We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, noncooperative regime of communication involving a strategic sender.
We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, noncooperative regime of communication involving a strategic sender.
We introduce a setting where a receiver aims to perfectly recover a source known privately to a \textit{strategic} sender over a possibly noisy channel. The sender is endowed with a utility function and sends signals to the receiver with the aim of maximizing this utility. Due to the strategic nature of the sender not all the transmitted information is truthful, which leads to question: how much true information can be recovered by the receiver from such a sender? We study this question in this paper. We pose the problem as a game between the sender and receiver, where the receiver tries to maximize the number of sequences that can be recovered perfectly and the sender maximizes its utility. We show that, in spite of the sender being strategic and the presence of noise in the channel, there is a strategy for the receiver by which it can perfectly recover an \textit{exponentially} large number of sequences. Our analysis leads to the notion of the \textit{information extraction capacity} of the sender which quantifies the growth rate of the number of recovered sequences with blocklength, in the presence of a noiseless channel. We identify cases where this capacity is equal to its theoretical maximum, and also when it is strictly less than maximum. In the latter case, we show that the capacity is sandwiched between the independence number and the Shannon capacity of a suitably defined graph. These results lead to an exact characterization of the information extraction capacity in large number of cases. We show that in the presence of a noisy channel, the rate of information extraction achieved by the receiver is the minimum of the zero-error capacity of the channel and the information extraction capacity of the sender. Our analysis leads to insights into a novel regime of communication involving strategic agents.
We consider a setting where a receiver tries to perfectly recover a source signal privately known to a sender who can send messages via a noisy channel. However, the sender is compromised and may have an incentive to lie about its information. We formulate the problem as a game between the sender and the receiver and show that there is a strategy for the receiver in which it can recover an exponential number of signals. We define a notion of a sender graph and the information extraction capacity of the sender which quantifies the maximum amount of information that can be extracted from the sender. We also show that the rate of information extraction is given by the minimum of the information extraction capacity of the sender and the zero-error capacity of the noisy channel.
This chapter begins our exploration of “dynamic” information-processing tasks in quantum Shannon theory, where the term “dynamic” indicates that a quantum channel connects a sender to a receiver and their goal is to exploit this resource for communication. We specifically consider the scenario where a sender Alice would like to communicate classical information to a receiver Bob, and the capacity theorem that we prove here is one particular generalization of Shannon's noisy channel coding theorem from classical information theory (overviewed in Section 2.2). In later chapters, we will see other generalizations of Shannon's theorem, depending on what resources are available to assist their communication or depending on whether they are trying to communicate classical or quantum information. For this reason and others, quantum Shannon theory is quite a bit richer than classical information theory. The naive approach to communicate classical information over a quantum channel is for Alice and Bob simply to mimic the approach used in Shannon's noisy channel coding theorem. That is, they select a random classical code according to some distribution pX(x) , and Bob performs individual measurements of the outputs of a noisy quantum channel according to some POVM. The POVM at the output induces some conditional probability distribution pY∣X(y∣x) , which we can in turn think of as an induced noisy classical channel. The classical mutual information I(X; Y) of this channel is an achievable rate for communication, and the best strategy for Alice and Bob is to optimize the mutual information over all of Alice's inputs to the channel and over all measurements that Bob could perform at the output.
In the classical communication setting multiple senders having access to the same source of information and transmitting it over channel(s) to a receiver in general leads to a decrease in estimation error at the receiver as compared with the single sender case. However, if the objectives of the information providers are different from that of the estimator, this might result in interesting strategic interactions and outcomes. In this work, we consider a hierarchical signaling game between multiple senders (information designers) and a single receiver (decision maker) each having their own, possibly misaligned, objectives. The senders lead the game by committing to individual information disclosure policies simultaneously, within the framework of a non-cooperative Nash game among themselves. This is followed by the receiver's action decision. With Gaussian information structure and quadratic objectives (which depend on the underlying state and receiver's action) for all the players, we show that in general the equilibrium is not unique. We hence identify a set of equilibria and further show that linear noiseless policies can achieve a minimal element of this set. Additionally, we show that competition among the senders is beneficial to the receiver, as compared with cooperation among the senders. Further, we extend our analysis to a dynamic signaling game of finite horizon with Markovian information evolution. We show that linear memoryless policies can achieve equilibrium in this dynamic game. We also consider an extension to a game with multiple receivers having coupled objectives. We provide algorithms to compute the equilibrium strategies in all these cases. Finally, via extensive simulations, we analyze the effects of multiple senders in varying degrees of alignment among their objectives.
The increase in the amount of data sent through the Internet is expected to scale up and accelerate in the coming years, along with the increasing number of connected devices. Current data rates via optical fiber communication channels are approaching the channel capacity and eventually, wireless communication will follow a similar trend. This means that message transmission may not be able to keep up with traffic demand in the future. Optimizing communication tasks and reducing the needed number of utilized radio resources will thus play a crucial role in goal-oriented communications. The latest theoretical and experimental works on message identification, a post-Shannon communication scheme, show promising results for addressing this problem. Under this scheme, the objective at the receiver is no longer to retrieve the content of the transmitted message, but to verify whether the sender is transmitting a specific message, in which the receiver may be interested or not. The sender does not know in advance which message the receiver is interested in. By using local randomness at the encoder, this allows for an exponential gain in the number of messages in identification compared to the available messages in classical transmission, potentially saving radio resources. In this paper, we review the pros and cons of identification and discuss its potential applications for task-oriented communications.
Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the use of one noisy channel to simulate another. For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. In the classical case, shared randomness between sender and receiver is a sufficient auxiliary resource, regardless of the nature of the source, but in the quantum case the requisite auxiliary resources for efficient simulation depend on both the channel being simulated, and the source from which the channel inputs are coming. For tensor power sources (the quantum generalization of classical IID sources), entanglement in the form of standard ebits (maximally entangled pairs of qubits) is sufficient, but for general sources, which may be arbitrarily correlated or entangled across channel inputs, additional resources, such as entanglement-embezzling states or backward communication, are generally needed. Combining existing and new results, we establish the amounts of communication and auxiliary resources needed in both the classical and quantum cases, the tradeoffs among them, and the loss of simulation efficiency when auxiliary resources are absent or insufficient. In particular we find a new single-letter expression for the excess forward communication cost of coherent feedback simulations of quantum channels (i.e. simulations in which the sender retains what would escape into the environment in an ordinary simulation), on non-tensor-power sources in the presence of unlimited ebits but no other auxiliary resource. Our results on tensor power sources establish a strong converse to the entanglement-assisted capacity theorem.