We are concerned with the problem of maximizing the worst-case lifetime of a data-gathering wireless sensor network consisting of a set of sensor nodes directly communicating with a base-station.We propose to solve this problem by modeling sensor node and base-station communication as the interactive communication between multiple correlated informants (sensor nodes) and a recipient (base-station). We provide practical and scalable interactive communication protocols for data gathering in sensor networks and demonstrate their efficiency compared to traditional approaches. In this paper, we first develop a formalism to address the problem of worst-case interactive communication between a set of multiple correlated informants and a recipient. We realize that there can be different objectives to achieve in such a communication scenario and compute the optimal number of messages and bits exchanged to realize these objectives. Then, we propose to adapt these results in the context of single-hop data-gathering sensor networks. Finally, based on this proposed formalism, we propose a clustering based communication protocol for large sensor networks and demonstrate its superiority over a traditional clustering protocol.
In @cite_13 , only the scenario in which two correlated informants communicate with a recipient is considered. It assumed that both the informants and recipient know the joint distribution of informants' data. Also, only the average of total number of bits exchanged is minimized. In @cite_25 , only two messages are allowed to be exchanged between the encoder and a decoder, which may not be optimal for the general communication problem. Conversely, it does not address the problem of computing the optimal number of messages exchanged between the encoder and a decoder as well as the optimal number of bits sent by the encoder and a decoder for the given objective of the communication in an interactive communication scenario. Also, unlike @cite_13 , this work concerns itself with the lossy compression at the encoders.
@cite_13 @cite_25
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This paper re-visits Shayevitz & Feder's recent ‘Posterior Matching Scheme’, an explicit, dynamical system encoder for communication with feedback that treats the message as a point on the [0,1] line and achieves capacity on memo-ryless channels. It has two key properties that ensure that it maximizes mutual information at each step: (a) the encoder sequentially hands the decoder what is missing; and (b) the next input has the desired statistics. Motivated by brain-machine interface applications and multi-antenna communications, we consider developing dynamical system feedback encoders for scenarios when the message point lies in higher dimensions. We develop a necessary and sufficient condition — the Jacobian equation — for any dynamical system encoder that maximizes mutual information. In general, there are many solutions to this equation. We connect this to the Monge-Kantorovich Optimal Transportation Problem, which provides a framework to identify a unique solution suiting a specific purpose. We provide two examplar capacity-achieving solutions — for different purposes — for the multi-antenna Gaussian channel with feedback. This insight further elucidates an interesting relationship between interactive decision theory problems and the theory of optimal transportation. The reduction in communication achievable by interaction is investigated. The model assumes two communicators: an informant having a random variable X, and a recipient having a possibly dependent random variable Y. Both communicators want the recipient to learn X with no probability of error, whereas the informant may or may not learn Y. To that end, they alternate in transmitting messages comprising finite sequences of bits. Messages are transmitted over an error-free channel and are determined by an agreed-upon, deterministic protocol for (X,Y) (i.e. a protocol for transmitting X to a person who knows Y). A two-message protocol is described, and its worst case performance is investigated. > Index coding studies multiterminal source-coding problems where a set of receivers are required to decode multiple (possibly different) messages from a common broadcast, and they each know some messages a priori . In this paper, at the receiver end, we consider a special setting where each receiver knows only one message a priori , and each message is known to only one receiver. At the broadcasting end, we consider a generalized setting where there could be multiple senders, and each sender knows a subset of the messages. The senders collaborate to transmit an index code. This paper looks at minimizing the number of total coded bits the senders are required to transmit. When there is only one sender, we propose a pruning algorithm to find a lower bound on the optimal (i.e., the shortest) index codelength, and show that it is achievable by linear index codes. When there are two or more senders, we propose an appending technique to be used in conjunction with the pruning technique to give a lower bound on the optimal index codelength; we also derive an upper bound based on cyclic codes. While the two bounds do not match in general, for the special case where no two distinct senders know any message in common, the bounds match, giving the optimal index codelength. The results are expressed in terms of strongly connected components in directed graphs that represent the index-coding problems. We develop communication strategies for the rate-constrained interactive decoding of a message broadcast to a group of interested users. This situation diers from the relay channel in that all users are interested in the transmitted message, and from the broadcast channel because no user can decode on its own. We focus on two-user scenarios, and describe a baseline strategy that uses ideas of coding with decoder side information. One user acts initially as a relay for the other. That other user then decodes the message and sends back random parity bits, enabling the first user to decode. We show how to improve on this scheme’s performance through a conversation consisting of multiple rounds of discussion. While there are now more messages, each message is shorter, lowering the overall rate of the conversation. Such multi-round conversations can be more ecient because earlier messages serve as side information known at both encoder and decoder. We illustrate these ideas for binary erasure channels. We show that multi-round conversations can decode using less overall rate than is possible with the single-round scheme.