On the capacity of a communication system with energy harvesting and a limited battery

We consider the problem of determining the capacity of an energy-harvesting transmitter with finite battery communicating over a discrete memoryless channel. When the battery is unlimited, or zero, the capacity has been determined, but it remains unknown for a finite non-zero battery. In this paper we assume that the harvested energy at each time, the total battery storage, and the transmitter signal energy at each time can be quantized to the same unit (i.e., the same energy interval). Under this assumption, we show that the capacity can be described using the Verdú-Han general framework. If we further assume that the transmitted symbol at each time depends only on the energy currently available, and not on the entire past history of energy harvests and symbols transmitted, then we show that the system reduces to a finite state channel (FSC) with the required ergodic and Markov properties so that lower bounds on the capacity can be readily numerically computed. We conjecture that our numerical bounds are tight. Our numerical results indicate that even the minimal possible battery storage can reap a significant fraction of the infinite battery capacity.

[1]  R. Gallager Information Theory and Reliable Communication , 1968 .

[2]  Hans-Andrea Loeliger,et al.  A Generalization of the Blahut–Arimoto Algorithm to Finite-State Channels , 2008, IEEE Transactions on Information Theory.

[3]  Sennur Ulukus,et al.  AWGN channel under time-varying amplitude constraints with causal information at the transmitter , 2011, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[4]  J. Kieffer,et al.  Markov Channels are Asymptotically Mean Stationary , 1981 .

[5]  Sennur Ulukus,et al.  Achieving AWGN Capacity Under Stochastic Energy Harvesting , 2012, IEEE Transactions on Information Theory.

[6]  Robert M. Gray,et al.  Ergodicity of Markov channels , 1987, IEEE Trans. Inf. Theory.

[7]  Aaron D. Wyner,et al.  Channels with Side Information at the Transmitter , 1993 .

[8]  Jing Yang,et al.  Optimal Broadcast Scheduling for an Energy Harvesting Rechargeable Transmitter with a Finite Capacity Battery , 2012, IEEE Transactions on Wireless Communications.

[9]  R. Gray Entropy and Information Theory , 1990, Springer New York.

[10]  Aylin Yener,et al.  Optimum Transmission Policies for Battery Limited Energy Harvesting Nodes , 2010, IEEE Transactions on Wireless Communications.

[11]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[12]  Neri Merhav,et al.  Hidden Markov processes , 2002, IEEE Trans. Inf. Theory.

[13]  Shlomo Shamai,et al.  On the capacity of some channels with channel state information , 1999, IEEE Trans. Inf. Theory.

[14]  Wei Zeng,et al.  Simulation-Based Computation of Information Rates for Channels With Memory , 2006, IEEE Transactions on Information Theory.

[15]  Jing Yang,et al.  Optimal Packet Scheduling in an Energy Harvesting Communication System , 2010, IEEE Transactions on Communications.