We consider a communication channel where there is no common clock between the transmitter and the receiver. This is motivated by the recent interest in building system-on-chip radios for Internet of Things applications, which cannot rely on crystal oscillators for accurate timing. We identify two types of clock uncertainty in such systems: timing jitter, which occurs at a time scale faster than the communication duration (or equivalently blocklength), and clock drift, which occurs at a slower time scale. We study the zero-error capacity under both types of timing imperfections and obtain optimal zero-error codes for some cases. Our results show that, as opposed to common practice, in the presence of clock drift, it is highly suboptimal to try to learn and track the clock frequency at the receiver; rather, one can design codes that come close to the performance of perfectly synchronous communication systems without any clock synchronization at the receiver.

Motivated by the recent emergence of energy harvesting and wirelessly powered transceivers, we study communication over a memoryless channel with a transmitter, whose battery is recharged at random or deterministic times known to the receiver. We characterize the capacity of this channel as the limit of an n-letter maximum mutual information rate under various assumptions: causal and noncausal transmitter knowledge of the battery recharges, with or without feedback from the receiver to the transmitter. While the resultant n-letter capacity expressions are not computable in the general case, we demonstrate their usefulness by focusing on two important special cases, namely, the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) channel, where they lead to some interesting, and somewhat surprising, insights. By focusing on the BEC, we show that output feedback can strictly increase the capacity of this channel, even though the channel is memoryless and the battery recharging process is independent over time. Interestingly, this provides a counter example to an old claim by Shannon stated without proof in his 1956 paper. On the other hand, by focusing on the AWGN channel, we are able to show that the capacity with noncausal knowledge of the battery recharging times at the transmitter is strictly larger than that with causal knowledge, even though the battery recharging process is independent over time and known to the receiver. The n-letter expressions can also be used to derive explicit upper and lower bounds on capacity. In particular, we derive simple upper and lower bounds on the capacity of the AWGN channel with random battery recharges, which are within 1.05 b/s/Hz of each other for all parameter values.

We study the problem of online power control for energy harvesting communication nodes with random energy arrivals and a finite battery. We assume a block i.i.d. stochastic model for the energy arrivals, in which the energy arrivals are constant for a fixed duration T, but are independent across different blocks, drawn from an arbitrary distribution. This model serves as a simple approximation to a random process with coherence time T. We propose a simple online power control policy, and prove that its performance gap to the optimal throughput is bounded by a constant which is independent of the parameters of the problem. This also yields a simple formula for the approximately optimal long-term average throughput, which sheds some light on the qualitative behavior of the throughput and how it depends on the coherence time of the energy arrival process. Our results show that, perhaps counter-intuitively, for a fixed mean energy arrival rate the approximate throughput decreases with increasing coherence time T of the energy arrival process. In particular, the battery size needed to approach the AWGN capacity of the channel increases linearly with the coherence time of the process. Finally, we show that our results can provide an approximation to the information-theoretic capacity of the same channel.

We consider a communication channel where there is no common clock between the transmitter and the receiver. This is motivated by the recent interest in building system-on-chip radios for Internet of Things applications, which cannot rely on crystal oscillators for accurate timing. We identify two types of clock uncertainty in such systems: timing jitter, which occurs at a time scale faster than the communication duration (or equivalently blocklength); and clock drift, which occurs at a slower time scale. We study the zero-error capacity under both types of timing imperfections, and obtain optimal zero-error codes for some cases. Our results show that, as opposed to common practice, in the presence of clock drift it is highly suboptimal to try to learn and track the clock frequency at the receiver; rather, one can design codes that come close to the performance of perfectly synchronous communication systems without any clock synchronization at the receiver.

We consider a general class of stochastic optimization problems, in which the state represents a certain level or amount which can be partly used and depleted, and subsequently filled by a random amount. This is motivated by energy harvesting applications, in which one manages the amount of energy in a battery, but is also related to inventory models and queuing models. We propose a simple policy that requires minimal knowledge of the distribution of the stochastic process involved, and show that it is a close approximation to the optimal solution with bounded guarantees. Specifically, under natural assumptions on the reward function, we provide constant multiplicative and additive gaps to optimality, which do not depend on the problem parameters. This allows us to obtain a simple formula for approximating the long-term expected average reward, which gives some insight on its qualitative behavior as a function of the maximal state and the distribution of the disturbance.

Motivated by the recent developments in wireless power transfer, we study communication with a remotely powered transmitter. We propose an information-theoretic model where a charger can dynamically decide on how much power to transfer to the transmitter based on its side information regarding the communication, while the transmitter needs to dynamically adapt its coding strategy to its instantaneous energy state, which in turn depends on the actions previously taken by the charger. We characterize the capacity as an n-letter mutual information rate under various levels of side information available at the charger. When the charger is finely tunable to different energy levels, referred to as a “precision charger,” we show that these expressions reduce to single-letter form and there is a simple and intuitive joint charging and coding scheme achieving capacity. The precision charger scenario is motivated by the observation that in practice the transferred energy can be controlled by simply changing the amplitude of the beamformed signal. When the charger does not have sufficient precision, for example, when it is restricted to use a few discrete energy levels, we show that the computation of the n-letter capacity can be cast as a Markov decision process if the channel is noiseless. This allows us to numerically compute the capacity for specific cases and obtain insights on the corresponding optimal policy, or even to obtain closed-form analytical solutions by solving the corresponding Bellman equations, as we demonstrate through examples. Our findings provide some surprising insights on how side information at the charger can be used to increase the overall capacity of the system.

