constellation shaping for bit-interleaved coded...

Constellation Shaping for Bit-Interleaved Coded APSK

Dr. Matthew C. Valenti, Xingyu Xiang

Lane Department of Computer Science and Electrical EngineeringWest Virginia University

ICC - June 6, 2011

Xingyu Xiang ( Lane Department of Computer Science and Electrical Engineering West Virginia University )Constellation Shaping ICC - June 6, 2011 1 / 25

Outline

1 Introduction

2 Constellation Shaping

3 Optimization Results

4 Implementation

5 Conclusion


Introduction

Outline

1 Introduction



4 Implementation

5 Conclusion


Introduction

Two Definitions

Constellation Shaping

Idea: transmit constellation signal points with lower energy morefrequently than those with higher energy

Goal: save transmit power, or achieve performance gain under thesame transmit power

How: we use non-linear short length shaping code in our paper

APSK (Amplitude phase-shift keying)

Included in DVB-S2 (second generation of the Digital VideoBroadcasting Satellite) and other communication standards

both spectral and energy efficient, well suited for nonlinear channels


Introduction

Background

Information–theoretic Optimization Practical Implementation

“System implementation” ‐‐‐‐‐‐‐

Stephane Y. Le Goff, et al. in

“Modulation Optimization”‐‐‐‐‐‐‐‐

R D G d i K Li li i Stephane Y. Le Goff, et al. in reference [5, 6]R. D. Gaudenzi, K. Liolis in reference [2], [3], respectively

J i t ti i ti d t l t i l ti

Our work

Joint optimization and actual system simulation

‐‐‐‐‐‐‐‐ICC 2011


Introduction

General flowchart

System with Optimum parametersconstellation shaping

(non‐uniform APSK modulation)

Capacity Analysis

Optimum parameters

modulation) Simulation Results

comparison

Performance Gain(Shaping gain)

Capacity A l i

System with uniform APSK

comparison ( p g g )

Analysismodulation


Introduction

Mutual Information( MI ) and Channel Capacity

MI between two random variables, X and Y is given by,

I(X;Y ) = E

[log

(p(Y |X)p(Y )

)]Channel Capacity is the highest rate at which information can betransmitted over the channel with low error probability. Given thechannel and the receiver, capacity is defined as

C = maxp(x)

I(X;Y )


Introduction

The mutual information between output Y and input X is

I(X;Y ) =

M−1∑j=0

p(xj)

∫p(y|xj) log2

p(y|xj)p(y)

dy.

M - number of input symbols.The integration can be solved using Gauss - Hermite Quadratures inAWGN channel.

-10 -5 0 5 10 15 20 250

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

SNR(dB)

Info

rmat

ion

Rat

e

Information rate results of uniform 32-APSK modulationgenerated by two methodologies

By Monte-Carlo SimulationBy Gauss - Hermite Quadratures



Outline

1 Introduction



4 Implementation

5 Conclusion



Constellation Shaping for APSK

Our strategy is from S. LeGoff, IEEE T. Wireless, 2007.

Use shaping code to choose low-energy symbols more frequently

For a fixed average energy, shaping strategy spreads out the symbols

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

(a) 16apsk

-2 -1 0 1 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

(b) 32apsk

( Es = ΣM−1i=0 p(xi)Ei = 1)



Shaping Encoder

We design the shaping encoder to output more zeros than ones. Oneexample is,

Table: (5,3) shaping code.

3 input data bits 5 output codeword bits0 0 0 0 0 0 0 00 0 1 0 0 0 0 10 1 0 0 0 0 1 00 1 1 0 0 1 0 01 0 0 0 1 0 0 01 0 1 1 0 0 0 01 1 0 0 0 0 1 11 1 1 1 0 1 0 0

p0: the probability of 0 in the codeword table, (p0 =3140 above)

p1: the probability of 1 in the codeword table, (p1 =940 above)



16/32 APSK symbol-labeling map based on DVB-S2standard

B2

00111(1011)

00101(1010)

10000(0100) B1

B2

B1

00001(1000) B2

00110(0011)

10001(1100)

