensional optimization problem
with countably many candidate points. Moreover, we show that the number of
candidate points is bounded by a polynomial function of the ratio of the
smallest diagonal element and the smallest eigenvalue of the Gram matrix.
Hence, as long as this ratio is upper bounded by a polynomial function of $n$,
the corresponding SLV problem can be solved in polynomial complexity. Our
investigations are motivated by the emergence of such lattices in the field of
Network Information Theory. Further applications may exist in other areas.
[Show abstract][Hide abstract] ABSTRACT: A new achievable rate region is given for the Gaussian cognitive many-to-one
interference channel. The proposed coding scheme is based on lattice codes and
incorporates all key ingredients from conventional coding schemes. Using the
idea of compute-and-forward to decode sums of codewords, our scheme improves
considerably upon the conventional coding schemes which treat interference as
noise or decode messages simultaneously. Roughly speaking, the novel scheme
asks the decoder to decode "just enough" interfering signals and use it for
extracting the desired information. Our strategy extends directly to the usual
many-to-one interference channels without cognitive messages. For some simple
channel settings, the proposed scheme gives constant gap or capacity results
which are independent of the number of users in the system.
IEEE Transactions on Information Theory 04/2014; 61(3). DOI:10.1109/TIT.2015.2394782 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Objective:
Intracortical brain-machine interfaces (BMIs) have predominantly utilized spike activity as the control signal. However, an increasing number of studies have shown the utility of local field potentials (LFPs) for decoding motor related signals. Currently, it is unclear how well different LFP frequencies can serve as features for continuous, closed-loop BMI control.
Approach:
We demonstrate 2D continuous LFP-based BMI control using closed-loop decoder adaptation, which adapts decoder parameters to subject-specific LFP feature modulations during BMI control. We trained two macaque monkeys to control a 2D cursor in a center-out task by modulating LFP power in the 0-150 Hz range.
Main results:
While both monkeys attained control, they used different strategies involving different frequency bands. One monkey primarily utilized the low-frequency spectrum (0-80 Hz), which was highly correlated between channels, and obtained proficient performance even with a single channel. In contrast, the other monkey relied more on higher frequencies (80-150 Hz), which were less correlated between channels, and had greater difficulty with control as the number of channels decreased. We then restricted the monkeys to use only various sub-ranges (0-40, 40-80, and 80-150 Hz) of the 0-150 Hz band. Interestingly, although both monkeys performed better with some sub-ranges than others, they were able to achieve BMI control with all sub-ranges after decoder adaptation, demonstrating broad flexibility in the frequencies that could potentially be used for LFP-based BMI control.
Significance:
Overall, our results demonstrate proficient, continuous BMI control using LFPs and provide insight into the subject-specific spectral patterns of LFP activity modulated during control.
[Show abstract][Hide abstract] ABSTRACT: We present a modified compute-and-forward scheme which utilizes Channel State
Information at the Transmitters (CSIT) in a natural way. The modified scheme
allows different users to have different coding rates, and use CSIT to achieve
larger rate region. This idea is applicable to all systems which use the
compute-and-forward technique and can be arbitrarily better than the regular
scheme in some settings.
[Show abstract][Hide abstract] ABSTRACT: Function computation of arbitrarily correlated discrete sources over Gaussian
networks with orthogonal components is studied. Two classes of functions are
considered: the arithmetic sum function and the type function. The arithmetic
sum function in this paper is defined as a set of multiple weighted arithmetic
sums, which includes averaging of the sources and estimating each of the
sources as special cases. The type or frequency histogram function counts the
number of occurrences of each argument, which yields many important statistics
such as mean, variance, maximum, minimum, median, and so on. The proposed
computation coding first abstracts Gaussian networks into the corresponding
modulo sum multiple-access channels via nested lattice codes and linear network
coding and then computes the desired function by using linear Slepian-Wolf
source coding. For orthogonal Gaussian networks (with no broadcast and
multiple-access components), the computation capacity is characterized for a
class of networks. For Gaussian networks with multiple-access components (but
no broadcast), an approximate computation capacity is characterized for a class
of networks.
[Show abstract][Hide abstract] ABSTRACT: In wireless sensor networks, various applications involve learning one or
multiple functions of the measurements observed by sensors, rather than the
measurements themselves. This paper focuses on type-threshold functions, e.g.,
the maximum and indicator functions. Previous work studied this problem under
the collocated collision network model and showed that under many probabilistic
models for the measurements, the achievable computation rates converge to zero
as the number of sensors increases. This paper considers two network models
reflecting both the broadcast and superposition properties of wireless
channels: the collocated linear finite field network and the collocated
Gaussian network. A general multi-round coding scheme exploiting not only the
broadcast property but particularly also the superposition property of the
networks is developed. Through careful scheduling of concurrent transmissions
to reduce redundancy, it is shown that given any independent measurement
distribution, all type-threshold functions can be computed reliably with a
non-vanishing rate in the collocated Gaussian network, even if the number of
sensors tends to infinity.
[Show abstract][Hide abstract] ABSTRACT: This paper explores the problem of feedback coding for a channel whose output is simultaneously used for two purposes: it is decoded to establish reliable communication, and it is used to control a dynamical system. In general, there is a tradeoff between the rate of communication and the accuracy of control. An intuitive communication and control strategy is analyzed and shown to be optimal in several cases of interest. Using methods from stochastic control, a corresponding upper bound is derived on the rate for a given cost, and this bound can be applied to find the capacity for an interesting class of channels. Under certain regularity conditions, the capacity has a simple characterization, and a series of examples is provided to demonstrate how it can be calculated.