We consider online power control for an energy harvesting system with random i.i.d. energy arrivals and a finite size battery. We propose a simple online power control policy for this channel that requires minimal information regarding the distribution of the energy arrivals and prove that it is universally near-optimal for all parameter values. In particular, the policy depends on the distribution of the energy arrival process only through its mean and achieves the optimal long-term average throughput of the channel within a constant gap. Existing heuristics for online power control fail to achieve such universal performance. This result also allows us to obtain a simple constant-gap approximation for the long-term average throughput of the system, which sheds some light on the qualitative behavior of the throughput, namely how it depends on the distribution of the energy arrivals and the size of the battery.

We consider an energy harvesting multiple access channel where the transmitters are powered by an exogenous stochastic energy harvesting process and equipped with finite batteries. We characterize the capacity region of this channel as n-letter mutual information rate and develop inner and outer bounds that differ by a constant gap. An interesting conclusion that emerges from our results is that in a symmetric system, where transmitters are statistically equivalent to each other, the largest achievable common rate point approaches that of a standard AWGN MAC with an average power constraint, as the number of users in the MAC becomes large.

Motivated by recent developments in wireless power transfer, we study communication with a remotely powered transmitter. We propose an information-theoretic model where a charger can dynamically decide on how much power to transfer to the transmitter based on its side information regarding the communication, while the transmitter needs to dynamically adopt its coding strategy to its instantaneous energy state, which in turn depends on the actions previously taken by the charger. We characterize the capacity as n-letter mutual information rate under various levels of side information available at the charger. In some special cases, motivated by different settings of practical interest, we simplify these expressions to single-letter form, or provide an algorithm to efficiently compute capacity using dynamic programming. Our results provide some surprising insights on how side information at the charger can be used to increase the overall capacity of the system.

We consider an energy harvesting channel, in which the transmitter is powered by an exogenous stochastic energy arrival process, which can be stored in a battery of finite size. We provide an n-letter expression for the capacity of this channel under various assumptions on the availability of energy arrival information: causal and noncausal knowledge of the energy arrivals at the transmitter with and without knowledge at the receiver. We then proceed to deriving lower and upper bounds on the capacity that are easier to compute and are within a constant gap of each other. In particular, we show that the power control problem for energy-harvesting communication, extensively studied in the communication theory literature over the recent years, provides an upper bound on the true information-theoretic capacity of the channel. For example, the offline power control problem provides an upper bound on the information-theoretic capacity with noncausal knowledge of the energy arrivals at the transmitter and the receiver, while the online problem is an upper bound on the capacity with causal information. Perhaps more surprisingly, we also show that given an optimal power control policy there is a natural way to construct an explicit scheme which achieves a rate within a constant gap of the upper bound for any i.i.d. energy harvesting process and any battery size. This shows that these two different formulations of the energy-harvesting communication problem, so far studied in isolation, are strongly coupled; solving the power control problem is almost sufficient to solve the information-theoretic problem.

We consider communication over the AWGN channel with a transmitter whose battery is recharged with RF energy transfer at random times known to the receiver. We assume that the recharging process is i.i.d. Bernoulli. We characterize the capacity of this channel as the limit of an n-letter maximum mutual information rate under both causal and noncausal transmitter knowledge of the battery recharges. With noncausal knowledge, it is possible to explicitly identify the maximizing input distribution, which we use to demonstrate that the capacity with noncausal knowledge of the battery recharges is strictly larger than that with causal knowledge. We then proceed to derive explicit upper and lower bounds on the capacity, which are within 1.05 bits/s/Hz of each other for all parameter values.

We investigate if feedback can increase the capacity of an energy harvesting communication channel where a transmitter powered by an exogenous energy arrival process and equipped with a finite battery communicates to a receiver over a memoryless channel. For a simple special case where the energy arrival process is deterministic and the channel is a BEC, we explicitly compute the feed-forward and feedback capacities and show that feedback can strictly increase the capacity of this channel. Building on this example, we also show that feedback can increase the capacity when the energy arrivals are i.i.d. known noncausally at the transmitter and the receiver.

This paper studies the multiple-access channel (MAC) with rate-limited feedback. The channel output is encoded into one stream of bits, which is provided causally to the two users at the channel input. An achievable rate region for this setup is derived, based on superposition of information, block Markov coding, and coding with various degrees of side information for the feedback link. The suggested region coincides with the Cover-Leung inner bound for large feedback rates. The result is then extended for cases where there is only a feedback link to one of the transmitters, and for a more general case where there are two separate feedback links to both transmitters. We compute achievable regions for the Gaussian MAC and for the binary erasure MAC. The Gaussian region is computed for the case of common rate-limited feedback, whereas the region for the binary erasure MAC is computed for one-sided feedback. It is known that for the latter, the Cover-Leung region is tight, and we obtain results that coincide with the feedback capacity region for high feedback rates.