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 trade-off 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 joint state estimation and message communication in a GMAC with state. We provide a complete characterization of the optimal distortion-rate trade-off 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.

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.

It is known that the capacity region of a two user physically degraded discrete memoryless (DM) broadcast channel (BC) is not enlarged by feedback. An identical result holds true for a physically degraded Gaussian BC, established later using a variant of the Entropy Power Inequality (EPI). In this paper, we extend the latter result to a physically degraded Gaussian Vector BC (PD-GVBC). However, the extension is not EPI based, but employs a recent result on the factorization of concave envelopes. While the existing concave envelope factorization results do not hold in the presence of feedback, we show that factorizing the corresponding directed information quantities suffice to attain the feedback capacity region of a PD-GVBC. Our work demonstrates that factorizing concave envelopes of directed information can handle situations involving feedback. We further show that the capacity region of a discrete memoryless reversely physically degraded BC is not enlarged by feedback.

A joint message and state communication problem over a fading Gaussian channel with additive state is considered. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and known non-causally at the transmitter, while the instantaneous fading gain is assumed to be known at both the encoder and the decoder. The receiver not only has to decode the message from the transmitter, but also needs to estimate the state process to meet a prescribed distortion limit. A complete characterization of the optimal rate versus distortion performance is provided. Moreover, the converse proof presented here might be of independent interest, since it gives a simpler and more compact way of establishing the converse for settings with non-fading links studied in the literature – by virtue of relying only upon the differential entropy maximizing property of Gaussian random variables for a given variance.

It is known that fiber nonlinearities induce crosstalk in a wavelength division multiplexed (WDM) system, which limits the capacity of such systems as the transmitted signal power is increased. A network user in a WDM system is an entity that operates around a given optical wavelength. Traditionally, the channel capacity of a WDM system has been analyzed under different assumptions for the transmitted signals of the other users, while treating the interference arising from these users as noise. In this paper, we instead take a multi-user information theoretic view and treat the optical WDM system impaired by cross-phase modulation and dispersion as an interference channel. We characterize an outer bound on the capacity region of simultaneously achievable rate pairs, assuming a simplified $K$ -user perturbative channel model using genie-aided techniques. Furthermore, an achievable rate region is obtained by time-sharing between certain single-user strategies. It is shown that such time-sharing can achieve better rate tuples compared to treating nonlinear interference as noise. The achievable rates using the latter strategy are known to exhibit a maximum for an optimum launch power, beyond which a further increase of power leads to a reduction in achievable rates. For the single-polarization single-span system under consideration and a power 3.5 dB above the optimum launch power, treating nonlinear interference as noise results in a rate of 4.25 bit/sym, while time-sharing gives a rate of 7.99 bit/sym.

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.