X1 X2

Encoding:

Bits are transmitting over 2 different independent channels. Rn bits Correlation channel (1-R)n bits Wireless channel

Code Design:

Possible Design Methodologies:

1)Design an LDPC code for the equivalent channel

2)Design a non-uniform LDPC code

Use ensemble of bipartite graphs, where, is the variable node degree distribution of each set and is the check node degree distribution.

),( g )}(),({ 21 xx )(xi )(x

Simulation:

0.

H(X2|X1)

ber

P=0.11 RX2=H(p)=0.5

LDPC rate=2/3, n=1000

}0993.01422.07585.0,{)( 8432 xxxxx }5.0,5.0{)( 1110 xxx

Extensions of Distributed Source coding of correlated sources

Mina Sartipi, Nazanin Rahnavard, Faramarz Fekri

Abstract

Energy-Efficient Data Gathering and Broadcasting in Sensor Networks using Channel Codes

Goal: Energy-efficient and reliable communication in wireless sensor networks

Communication involves: Data Gathering (Sensors to sink)

Multicasting / Broadcasting (Sink to sensors)

Data Gathering: Correlated Data

Distributed Source Coding

Multicasting / Broadcasting Redundant Transmission Correlated Data

Rateless Code

RX1

RX2

A

B

C

H(X2|X1)

H(X2)

H(X1|X2) H(X1)

+

Corner Point:RX1 = H(X1)

RX2 = H(X2 | X1)

Encode X2 as follows:

X2 is fed into a rate R systematic LDPC encoder.

PX2 , the corresponding parity bits, is sent through the wireless channel.

RX2=1/R-1 bit per input bit.

RX1 H(X1|X2)

RX2 H(X2|X1)

RX1 +RX2 H(X1,X2)

Correlation Model:

Distributed Source Coding on Corner Points:

X1, X2 : I.I.D binary sequence; Prob [ Xi =0] = Prob [ Xi=1]=1/2.

Prob [ X1 X2 | X1 ]=p

BSCp

Slepian-Wolf rate region for two sources:

Distributed Source coding of correlated sources using LDPC Codes

Motivation:

Distributed Source Coding:

Many sensors have highly correlated data that is slowly varying.

How do we exploit correlation structure with low-power algorithms?

X2 22 XX ˆEncoder Decoder

X1

Goal: Compressing X2

With the knowledge that X1 is present at the decoder

Without communicating with X1

c1

(X2 ,PX2 )

k

(1-R)n

Decoder P'X2

PX2

X2

Channel

X1

Encoder

X2

CorrelationChannel

Wireless

n

Systematic

Channel Rate R

Rn

c2

X2

Non-uniform Channels

Modeling Distributed Source Coding with Parallel Channels:

method 2 outperforms method 1

Scaling to more than two correlated sources DSC at arbitrary rate on Slepian-Wolf rate region DSC with unknwon correlation parameter

Future activity: Energy-efficient broadcasting

Motivation An easy, energy-efficient, and scalable broadcasting scheme Providing reliability with little penalty Low complexity Require no optimization and no topology information

Proposed Approach Use an efficient erasure coding (rateless coding) to recover for losses

Channel parameters are different and unknown A source can generate potentially infinite supply of encoding packets from the original data Any receiver collects as many packets as it needs to complete the decoding Receivers are at one hop distance from the sender Extra cares needed for multi-hop wireless networks!

BEC (2)

Rec 1

Rec 2

Rec i

Rateless coding

0

0

1

1

BEC (1)

BEC (i)0

Future workFuture work

Rateless (Fountain) CodesRateless (Fountain) Codes

Distributed source coding Implement the algorithm on testebed to evaluate the real energy saving benefits (considering the power usage for encoding/decoding) Study the extensions of DSC

Multicasting / Broadcasting: Propose an energy-efficient method for broadcasting / multicasting Apply distributed source coding to eliminate redundancy Need route optimization while having load balancing