Optimal Information Rate Research Articles

Friendship Paradox Redux: Your Friends Are More Interesting Than You

Feld's friendship paradox states that "your friends have more friends than you, on average." This paradox arises because extremely popular people, despite being rare, are overrepresented when averaging over friends. Using a sample of the Twitter firehose, we confirm that the friendship paradox holds for >98% of Twitter users. Because of the directed nature of the follower graph on Twitter, we are further able to confirm more detailed forms of the friendship paradox: everyone you follow or who follows you has more friends and followers than you. This is likely caused by a correlation we demonstrate between Twitter activity, number of friends, and number of followers. In addition, we discover two new paradoxes: the virality paradox that states your friends receive more viral content than you, on average, and the activity paradox, which states your friends are more active than you, on average." The latter paradox is important in regulating online communication.It may result in users having difficulty maintaining optimal incoming information rates, because following additional users causes the volume of incoming tweets to increase super-linearly.While users may compensate for increased information flow by increasing their own activity, users become information overloaded when they receive more information than they are able or willing to process. We compare the average size of cascades that are sent and received by overloaded and underloaded users. And we show that overloaded users post and receive larger cascades and they are poor detector of small cascades.

Hybrid game approach‐based channel congestion control for the Internet of Vehicles

Communications between the Internet of Vehicles in smart cities helps increase the awareness and safety among drivers. However, the channel congestion problem is considered as a key challenge for the communication networks due to continuing collection and exchange of traffic information in dense environments. The channel congestion problem degrades the efficiency and reliability of the ad hoc network. Therefore, the adaptation of the data rate and power control is considered as one of the effective solutions to mitigate channel congestion. This paper develops a new hybrid game transmission rate and power channel congestion control approach on the Internet of Vehicle networks where the nodes play as greedy opponents demanding high information rates with the maximum power level. Furthermore, the existence of a Nash equilibrium, which is the optimal information rate and power transmission for every vehicle, is established. Simulation results demonstrate that the proposed approach enhances the network performance by an overall percentage of 42.27%, 43.94% and 47.66% regarding of channel busy time, messages loss and data collision as compared to others. This increases the awareness and performance of the vehicular communication network.

The lower bound and exact value of the information rate of some developed graph access structures

Various studies have focused on secret sharing schemes and in all of them, each shareholder is interested in a shorter share. The information rate of a secret sharing scheme shows the ratio between the size of the secret to the maximum number of shares given to each shareholder. In this regard, the researchers investigated the optimal information rate of the graph access structure. This paper aims to discover the exact values for the optimal information rates of the two graph access structures, which remained as open problems in Van Dijk’s paper. Furthermore, we introduced the developed multipartite graph and the developed cycle graph and calculated the exact value of their optimal information rate. Moreover, we presented a lower bound on the information rate for other developed graph access structures.

Compression-Based Regularization With an Application to Multitask Learning

This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to fully describe the data itself, in order to build meaningful representations of a relevant content (multiple labels). We begin by introducing the noisy lossy source coding paradigm with the log-loss fidelity criterion which provides the fundamental tradeoffs between the \emph{cross-entropy loss} (average risk) and the information rate of the features (model complexity). Our approach allows an information theoretic formulation of the \emph{multi-task learning} (MTL) problem which is a supervised learning framework in which the prediction models for several related tasks are learned jointly from common representations to achieve better generalization performance. Then, we present an iterative algorithm for computing the optimal tradeoffs and its global convergence is proven provided that some conditions hold. An important property of this algorithm is that it provides a natural safeguard against overfitting, because it minimizes the average risk taking into account a penalization induced by the model complexity. Remarkably, empirical results illustrate that there exists an optimal information rate minimizing the \emph{excess risk} which depends on the nature and the amount of available training data. An application to hierarchical text categorization is also investigated, extending previous works.