IEEE Transactions on Information Theory 10/2013; 59(10):6243-6257. DOI:10.1109/TIT.2013.2272035 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Recent progress in brain-machine interfaces (BMIs) has shown tremendous improvements in task complexity and degree of control. In particular, closed-loop decoder adaptation (CLDA) has emerged as an effective paradigm for both improving and maintaining the performance of BMI systems. Here, we demonstrate the first reported use of a CLDA algorithm to rapidly achieve high-performance control of a BMI based on local field potentials (LFPs). We trained a non-human primate to control a 2-D computer cursor by modulating LFP activity to perform a center-out reaching task, while applying CLDA to adaptively update the decoder. We show that the subject is quickly able to readily reach and hold at all 8 targets with an average success rate of 74% ± 7% (sustained peak rate of 85%), with rapid convergence in the decoder parameters. Moreover, the subject is able to maintain high performance across 4 days with minimal adaptations to the decoder. Our results indicate that CLDA can be used to facilitate LFP-based BMI systems, allowing for both rapid improvement and maintenance of performance.
Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference 07/2013; 2013:285-288. DOI:10.1109/EMBC.2013.6609493
[Show abstract][Hide abstract] ABSTRACT: It is plausible to hypothesize that the spiking responses of certain neurons represent functions of the spiking signals of other neurons. A natural ensuing question concerns how to use experimental data to infer what kind of a function is being computed. Model-based approaches typically require assumptions on how information is represented. By contrast, information measures are sensitive only to relative behavior: information is unchanged by applying arbitrary invertible transformations to the involved random variables. This paper develops an approach based on the information bottleneck method that attempts to find such functional relationships in a neuron population. Specifically, the information bottleneck method is used to provide appropriate compact representations which can then be parsed to infer functional relationships. In the present paper, the parsing step is specialized to the case of remapped-linear functions. The approach is validated on artificial data and then applied to recordings from the motor cortex of a macaque monkey performing an arm-reaching task. Functional relationships are identified and shown to exhibit some degree of persistence across multiple trials of the same experiment.
[Show abstract][Hide abstract] ABSTRACT: Previous research has shown that postnatal exposure to simple, synthetic sounds can affect the sound representation in the auditory cortex as reflected by changes in the tonotopic map or other relatively simple tuning properties, such as AM tuning. However, their functional implications for neural processing in the generation of ethologically-based perception remain unexplored. Here we examined the effects of noise-rearing and social isolation on the neural processing of communication sounds such as species-specific song, in the primary auditory cortex analog of adult zebra finches. Our electrophysiological recordings reveal that neural tuning to simple frequency-based synthetic sounds is initially established in all the laminae independent of patterned acoustic experience; however, we provide the first evidence that early exposure to patterned sound statistics, such as those found in native sounds, is required for the subsequent emergence of neural selectivity for complex vocalizations and for shaping neural spiking precision in superficial and deep cortical laminae, and for creating efficient neural representations of song and a less redundant ensemble code in all the laminae. Our study also provides the first causal evidence for 'sparse coding', such that when the statistics of the stimuli were changed during rearing, as in noise-rearing, that the sparse or optimal representation for species-specific vocalizations disappeared. Taken together, these results imply that a layer-specific differential development of the auditory cortex requires patterned acoustic input, and a specialized and robust sensory representation of complex communication sounds in the auditory cortex requires a rich acoustic and social environment.
PLoS ONE 04/2013; 8(4):e61417. DOI:10.1371/journal.pone.0061417 · 3.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Polar codes are introduced for discrete memoryless broadcast channels. For
$m$-user deterministic broadcast channels, polarization is applied to map
uniformly random message bits from $m$ independent messages to one codeword
while satisfying broadcast constraints. The polarization-based codes achieve
rates on the boundary of the private-message capacity region. For two-user
noisy broadcast channels, polar implementations are presented for two
information-theoretic schemes: i) Cover's superposition codes; ii) Marton's
codes. Due to the structure of polarization, constraints on the auxiliary and
channel-input distributions are identified to ensure proper alignment of
polarization indices in the multi-user setting. The codes achieve rates on the
capacity boundary of a few classes of broadcast channels (e.g., binary-input
stochastically degraded). The complexity of encoding and decoding is $O(n*log
n)$ where $n$ is the block length. In addition, polar code sequences obtain a
stretched-exponential decay of $O(2^{-n^{\beta}})$ of the average block error
probability where $0 < \beta < 0.5$.
[Show abstract][Hide abstract] ABSTRACT: We develop a network-decomposition framework to provide elementary parallel subnetworks that can constitute an original network without loss of optimality. In our earlier work, a network decomposition is constructed for the Avestimehr-Diggavi-Tse deterministic network which well captures key properties of wireless Gaussian networks. In this work, we apply this decomposition framework to general problem settings where receivers intend to compute functions of the messages generated at transmitters. Depending on functions, these settings include a variety of network problems, ranging from classical communication problems (such as multiple-unicast and multicast problems) to function computation problems. For many of these problems, we show that coding separately over the decomposed orthogonal subnetworks provides optimal performances, thus establishing a separation principle.
Signal Processing Advances in Wireless Communications (SPAWC), 2013 IEEE 14th Workshop on; 01/2013