We investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel (MAC-WT). In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver on observing the channel output must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. Furthermore, we demand that an external eavesdropper learns essentially nothing about the sources and the simulated output sequence by observing its corresponding MAC-WT output. This is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder. The shared randomness rate tuples which permit such channel simulation with strong secrecy are of interest. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are independent and the legitimate receiver's channel is composed of deterministic links.

We investigate the problem of multi-terminal strong coordination over a network of noiseless links with degraded source observations. In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters, with one of the source observations being common while the other one is private. The transmitters communicate their source descriptions over noiseless links to the receiver, which must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. This is aided by the presence of common randomness shared between all three parties. The communication and common randomness rate tuples which permit such channel simulation are of interest. We derive a complete characterization for this multi-terminal strong coordination problem. It is observed that the optimal scheme is based on a superposition structure, where the common source description forms the base layer and the private source description forms the top layer.

We study the problem of simulating a two-user multiple-access channel (MAC) over a multiple access network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links between each encoder and the decoder, and there is independent pairwise shared randomness between all the three possible pairs of nodes. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the two sources and the side information. We are interested in the rate tuples which permit this simulation. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). When the pairwise shared randomness between the encoders is absent, the setting reduces to a special case of MAC simulation using another MAC studied by Haddadpour et al. (2013). We establish that the presence of encoder shared randomness can strictly improve the communication rate requirements. We first show that the inner bound derived from Haddadpour et al. (2013) is tight when the sources at the encoders are conditionally independent given the side-information at the decoder. This result recovers the existing results on point-to-point channel simulation and function computation over such multi-terminal networks. We then explicitly compute the communication rate regions for an example both with and without the encoder shared randomness and demonstrate that its presence strictly reduces the communication rates. Inner and outer bounds for the general case are also obtained.

We study the problem of simulating a multiple access channel over a network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links and independent pairwise shared randomness resources between each encoder and the decoder. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the observed random variables. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). General inner and outer bounds on the rate region are derived. For the special case when the sources at the encoders are conditionally independent given the side-information at the decoder, we completely characterize the rate region. Our bounds recover the existing results on deterministic function computation over such multi-terminal networks. We then show through an example that an additional independent source of shared randomness between the encoders that is not available to the decoder strictly improves the communication rates.

We consider a strong coordination setup, where two nodes must produce a joint distribution on their actions that is close in total variation distance to independent and identical copies from a given joint probability distribution. The first node, which we call the encoder, observes an independent and identically distributed (i.i.d.) source. In order to coordinate the source with the reconstructed outputs of the second node (the decoder), they have access to a noiseless rate limited link and common randomness. The decoder also has additional side information. The reconstruction at the decoder is to be coordinated with the source process as well as the available side information. We allow the side information to be driven by another encoding process, which does not share common randomness with the two nodes. General inner and outer bounds on the rate-coordination region for this set up are derived, and our bounds match for an important special case. We also show an example with no encoding of the side information, where coordination of the source and reconstruction can be obtained as a union of three way coordination regions involving the side information as well.

In an action dependent state channel (ADSC), there are two encoders, viz. an action encoder and a channel encoder. We consider a Gaussian ADSC (GADSC) setup where the state process is generated by passing the action symbols through an AWGN channel. The receiver observes the superposition of the channel encoder symbols, state process, and independent AWGN.In our model, in addition to decoding the messages, the receiver is required to produce an estimate of the state process within some prescribed mean-squared error distortion. While joint state estimation and communication for a discrete memoryless ADSC with strictly causal state information has been solved, its non-causal counterpart remains open. We resolve this for the GADSC under average power constraints at the two encoders. Furthermore, we allow an additional independent message stream at the channel encoder and characterize the optimal distortion-rate trade-off region. Interestingly, our results also characterize the capacity region of a state-dependent Gaussian multiple access channel (MAC) with degraded message sets and state estimation constraints.

A hybrid communication network with a common analog source signal and independent digital data streams at the transmitters of a multiple access network is considered. The receiver has to estimate the analog signal samples with a given fidelity, and decode the digital streams with a low error probability. The main goal of this paper is to characterize the optimal tradeoff between the mean-squared error distortion in source estimation and the data rates available to each user. To this end, we consider a Gaussian multiple access channel (GMAC) setup with additive state, where the state is nothing but a scaled version of the source process itself. The state process is assumed to be non-causally available to all the transmitting nodes. The problem now becomes that of the joint state estimation and message communication in a GMAC with state. We provide a complete characterization of the optimal distortion-rate tradeoff for an N - sender GMAC. Our results show that, similar to the single-user results, it is optimal to amplify the state using uncoded transmissions, whereas the digital streams are superposed using appropriate Gaussian codebooks in conjunction with dirty paper coding (DPC). Since the variance of the additive state is controlled by a scaling factor in our model, we also recover the results for communicating a common source and independent messages over a GMAC without state as a special case.

A common reconstruction (CR) problem, where the common additive state to a Gaussian broadcast channel (BC) is to be estimated at two receivers, is considered. The state process is assumed to be IID Gaussian, and known non-causally at the encoder. Each receiver has to make separate estimates of the state-process, with the CR constraints that the individual receiver's estimate should match a corresponding estimate at the transmitter. We study the trade-offs between the two distortions and a private rate to the strong receiver. We compute inner and outer bounds which are numerically shown to characterize the optimal performance in several regimes of interest. Interestingly, it is observed that allowing the weak user to decode part of the private message to the stronger user helps the distortion trade-offs, even though the objective concerns only a private rate to the strong user. Also, as a special case of our BC results, we show that Gaussian auxiliaries are optimal for a single user Gaussian CR problem.