Universal secure rank-metric coding schemes with optimal communication overheads

We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to reducing communication overheads in universal secure linear network coding and secure distributed storage with crisscross errors and erasures and in the presence of a wire-tapper. Our main contribution is a method to transform coding schemes based on linear rank-metric codes, with certain properties, to schemes with lower communication overheads. By applying this method to pairs of Gabidulin codes, we obtain coding schemes with optimal information rate with respect to their security and rank error correction capability, and with universally optimal communication overheads, when n ≤ m, being n and m the number of columns and number of rows, respectively. Moreover, our method can be applied to other families of maximum rank distance codes when n > m. The downside of the method is generally expanding the packet length, but some practical instances come at no cost.

Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms

We investigate the problem of estimating the causal effect of a treatment on individual subjects from observational data, this is a central problem in various application domains, including healthcare, social sciences, and online advertising. Within the Neyman Rubin potential outcomes model, we use the Kullback Leibler (KL) divergence between the estimated and true distributions as a measure of accuracy of the estimate, and we define the information rate of the Bayesian causal inference procedure as the (asymptotic equivalence class of the) expected value of the KL divergence between the estimated and true distributions as a function of the number of samples. Using Fano method, we establish a fundamental limit on the information rate that can be achieved by any Bayesian estimator, and show that this fundamental limit is independent of the selection bias in the observational data. We characterize the Bayesian priors on the potential (factual and counterfactual) outcomes that achieve the optimal information rate. As a consequence, we show that a particular class of priors that have been widely used in the causal inference literature cannot achieve the optimal information rate. On the other hand, a broader class of priors can achieve the optimal information rate. We go on to propose a prior adaptation procedure (which we call the information based empirical Bayes procedure) that optimizes the Bayesian prior by maximizing an information theoretic criterion on the recovered causal effects rather than maximizing the marginal likelihood of the observed (factual) data. Building on our analysis, we construct an information optimal Bayesian causal inference algorithm.

Publicly verifiable secret sharing scheme and its application with almost optimal information rate

AbstractIt is well known that the construction of publicly verifiable secret sharing scheme with high information rate is a challenge. The information rates of the existing schemes are generally less than one‐half; for this problem, we put forward a publicly verifiable secret sharing scheme with almost optimal information rate based on multilinear Diffie–Hellman assumption. First, we construct a knowledge commitment scheme by using multilinear map; on the basis of this scheme, we propose a publicly verifiable secret sharing scheme whose information rate is (m − 1)/m (The secret is (m − 1)‐dimensional vector), which is almost asymptotically optimal. Second, the public verifiability of the scheme is achieved by using the multiple linear property of a multilinear map. Again, under multilinear Diffie–Hellman assumption, we proved the security of our scheme. And we apply our publicly verifiable secret sharing scheme to public‐key encryption system skillfully. At last, the performance analysis results show the effectiveness and practicality of our scheme. Copyright © 2017 John Wiley & Sons, Ltd.

Optimal Power Allocation Schemes for the Single AF Relay and Jammer Wiretap Channels

This paper considers the wiretap channel in which a source node communicates with a destination node with the aid of a single helper and in the presence of an eavesdropper. The helper can apply either amplify-and-forward (AF) relaying or jamming. The secrecy capacity and respective optimal power allocation schemes at the source and the helper are investigated under both individual and joint power constraints. Given that the links among the nodes might not always be available for transmission (e.g., due to heavy shadowing), several network topologies are considered for relaying. To deal with the related nonconcave optimization problems in solving the optimal power allocation schemes, we first propose an analytical approach based on Descartes' rule of signs. Using this approach, optimal power allocation strategies are derived for some relay topologies and for the jamming system. Insights into the proposed schemes for different transmission power ranges and comparisons to the optimal information rate power allocations are also discussed. Simulation results are finally provided to quantify the optimality of the proposed schemes.

The optimal information rate for graph access structures of nine participants

The information rate is an important metric of the performance of a secret-sharing scheme. In this paper we consider 272 non-isomorphic connected graph access structures with nine vertices and eight or nine edges, and either determine or bound the optimal information rate in each case. We obtain exact values for the optimal information rate for 231 cases and present a method that is able to derive information-theoretical upper bounds on the optimal information rate. Moreover, we apply some of the constructions to determine lower bounds on the information rate. Regarding information rate, we conclude with a full listing of the known optimal information rate (or bounds on the optimal information rate) for all 272 graphs access structures of nine participants.

