Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

Efficient Interactive Coding against Adversarial Noise

Abstract: In this work, we study the problem of constructing interactive protocols that are robust to noise, a problem that was originally considered in the seminal works of Schulman (FOCS '92, STOC '93), and has recently regained popularity. Robust interactive communication is the interactive analogue of error correcting codes: Given an interactive protocol which is designed to run on an error-free channel, construct a protocol that evaluates the same function (or, more generally, simulates the execution of the original protocol) over a noisy channel. As in (non-interactive) error correcting codes, the noise can be either stochastic, i.e.\ drawn from some distribution, or adversarial, i.e.\ arbitrary subject only to a global bound on the number of errors. We show how to \emph{efficiently} simulate any interactive protocol in the presence of constant-rate \emph{adversarial} noise, while incurring only a constant blow-up in the communication complexity (CC). Our simulator is randomized, and succeeds in simulating the original protocol with probability at least $1-2^{-\Omega(CC)}$.

The One-Way Communication Complexity of Hamming Distance

Abstract: Consider the following version of the Hamming distance problem for ±1 vec- tors of length n: the promise is that the distance is either at least n + p n or at most n p n, and the goal is to find out which of these two cases occurs. Woodruff (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2004) gave a linear lower bound for the randomized one-way communication complexity of this problem. In this note we give a simple proof of this result. Our proof uses a simple reduction from the indexing problem and avoids the VC-dimension arguments used in the previous paper. As shown by Woodruff (loc. cit.), this implies an W(1/e 2 )-space lower bound for approximating frequency moments within a factor 1+e in the data stream model.

Fast Private Set Intersection from Homomorphic Encryption.

Abstract: Private Set Intersection (PSI) is a cryptographic technique that allows two parties to compute the intersection of their sets without revealing anything except the intersection. We use fully homomorphic encryption to construct a fast PSI protocol with a small communication overhead that works particularly well when one of the two sets is much smaller than the other, and is secure against semi-honest adversaries. The most computationally efficient PSI protocols have been constructed using tools such as hash functions and oblivious transfer, but a potential limitation with these approaches is the communication complexity, which scales linearly with the size of the larger set. This is of particular concern when performing PSI between a constrained device (cellphone) holding a small set, and a large service provider (e.g. WhatsApp), such as in the Private Contact Discovery application. Our protocol has communication complexity linear in the size of the smaller set, and logarithmic in the larger set. More precisely, if the set sizes are Ny Nx, we achieve a communication overhead of O(Ny log Nx). Our running-time-optimized benchmarks show that it takes 36 seconds of online-computation, 71 seconds of non-interactive (receiver-independent) pre-processing, and only 12.5MB of round trip communication to intersect five thousand 32-bit strings with 16 million 32-bit strings. Compared to prior works, this is roughly a 38--115x reduction in communication with minimal difference in computational overhead.

Contention-free MAC protocols for wireless sensor networks

Abstract: A MAC protocol specifies how nodes in a sensor network access a shared communication channel. Desired properties of such MAC protocol are: it should be distributed and contention-free (avoid collisions); it should self-stabilize to changes in the network (such as arrival of new nodes), and these changes should be contained, i.e., affect only the nodes in the vicinity of the change; it should not assume that nodes have a global time reference, i.e., nodes may not be time-synchronized. We give the first MAC protocols that satisfy all of these requirements, i.e., we give distributed, contention-free, self-stabilizing MAC protocols which do not assume a global time reference. Our protocols self-stabilize from an arbitrary initial state, and if the network changes the changes are contained and the protocol adjusts to the local topology of the network. The communication complexity, number and size of messages, for the protocol to stabilize is small (logarithmic in network size).

Adaptive Power Loading for OFDM-Based Cognitive Radio Systems with Statistical Interference Constraint

Abstract: In this letter, we develop an optimal power allocation algorithm for the orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems with different statistical interference constraints imposed by different primary users (PUs). Given the fact that the interference constraints are met in a statistical manner, the CR transmitter does not require the instantaneous channel quality feedback from the PU receivers. A suboptimal algorithm with reduced complexity has been proposed and the performance has been investigated. Presented numerical results show that with our proposed optimal power allocation algorithm CR user can achieve significantly higher transmission capacity for given statistical interference constraints and a given power budget compared to the classical power allocation algorithms namely, uniform and water-filling power allocation algorithms. The suboptimal algorithm outperforms both water-filling algorithm and uniform power loading algorithm. The proposed suboptimal algorithm give an option of using a low complexity power allocation algorithm where complexity is an issue with a certain amount of transmission rate degradation.