This note is prepared based on the article titled “Linear Sketching over F2”(ECCC TR16-174) by Sampath Kannan, Elchanan Mossel and Grigory Yaroslavtsev. We quantitatively improve the parameters of Theorem 1.4 of the above work, as well as an earlier bound of ours. In particular, our result implies that for every ∈ (0, 12 ) and every constant δ > 0, the one-way communication complexity of any Bo...

Consider the following version of the Hamming distance problem for ±1 vectors of length n: the promise is that the distance is either at least 2 + √ n or at most 2 − √ 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 th...

This paper considers a two-way relay network, where two source nodes exchange messages through several relays in the presence of an eavesdropper, and the channel state information (CSI) of the eavesdropper is imperfectly known. The amplify-and-forward relay protocol is used and the relay beamforming weights are designed. The model is built up to minimize the total relay transmit power while gua...

An important discovery in quantum information processing is that quantum one-way communication protocols can be exponentially more efficient than classical protocols. Those extraordinary quantum advantages were demonstrated through the Hidden Matching Problem and its variants, where the underlying basic task is to determine the parity of some k = 2 bits of an n-bit string. We prove that for lar...

N etwork congestion is a fundamental problem facing Internet users today. Many common complaints — “Why is this streaming video clip so jerky?” “Why are these Web pages taking so long to download compared to yesterday?” and “Why are my pings so high in Quake?” — usually reflect congestion somewhere in the network. Traditional approaches to congestion control have viewed the Internet as a cooper...

In call centers, call blending consists in the mixing of incoming and outgoing call activity. Artalejo and Phung-Duc recently provided an apt model for such a setting, with a two way communication retrial queue. However, by assuming a classical (proportional) retrial rate for the incoming calls, the outgoing call activity is largely blocked when many incoming calls are in orbit, which may be un...

We consider attacks on two-way quantum key distribution protocols in which an undetectable eavesdropper copies all messages in the message mode. We show that under the attacks, there is no disturbance in the message mode and that the mutual information between the sender and the receiver is always constant and equal to one. It follows that recent proofs of security for two-way protocols cannot ...

The modern workplace is inherently collaborative, and this collaboration relies on effective communication among co-workers. Instant messaging is the multi-tasking tools of choice most people chatting over IM do other things at the same time. The use of IM in workplace is less intrusive than the use of phone, more immediate than email and has added advantage due to the ability to detect presenc...

In contrast to the conventional send/receive model, the one-way communication model—using Put and Synch—allows the decoupling of message transmission from synchronization. This opens up new opportunities not only to further optimize communication but also to reduce synchronization overhead. In this paper, we present a general technique which uses a global dataflow framework to optimize communic...