Diversity-Multiplexing Tradeoff of Asynchronous Cooperative Diversity in Wireless Networks

Synchronization of relay nodes is an important and critical issue in exploiting cooperative diversity in wireless networks. In this paper, two asynchronous cooperative diversity schemes are proposed, namely, distributed delay diversity and asynchronous space-time coded cooperative diversity schemes. In terms of the overall diversity-multiplexing (DM) tradeoff function, we show that the proposed independent coding based distributed delay diversity and asynchronous space-time coded cooperative diversity schemes achieve the same performance as the synchronous space-time coded approach which requires an accurate symbol-level timing synchronization to ensure signals arriving at the destination from different relay nodes are perfectly synchronized. This demonstrates diversity order is maintained even at the presence of asynchronism between relay node. Moreover, when all relay nodes succeed in decoding the source information, the asynchronous space-time coded approach is capable of achieving better DM-tradeoff than synchronous schemes and performs equivalently to transmitting information through a parallel fading channel as far as the DM-tradeoff is concerned. Our results suggest the benefits of fully exploiting the space-time degrees of freedom in multiple antenna systems by employing asynchronous space-time codes even in a frequency flat fading channel. In addition, it is shown asynchronous space-time coded systems are able to achieve higher mutual information than synchronous space-time coded systems for any finite signal-to-noise-ratio (SNR) when properly selected baseband waveforms are employed

Coupling the reduced-order model and the generative model for an importance sampling estimator

In this work, we develop an importance sampling estimator by coupling the reduced-order model and the generative model in a problem setting of uncertainty quantification. The target is to estimate the probability that the quantity of interest (QoI) in a complex system is beyond a given threshold. To avoid the prohibitive cost of sampling a large scale system, the reduced-order model is usually considered for a trade-off between efficiency and accuracy. However, the Monte Carlo estimator given by the reduced-order model is biased due to the error from dimension reduction. To correct the bias, we still need to sample the fine model. An effective technique to reduce the variance reduction is importance sampling, where we employ the generative model to estimate the distribution of the data from the reduced-order model and use it for the change of measure in the importance sampling estimator. To compensate the approximation errors of the reduced-order model, more data that induce a slightly smaller QoI than the threshold need to be included into the training set. Although the amount of these data can be controlled by a posterior error estimate, redundant data, which may outnumber the effective data, will be kept due to the epistemic uncertainty. To deal with this issue, we introduce a weighted empirical distribution to process the data from the reduced-order model. The generative model is then trained by minimizing the cross entropy between it and the weighted empirical distribution. We also introduce a penalty term into the objective function to deal with the overfitting for more robustness. Numerical results are presented to demonstrate the effectiveness of the proposed methodology

Topological and Algebraic Properties of Chernoff Information between Gaussian Graphs

In this paper, we want to find out the determining factors of Chernoff information in distinguishing a set of Gaussian graphs. We find that Chernoff information of two Gaussian graphs can be determined by the generalized eigenvalues of their covariance matrices. We find that the unit generalized eigenvalue doesn't affect Chernoff information and its corresponding dimension doesn't provide information for classification purpose. In addition, we can provide a partial ordering using Chernoff information between a series of Gaussian trees connected by independent grafting operations. With the relationship between generalized eigenvalues and Chernoff information, we can do optimal linear dimension reduction with least loss of information for classification.Comment: Submitted to Allerton2018, and this version contains proofs of the propositions in the pape

Asymptotic Error Free Partitioning over Noisy Boolean Multiaccess Channels

In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, multi-access channel where $K$ active users (out of a total of $N$ users) seek to access. A solution to the partition problem places each of the $N$ users in one of $K$ groups (or blocks) such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative case of $K=2$ active users and study the number of steps $T$ used to solve the partition problem. By random coding and a suboptimal decoding scheme, we show that for any $T\geq (C_1 +\xi_1)\log N$, where $C_1$ and $\xi_1$ are positive constants (independent of $N$), and $\xi_1$ can be arbitrary small, the partition problem can be solved with error probability $P_e^{(N)} \to 0$, for large $N$. Under the same scheme, we also bound $T$ from the other direction, establishing that, for any $T \leq (C_2 - \xi_2) \log N$, the error probability $P_e^{(N)} \to 1$ for large $N$; again $C_2$ and $\xi_2$ are constants and $\xi_2$ can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower-bound in terms of $T \geq (C_g +\xi)\log N$ for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing.Comment: This paper was submitted in June 2014 to IEEE Transactions on Information Theory, and is under review no

Synthesis of Gaussian Trees with Correlation Sign Ambiguity: An Information Theoretic Approach

In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: First, we quantify the amount of information loss due to unrecoverable sign information. Second, we show the importance of such information in determining the maximum achievable rate region, in which the observed output vector can be synthesized, given its probability density function. In particular, we model the graphical model as a communication channel and propose a new layered encoding framework to synthesize observed data using upper layer Gaussian inputs and independent Bernoulli correlation sign inputs from each layer. We find the achievable rate region for the rate tuples of multi-layer latent Gaussian messages to synthesize the desired observables.Comment: 14 pages, 9 figures, part of this work is submitted to Allerton 2016 conference, UIUC, IL, US

Enhancement of Secrecy of Block Ciphered Systems by Deliberate Noise

This paper considers the problem of end-end security enhancement by resorting to deliberate noise injected in ciphertexts. The main goal is to generate a degraded wiretap channel in application layer over which Wyner-type secrecy encoding is invoked to deliver additional secure information. More specifically, we study secrecy enhancement of DES block cipher working in cipher feedback model (CFB) when adjustable and intentional noise is introduced into encrypted data in application layer. A verification strategy in exhaustive search step of linear attack is designed to allow Eve to mount a successful attack in the noisy environment. Thus, a controllable wiretap channel is created over multiple frames by taking advantage of errors in Eve's cryptanalysis, whose secrecy capacity is found for the case of known channel states at receivers. As a result, additional secure information can be delivered by performing Wyner type secrecy encoding over super-frames ahead of encryption, namely, our proposed secrecy encoding-then-encryption scheme. These secrecy bits could be taken as symmetric keys for upcoming frames. Numerical results indicate that a sufficiently large secrecy rate can be achieved by selective noise addition.Comment: 11 pages, 8 figures, journa