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Code Design for Relay Channels

Behnaam Aazhang

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Credits

Arnab Chakrabarti

Alexandre de Baynast

Ashutosh Sabharwal

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Basic Idea

Network-Channel

Explore all available dimensions

Signal Space

Network

SD

R

X1

U1

U2

D

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Focus

The gap

Information theory results

Algorithms

Protocols

Synchronization--CSI

Coding

Implementation

SD

R

SD

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Assumptions

Power constraint

AWGN channels with collinear path loss

PPttPMAMACBCRSS ))(1(

X1

X2Y1 = h12X1+ Z1

Y0= h10X1+ h20 X2+ Z0

Source

h10

Z1

Z0

h12

h20

Relay

Destination

,)1(1,1

SRDSR

dd

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Assumptions

Fading

AWGN relay codes could be used!

Channel (network) state information

Power control [Ahmed, et. al. 04]

Rate control [Ahmed, et. al. 05]

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Relay Operation

Full duplex

Half duplex

Relay will not receive and transmit same timeand same frequency band

SD

R

SD

R1st time slot 2nd time slot

Broadcast

Multiple access

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Relay Function

Fixed relaying

Decode and forward

Estimate and forward

Amplify and forward

Adaptive relaying

Selection

Incremental

decoNot to

Decode

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Relay Channel

Achievable rates

BSC, DMC, Binary AWGN, AWGN, fading

Code design

Turbo, LDPC

Convolutional with CRC

S D

R

X1

Y1

Y0

X2

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Coding for Relay Channels

BC mode

Relay can decode

Destination may not

MAC mode Relay re-encodes/transmits

Source transmits

New information Repeats previous information

Destination decodes correlation

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Low SNR: Stay with Binary

Binary relay

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Lessons at Low SNR

Binary

Coding

Half duplex Correlation 1

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LDPC

Binary linear block codes

Information vectoruis 1xK

Code vectorcis 1xn

The kxn generatorG produces codes c=uG

Sparse parity check matrix HcT=0

LDPC on bipartite graph

Variable nodes

Check nodes

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LDPC

Codes with sparse parity-check nodes

Cycles

Belief propagation

Degree profiles

Large n, only the distribution of node degrees

determines performance

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Coding Methodology

Variable nodes sent by R for MAC mode

Check nodes for relay MAC code

Variable nodes for BC mode

Check nodes for BC mode SR code

Additional check nodes for BC mode SD code

Variable nodes sent by S for MAC mode

Check nodes for source MAC code

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LDPC Codes

Structural relationship between

SR code in BC

SD code in MAC

SR subgraph of SD

Joint optimization of degree profiles for the two

codes

Additional constraints on degree distributions

Check nodes

Variable nodes

Modified density evolution.

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LDPC Codes for Relay

Modeling the densities of messages in

belief propagation

Gaussians

Noise thresholds

Code profiles

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High rateLow rate Beamforming

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First phase of

successive decoding

More iterations

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Challenges

SR link in BC mode high rate

Check node large degree

SD link in MAC mode low rate

Check node smaller degree

Variable nodes for BC mode

Check nodes for BC mode SR code

Additional check nodes for BC mode SD code

Subgraph

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Challenges

Belief propagation

Speed of convergence

Variance of degree profile

Reliability factor in messages

Weighted belief propagation

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TAP: A Mesh Network

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Research Platform

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Board at Work

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Progress

RF board--Daughtercard

2.4GHz ISM band

Half duplex

Baseband processing board FPGA basedmodular

Front end

Single carrier and OFDM

LDPC coding and decoding

Coherent combing!

Superposition decoding!

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Estimate and Forward

Relay transmits an

estimate of

information in MAC

mode Destination decodes

SD in MAC mode

with side information

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Estimate and Forward

Side information for D

Vector quantization

LDPC