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Coding for joint energy and information transfer. A. M. Fouladgar † , O. Simeone † , and E. Erkip ‡ † CWCSPR, New Jersey Institute of Technology, Newark, NJ, USA ‡ ECE Dept., Polytechnic Inst. of NYU Brooklyn, NY, USA. Background and Contribution. System Model. Numerical Results.

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Coding for joint energy and information transfer

A. M. Fouladgar†,O. Simeone†, and E. Erkip‡

† CWCSPR, New Jersey Institute of Technology, Newark, NJ, USA

‡ECE Dept., Polytechnic Inst. of NYU Brooklyn, NY, USA

Background and Contribution

System Model

Numerical Results

Joint Energy and Information Transfer

  • Due to the finite capacity of the battery, there may be battery overflows and underflows.
  • The received signal is used by the decoder both to decode the information message M and to perform energy harvesting.
  • Battery evolution:
  • Conventional assumption: the energy received from an information bearing signal cannot be reused.
  • Exceptions:
  • Matching the code structure to the receiver’s energy utilization model:
  • Small q0: type-0 (d; k)-RLL codes with a small k.
  • Large q0: larger k is required
  • Overflow event:
  • Underflow event:

Passive RFID

  • Body area networks
  • Example:
    • Point-to-point channel
    • 4-PAM signal {-3,-1, 1,3}
      • Maximum information: Rate: 2bit/symbol, Avg. Energy: 5
      • Maximum energy: Rate: 1bit/symbol, Avg. Energy: 9
  • Probabilities of underflow and overflow:
  • Small rate: k=1 is sufficient
  • Larger rate: increase the value of k, while keeping d as small as possible
  • By appropriately choosing d and k, RLL codes can provide relevant advantages.

Related work & Contribution

  • Information-theoretic and signal processing considerations on joint energy and information transfer [1]-[3].
  • This work: code design for systems with joint information and energy transfer.
  • The receiver’s energy requirements are related to, e.g., sensing or radio transmission functionalities.
  • Energy transfer effectiveness measured by the probabilities of overflow and underflow of the battery at the receiver.

Classical codes vs. constrained run-length limited (RLL) codes

  • As the losses on the channel become more pronounced gain decreases due to the reduced control of the received signal afforded by designing the transmitted signal.


  • Classical codes: maximize information rate  unstructured (i.e., random-like)
  • RLL codes: constraint the bursts of 0/1 in the codewords control on energy transfer.
  • Type-0/1 (d,k) -RLL code state machine:
  • Memoryless process Zi , i.e., q1=1- q0
  • Achievable joint energy and information transfer rate:
  • Achievable joint energy and information transfer rate:

Constrained codes

Unconstrained codes

Concluding Remarks

  • Constrained run-length limited (RLL) codes enhance the achievable performance in terms of simultaneous information and energy transfer.
  • Constrained codes enable the transmission strategy to be better adjusted to the receiver’s energy utilization pattern as compared to classical unstructured codes.
  • Interesting future work includes the investigation of nonbinary codes and multi-terminal scenarios

System Model

  • Where is the steady state distribution of the states of the constrained code and collects the steady state probabilities of the birth-death Markov process:


  • 1: “on” symbol; 0: “off” symbol
  • p10: probability of energy loss
  • The receiver’s energy utilization is modeled as a stochastic process Zi (Zi=1: energy required at time i)

[1] L. R. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT 2008), pp. 1612-1616, Toronto, Canada, Jul. 2008.

[2] P. Grover and A. Sahai, “Shannon meets Tesla: Wireless information and power transfer,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT 2010), pp. 2363-2367, Austin, TX, Jun. 2010.

[3] R. Zhang and C. Keong Ho, “MIMO broadcasting for simultaneous wireless information and power transfer,” in Proc. IEEE GLOBECOM 2011, pp. 1-5, Houston, TX, Dec. 2011.

[4] B. Marcus, R. Roth, P. Siegel, Introduction to Coding for Constrained Systems, available at:

[5] R. G. Gallager, Discrete Stochastic Processes, Kluwer, Norwell MA, 1996.

[6] E. Zehavi and J. K. Wolf, "On runlength codes," IEEE Trans. Inform. Theory, vol. 34, no. 1, pp. 45-54, Jan. 1988.

  • Proof: Based on renewal-reward argument [5]:
    • Renewal occurs every time the state of the constrained code Ci is equal to 0.