The Optimal Information Rates of the Graph Access Structures on Seven Participants

The information rate is an important metric of the performance of a secret-sharing scheme. In this paper, we deal with determining the exact values for the optimal information rates of the six graph access structures and improving the information rate of a graph access structure on seven participants, which remained as open problems in Song's and Wang's paper([1,2]). We prove that the optimal information rate for each of the six graph access structures is equal to 4/7

Delay‐limited throughput analysis of cooperative hybrid automatic repeat request in asymmetric fading channels

This study analyses the delay-limited throughput performance of an uplink cellular relay network utilising hybrid automatic repeat request (HARQ) protocol in which one mobile station (MS) communicates with one base station (BS) with the aid of one amplify-and-forward relay station (RS). The authors’ analysis allows for a practical fading scenario where MS → RS and RS → BS channels undergo independent Rayleigh and Rician fading, respectively. Delay-limited throughput expressions for two HARQ protocols are derived, respectively, namely Repetition Time Diversity and Incremental Redundancy. Furthermore, the impact of different parameters on the achievable throughput, such as the maximum HARQ round number L, line-of-sight signal K, information rate R etc., is analysed. The authors’ analysis unveils that, for the presumed dual-hop cooperation model with the specified tolerable delay requirement and given channel condition, there exists an optimal information rate R* that achieves the maximum delay-limited throughput for the two HARQ protocols. Moreover, it is disclosed that, both HARQ protocols with the adaptive optimised information rate outperform the counterpart with the fixed information rate in low and moderate SNR regions, suggesting that an adaptive transmission scheme should be employed to achieve a better throughput performance.

Optimal Information Rate of Secret Sharing Schemes on Trees

The information rate for an access structure is the reciprocal of the load of the optimal secret sharing scheme for this structure. We determine this value for all trees: it is (2-1/c)-1, where c is the size of the largest core of the tree. A subset of the vertices of a tree is a core if it induces a connected subgraph and for each vertex in the subset one finds a neighbor outside the subset. Our result follows from a lower and an upper bound on the information rate that applies for any graph and happen to coincide for trees because of a correspondence between the size of the largest core and a quantity related to a fractional cover of the tree with stars.

A note on secret sharing schemes with three homogeneous access structure

A secret sharing scheme is a method which allows a secret to be shared among a set of participants in such a way that only qualified subsets of participants can recover the secret. The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. This paper deals with these problems for 3-homogeneous access structures, that is, whenever the minimal qualified subsets have exactly three participants.

Improved constructions of secret sharing schemes by applying [formula omitted]-decompositions

By using threshold schemes, λ-decompositions were introduced by Stinson [D.R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory IT-40 (1994) 118–125] and used to achieve often optimal worst-case information rates of secret sharing schemes based on graphs. By using the broader class of ramp schemes, ( λ , ω ) -decompositions were introduced in [M. van Dijk, W.-A. Jackson, K.M. Martin, A general decomposition construction for incomplete secret sharing schemes, Des. Codes Cryptogr. 15 (1998) 301–321] together with a general theory of decompositions. However, no improvements of existing schemes have been found by using this general theory. In this contribution we show for the first time how to successfully use ( λ , ω ) -decompositions. We give examples of improved constructions of secret sharing schemes based on connected graphs on six vertices.

