In certain communication systems where information is to be transmitted from one point to another, additional side information is available at the transmitting point. This side information relates to the state of the transmission channel and can be used to aid in the coding and transmission of information. In this paper a type of channel with side information is studied and its capacity determined.

Channels with Side Information at the Transmitter

Tbe problem of transmission of separate messages to each of two receivers over a general binary-input broadcast channel is investigated. A new approach to a class of information-theoretic problems is developed and applied to obtain bounds on the cardinalities of auxiliary random variables. These bounds permit the calculation of two different regions of achievable rate pairs which are derived from the Cover-van der Meulen region {\cal R} of achievable rate triples. Numerical evaluation of these regions of rate pairs for two examples demonstrates that the region {\cal R} can be enlarged. This enlargement is accomplished by making {\cal R} internally consistent, as the true capacity region must be. The results display complex interactions between common and separate information in broadcast problems.

Evaluation of an achievable rate region for the broadcast channel.

Random Matrix Methods for Wireless Communications: Perspectives

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Stochastic Dynamic Programming And The Control Of Queueing Systems

Private simultaneous message (PSM) protocols were introduced by Feige, Kilian, and Naor (STOC ’94) as a minimal non-interactive model for information theoretic three-party secure computation. While it is known that every function $$f:\{0,1\}^k\times \{0,1\}^k \rightarrow \{0,1\}$$ admits a PSM protocol with exponential communication of $$2^{k/2}$$ (Beimel et al., TCC ’14), the best known (non-explicit) lower-bound is $$3k-O(1)$$ bits. To prove this lower-bound, FKN identified a set of simple requirements, showed that any function that satisfies these requirements is subject to the $$3k-O(1)$$ lower-bound, and proved that a random function is likely to satisfy the requirements. We revisit the FKN lower-bound and prove the following results: (Counterexample) We construct a function that satisfies the FKN requirements but has a PSM protocol with communication of $$2k+O(1)$$ bits, revealing a gap in the FKN proof. (PSM lower-bounds) We show that by imposing additional requirements, the FKN argument can be fixed leading to a $$3k-O(\log k)$$ lower-bound for a random function. We also get a similar lower-bound for a function that can be computed by a polynomial-size circuit (or even polynomial-time Turing machine under standard complexity-theoretic assumptions). This yields the first non-trivial lower-bound for an explicit Boolean function partially resolving an open problem of Data, Prabhakaran, and Prabhakaran (Crypto ’14, IEEE Information Theory ’16). We further extend these results to the setting of imperfect PSM protocols which may have small correctness or privacy error. (CDS lower-bounds) We show that the original FKN argument applies (as is) to some weak form of PSM protocols which are strongly related to the setting of Conditional Disclosure of Secrets (CDS). This connection yields a simple combinatorial criterion for establishing linear $$\varOmega (k)$$-bit CDS lower-bounds. As a corollary, we settle the complexity of the inner-product predicate resolving an open problem of Gay, Kerenidis, and Wee (Crypto ’15).

The Communication Complexity of Private Simultaneous Messages, Revisited.

A hybrid communication network with a common analog signal and an independent digital data stream as input to each node in a multiple access network is considered. The receiver/base-station has to estimate the analog signal with a given fidelity, and decode the digital streams with a low error probability. Treating the analog signal as a common state process, we set up a joint state estimation and communication problem in a Gaussian multiple access channel (MAC) with additive state. The transmitters have non-causal knowledge of the state process, and need to communicate independent data streams in addition to facilitating state estimation at the receiver. We first provide a complete characterization of the optimal trade-off between mean squared error distortion performance in estimating the state and the data rates for the message streams from two transmitting nodes. This is then generalized to an N-sender MAC. To this end, we show a natural connection between the state-dependent MAC model and a hybrid multi-sensor network in which a common source phenomenon is observed at N transmitting nodes. Each node encodes the source observations as well as an independent message stream over a Gaussian MAC without any state process. The receiver is interested estimating the source and all the messages. Again the distortion-rate performance is characterized.

Joint State Estimation and Communication over a State-Dependent Gaussian Multiple Access Channel

We consider a two-user block-fading MAC with distributed channel state information (CSI), where each user has access to only its own fading coefficients. The average rate-pairs of communication while employing within-block coding is known as the adaptive capacity region, where each user adapts the rate based on its perceived link gain. We evaluate the adaptive sum-capacity of MAC channels with general fading distributions, for discrete as well as continuous valued ones.

On the adaptive sum-capacity of fading MACs with distributed CSI and non-identical links

We consider a distributed MAC setting with block-wise flat fading links and full receiver CSI (channel state information). Each user has individual CSI (knowledge of its own fading coefficient) and is unaware of the link quality of other links. Outage is not allowed in any communication block. In this distributed set up, throughput optimal power-rate allocation strategies are of interest. The average sum-throughput is also known as power controlled adaptive sum-capacity in literature, an open-problem for several interesting fading models like Rayleigh fading. Part of this problem was recently solved for the case where the users have identical power constraints and fading statistics. We extend this result in two directions. 1) We find the power controlled adaptive sum-capacity when the users have different average power constraints and identical channel statistics, and propose bounds when the channel statistics are different. 2) We analyze the impact of finite-rate additional CSI on the fading coefficients of the other links, and compute the optimal throughput in some interesting cases.

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Power controlled adaptive sum-capacity in the presence of distributed CSI

We consider a fast fading AWGN multiple-access channel (MAC) with full receiver CSI and distributed CSI at the transmitters. The objective is to evaluate the ergodic sum-capacity of this decentralized model, under identical average powers and channel statistics across users. While an optimal water-filling solution can be found for centralized MACs with full CSI at all terminals, such an explicit solution is not considered feasible in distributed CSI models. Our main contribution is an upper-bound on the ergodic sum-capacity when each transmitter is aware only of its own fading coefficients. Interestingly, our techniques also suggest an appropriate lower bound. These bounds are shown to be very close to each other, suggesting the tight nature of the results.

On the Ergodic Sum-Capacity of Decentralized Multiple Access Channels

A two-way half-duplex communication model is considered, where two nodes want to exchange a fixed number of bits with each other, and both nodes are powered by energy harvesting (EH) sources. The problem of minimizing the sum of the time required to send the required bits in both the directions is considered. The model also includes the processing cost at each node, that models the power needed for nodes to stay powered on during transmission. In the offline setting, where the EH arrival profile is known non-causally, an iterative algorithm based on alternating maximization is shown to be optimal. In the more realistic setting of causal knowledge of the EH arrival profile, an online algorithm is shown to be optimal in terms of the competitive ratio and the optimal competitive ratio is shown to be 2.

Sibi Raj B Pillai

Papers

Joint State Estimation and Communication over a State-Dependent Gaussian Multiple Access Channel

On the adaptive sum-capacity of fading MACs with distributed CSI and non-identical links

Power controlled adaptive sum-capacity in the presence of distributed CSI

On the Ergodic Sum-Capacity of Decentralized Multiple Access Channels

Opportunistic scheduling in two-way wireless communication with energy harvesting