Low Complexity Power and Scheduling Policies for Wireless Networks to Provide Quality of Service

We consider optimal power allocation policies for a single server, multiuser system. The power is consumed in transmission of data only. The transmission channel may experience multipath fading. We obtain very efficient, low computational complexity algorithms which minimize power and ensure stability of the data queues. We also obtain policies when the users may have mean delay constraints. If the power required is a linear function of rate then we exploit linearity and obtain linear programs with low complexity.

Secure Compute-and-Forward in a Bidirectional Relay

We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple-access channel (MAC), and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this paper, we study the problem under an additional security constraint, which requires that each user's message be kept secure from the relay. We consider two types of security constraints: 1) perfect secrecy, in which the MAC channel output seen by the relay is independent of each user's message and 2) strong secrecy, which is a form of asymptotic independence. We propose a coding scheme based on nested lattices, the main feature of which is that given a pair of nested lattices that satisfy certain goodness properties, we can explicitly specify probability distributions for randomization at the encoders to achieve the desired security criteria. In particular, our coding scheme guarantees perfect or strong secrecy even in the absence of channel noise. The noise in the channel only affects reliability of computation at the relay, and for Gaussian noise, we derive achievable rates for reliable and secure computation. We also present an application of our methods to the multihop line network in which a source needs to transmit messages to a destination through a series of intermediate relays.

Converses For Secret Key Agreement and Secure Computing

We consider information theoretic secret key (SK) agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the SK length, which is derived using a reduction of binary hypothesis testing to multiparty SK agreement. Building on this basic result, we derive new converses for multiparty SK agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to SK agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.

On the Bounds of Certain Maximal Linear Codes in a Projective Space

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) + dim(Y)-2dim(X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P-q(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Spectral Clustering with Jensen-type kernels and their multi-point extensions

Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multipoint' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these can be extended to measure similarity among multiple points. We study tensor flattening methods and develop a multi-point (kernel) spectral clustering (MSC) method. We further emphasize on a special case of the proposed kernels, which is a multi-point extension of the linear (dot-product) kernel and show the existence of cubic time tensor flattening algorithm in this case. Finally, we illustrate the usefulness of our contributions using standard data sets and image segmentation tasks.

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.

Two-Dimensional Noise-Predictive Maximum Likelihood Method for Magnetic Recording Channels

Noise-predictive maximum likelihood (NPML) is a well known signal detection technique used in partial response maximum likelihood (PRML) scheme in 1D magnetic recording channels. The noise samples colored by the partial response (PR) equalizer are predicted/ whitened during the signal detection using a Viterbi detector. In this paper, we propose an extension of the NPML technique for signal detection in 2D ISI channels. The impact of noise prediction during signal detection is studied in PRML scheme for a particular choice of 2D ISI channel and PR targets.

The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint

The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1, infinity)-RLL constraint. We derive the capacity for this setting, which can be expressed as C-is an element of = max(0 <= p <= 0.5) (1-is an element of) H-b (p)/1+(1-is an element of) p, where is an element of is the erasure probability and Hb(.) is the binary entropy function. Moreover, we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming (DP) formulation with an optimal average-reward that is equal to the capacity. Furthermore, we obtained an optimal encoding procedure from the solution of the DP, leading to a capacity-achieving, zero-error coding scheme for our setting. DP is, thus, shown to be a tool not only for solving optimization problems, such as capacity calculation, but also for constructing optimal coding schemes. The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.

On the Gaussian Many-to-One X Channel

In this paper, the Gaussian many-to-one X channel (XC), which is a special case of general multiuser XC, is studied. In the Gaussian many-to-one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the XC assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding manyto- one interference channel (IC). Transmission strategies, which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise, are formulated for the above channel. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a 3 x 3 many-to-one XC is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the K x K case. Next, a region in which the many-to-one XC can be operated as a many-to-one IC without the loss of sum-rate is identified. Furthermore, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieve a rate point that is within K/2 -1 bits from the sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated, and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within K/2 -1 bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3 x 3 many-to-one XC and the corresponding many-to-one IC.

The cross-entropy method for blind multiuser detection

We consider the problem of blind multiuser detection. We adopt a Bayesian approach where unknown parameters are considered random and integrated out. Computing the maximum a posteriori estimate of the input data sequence requires solving a combinatorial optimization problem. We propose here to apply the Cross-Entropy method recently introduced by Rubinstein. The performance of cross-entropy is compared to Markov chain Monte Carlo. For similar Bit Error Rate performance, we demonstrate that Cross-Entropy outperforms a generic Markov chain Monte Carlo method in terms of operation time.