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
Joint Energy and Information Transfer

Conventional assumption: the energy received from an information bearing
signal cannot be reused.


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.
Exceptions:
Passive RFID

Numerical Results
Body area networks
Battery evolution:

Overflow event:

Underflow event:
Point-to-point channel

Probabilities of underflow and overflow:

4-PAM signal {-3,-1, 1,3}

Maximum information: Rate: 2bit/symbol, Avg. Energy: 5

Maximum energy: Rate: 1bit/symbol, Avg. Energy: 9


 Matching the code structure
to the receiver’s energy
utilization model:
 Small q0: type-0 (d; k)-RLL
codes with a small k.
Oi  1Bi  Bmax , Yi  1 and Zi  0
Example:


Bi 1  min Bmax ,  Bi  Yi  Zi 

q1  0, R  0.1, Bmax  2, p10  0
 Large q0: larger k is required
Ui  1Bi  0, Yi  0 and Zi  1
q0  q1  0, Bmax  2, p10  0
n
1
Pr U  lim sup  E U i 
n i 1
n
n
1
Pr O   limsup  E Oi 
n i 1
n
 Small rate: k=1 is sufficient
 Larger rate: increase the value
of k, while keeping d as small
as possible
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.



 By appropriately choosing d
and k, RLL codes can provide
relevant advantages.
k  3, R  0.01, q0  q1  0
Classical codes vs. constrained run-length limited (RLL) codes
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:



Analysis

Memoryless process Zi , i.e., q1=1- q0

Achievable joint energy and information transfer
rate:
of , Puf ) :  p y   0,1  p10  such that
R  H( p y ) 
1  p10
Constrained codes
of
{( R , P
py
 Achievable joint energy and information transfer rate:
{( R , P
Unconstrained codes
System Model
H( p10 )
Pof  O( p y ), Puf  U( p y )}
, Puf ) :  P  pd , pd 1 ,..., pk 1   0,1 such that
n
k 1
R
  H ((1  p )(1  p
j d
j
Pr  U   0 (1  p y )q
j
10
))
 (1  p j )H( p10 )
 B E OB 
Pof 
max
where
Pr O    Bmax p y (1  q)
E I 
max
Bmax
O( p y ) and
U( p y )

and Puf  b 0
b
E U b 
E I 
}
Where  j for j  [0, k ]is the steady state distribution of the
states of the constrained code and  bcollects the steady state
probabilities of the birth-death Markov process:



 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.
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)
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 multiterminal scenarios
References
[1]
[2]
 Proof: Based on renewal-reward argument [5]:
Renewal occurs every time the state of the constrained code Ci
is equal to 0.
[3]
[4]
[5]
[6]
L. R. Varshney, “Transporting information and energy simultaneously,” in Proc.
IEEE Int. Symp. Inform. Theory (ISIT 2008), pp. 1612-1616, Toronto, Canada,
Jul. 2008.
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.
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.
B. Marcus, R. Roth, P. Siegel, Introduction to Coding for Constrained Systems,
available at: http://www.math.ubc.ca/~marcus/Handbook/
R. G. Gallager, Discrete Stochastic Processes, Kluwer, Norwell MA, 1996.
E. Zehavi and J. K. Wolf, "On runlength codes," IEEE Trans. Inform. Theory, vol.
34, no. 1, pp. 45-54, Jan. 1988.