Concluding Remarks

Coding for joint energy and information transferA. 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

Joint Energy and Information TransferNumerical

Results Conventional assumption: the energy received from an

information bearing signal cannot be reused.

Exceptions:

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

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.

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.

References

System Model

Background and Contribution

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

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

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:

System Model

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)

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: 1 min ,i max i i iB B B Y Z

1 , 1 and 0i i max i iO B B Y Z

Underflow event:

1 0, 0 and 1i i i iU B Y Z

Probabilities of underflow and overflow:

1 1

1 1Pr sup E Prlim l msup Ei

n n

i ii in n

U On n

U O

Unconstrained codes

Constrained codes

max

10

1010

0

( , , ) : 0,1 such that

H( ) H( )1

O( ), U( )

where

Pr (1 ) O( ) and

Pr (1 ) U(

)

{

}

of uf y

yy

of y uf y

B y y

y y

R P P p p

pR p p

p

P p P p

p q p

p q p

O

U

max max

1 1

1

10

10

( , , ) : , ,..., 0,1 such that

((1 )(1 ))

(1 )H( )

{ n

of uf d d k

k

j jj d

j

B B

of

R P P p p p

R H p p

p p

E OP

E I

P

max

0 and }

B

b bb

uf

E UP

E I

max 101 0.1, 20, 0 ,R Bq p

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.

[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: http://www.math.ubc.ca/~marcus/Handbook/

[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.

Overflow event:

max0 1 102, 0, 0q q B p

0 13, 0.01, 0k R q q

Analysis Memoryless process Zi , i.e., q1=1- q0

Achievable joint energy and information transfer rate:

Achievable joint energy and information transfer rate:

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:

b

Proof: Based on renewal-reward argument [5]:

Renewal occurs every time the state of the constrained code Ci is equal to 0.

for [0, ]j j k