A cross-layer TCP modelling framework for MIMO wireless systems

We propose a general framework based in the Gilbert model for cross-layer analysis of TCP and UDP over MIMO wireless systems. Our framework takes into consideration diverse system characteristics often difficult to express as a Gilbert model such as fading, space-time transmission schemes, modulation, channel coding and ARQ. We apply our framework to analyze the TCP performance of two representative MIMO systems, namely, the BLAST system and the orthogonal space-time block coded (STBC) system. In particular, we investigate the optimal information rate that maximizes the TCP throughput, the effect of Doppler on the optimal TCP throughput and the optimal channel coding rate for various modulations. We provide simulations results from the ns-2 network simulator to demonstrate the accuracy of the proposed analytical framework in characterizing the TCP performance. We further apply the framework to two additional cross-layer applications: the analysis of the buffer occupancy on the base station, and the analysis of CBR video transmission over MIMO systems. We show that while the optimal rate for maximum TCP throughput is far from the channel capacity, the optimal rate for error and delay-tolerant video transmission requires much higher rates, and so the physical layer should be aware and adapt to the type of application in order to increase the system performance. We also show that mobility benefits systems with larger buffers, especially for TCP, as the ARQ scheme is able to recover the shorter burst errors. In general, our investigation shows that the type of application plays a crucial role in the optimization of a wireless system, and that our modelling framework is useful for the cross-layer analysis and design of those systems.

Time reversal communication in Rayleigh-fading broadcast channels with pinholes

The Letter presents an analysis of the time reversal in independent-multipath Rayleigh-fading channels with N inputs (transmitters) and M outputs (receivers). The main issues addressed are the condition of statistical stability, the rate of information transfer and the effect of pinholes. The stability condition is proved to be M C ≪ N eff B for broadband channels and M ≪ N eff for narrowband channels where C is the symbol rate, B is the bandwidth and N eff is the effective number (maybe less than 1) of transmitters. It is shown that when the number of screens, n − 1 , is relatively low compared to the logarithm of numbers of pinholes N eff is given by the harmonic (or inverse) sum of the number of transmitters and the numbers of pinholes at all screens. The novel idea of the effective number of time reversal array (TRA) elements is introduced to derive the stability condition and estimate the channel capacity in the presence of multi-screen pinholes. The information rate, under the constraints of the noise power ν per unit frequency and the average total power P, attains the supremum P / ν in the regime M ∧ N eff ≫ P / ( ν B ) . In particular, when N eff ≫ M ≫ P / ( B ν ) the optimal information rate can be achieved with statistically stable, sharply focused signals.

Secret sharing schemes on access structures with intersection number equal to one

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, structures such that there is at most one participant in the intersection of any two different minimal qualified subsets. The main result in this work is the complete characterization of the ideal access structures with intersection number equal to one. In addition, bounds on the optimal information rate are provided for the non-ideal case.

Secret Sharing Schemes with Three or Four Minimal Qualified Subsets

In this paper we study secret sharing schemes whose access structure has three or four minimal qualified subsets. The ideal case is completely characterized and for the non-ideal case we provide bounds on the optimal information rate.

Secret Sharing Schemes on Sparse Homogeneous Access Structures with Rank Three

One of the main open problems in secret sharing is the characterization of the ideal access structures. This problem has been studied for several families of access structures with similar results. Namely, in all these families, the ideal access structures coincide with the vector space ones and, besides, the optimal information rate of a non-ideal access structure is at most $2/3$. An access structure is said to be $r$-homogeneous if there are exactly $r$ participants in every minimal qualified subset. A first approach to the characterization of the ideal $3$-homogeneous access structures is made in this paper. We show that the results in the previously studied families can not be directly generalized to this one. Nevertheless, we prove that the equivalences above apply to the family of the sparse $3$-homogeneous access structures, that is, those in which any subset of four participants contains at most two minimal qualified subsets. Besides, we give a complete description of the ideal sparse $3$-homogeneous access structures.

Improving the trade-off between storage and communication in broadcast encryption schemes

The most important point in the design of broadcast encryption schemes (BESs) is to obtain a good trade-off between the amount of secret information that must be stored by every user and the length of the broadcast message, which are measured, respectively, by the information rate ρ and the broadcast information rate ρ B. In this paper, we present a simple method to combine two given BESs in order to improve the trade-off between ρ and ρ B by finding BESs with good information rate ρ for arbitrarily many different values of the broadcast information rate ρ B. We apply this technique to threshold ( R, T)-BESs and we present a method to obtain, for every rational value 1/ R⩽ ρ B⩽1, a ( R, T)-BES with optimal information rate ρ among all ( R, T)-BESs that can be obtained by combining two of the ( R, T)-BESs proposed by Blundo et al. (Lecture Notes in Comput. Sci. 1190 (1996) 387–400).