B3

01110

C2

11110B

301010

D11011

D11001

D11101

C2

11000 B

301000

D11111

C3

01101

C2

11100

10110(0111)

B3

01100

10111(1111)

A

10010(0101)

00010(0001)

B1

B1

10100(0110)

A

B2AA

00000(0000)

C3

01001

C1

C1

C1

C2

11010

00011(1001)

C1

10011(1101)

C3

01011

00100(0010)

C3

01111

10101(1110)



Shaping Operation

Channel101011101101 100101100110000100Channel Encoder

101011101101Bit Separation

1100

1100

1001

10000

110

ENC

00

0bitrd3

1

0101

bitnd20 0

00

0bitst1

0

0bit (MSB)th0

0



32-APSK results with continuous output optimized over p0

-10 -5 0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Es/No (dB)

mut

ual i

nfor

mat

ion

32APSK in AWGN

Uniformg=1g=2g=3

11.4 11.6 11.8 123.83

3.84

3.85

3.86

3.87

3.88


Optimization Results

Outline

1 Introduction



4 Implementation

5 Conclusion



Algorithm used for jointly optimization

p0

γg

Capacity Results Comparison

Optimized parameters

1 Fix the SNR, radius ratios γ,number of shaping bits(g).

2 Vary p0 from 0.5 to 0.99 inincrements of 0.005.

3 For each value of p0, compute thecorresponding information rate.

4 Go over the information rate arrayand find the highest informationrate, record the values of p0 andγ, g that produce it.



Shaping Gain and its evaluation

0 1 2 3 4 5-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Information Rate

Shap

ing

Gai

n (d

B)

32-APSK shaping gain with different shaping bits

g=1g=2g=3

(3.99, 0.3077)

(4.1, 0.175)

(3.88, 0.2648)

-10 0 10 20 300

1

2

3

4

5

Es/No (dB)m

utua

l inf

orm

atio

n

11.211.411.611.8 12

3.8

3.9

4

uniformshaping g=1



optimum p0 and γ

-10 -5 0 5 10 15 20 25 30

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Es/No

optim

al p

0

Optimal p0 of 32APSK in AWGN channel

Uniformg=1g=2g=3

(a) optimal p0 of 32APSK

-10 -5 0 5 10 15 20 25 301

1.5

2

2.5

3

3.5

4

4.5

5

Es/Noop

timal

in

dex

Optimal index of 32APSK in AWGN channel

Uniformg=1g=2g=3

(b) optimal γ index of 32APSK


Implementation

Outline

1 Introduction



4 Implementation

5 Conclusion


Implementation

Implementation

BICM-ID (bit-interleaved coded-modulation with iterative decoding)System

f iInformation sequence

Turbo BitShaping EncoderTurbo

EncoderBit

SeparatorEncoder Modulator

Channel

b

Estimated bit probabilities

Shaping

DemodulatorTurbo DecoderBit

SeparatorDecoder

feedback‐1

FeedbackInformation


Implementation

Optimum Parameters

Maximum shaping gain achieved in AWGN for M-APSK with g shapingbits. The optimized p0 and γ are shown. The related information rate andSNR value(in dB) are also listed.

M g R Eb/N0 (capacity value) gain p0 γ

161 3.09 4.714 dB 0.091 dB 0.623 2.702 2.95 4.077 dB 0.322 dB 0.688 2.57

321 3.88 5.915 dB 0.265 dB 0.716 {2.64,4.64}2 4.06 6.517 dB 0.175 dB 0.623 {2.53,4.30}3 3.89 5.898 dB 0.310 dB 0.656 {2.53,4.30}


Implementation

BER Curves

Parameters used for the 32-APSK simulation

γ R Rc Rs Eb/N0 (capacity value){2.64,4.64} 3.849 5000/6491 1 6.092 dB3.858 5000/6190 7/9 5.834 dB

BER curves of 32-APSK in AWGN at rate R=3.85 bits/symbol

5 5.5 6 6.5 7 7.5 8 8.5 910 5

10 4

10 3

10 2

10 1

100

Eb/N0 in dB

BER

Uniform BICMUniform BICM IDBICM ID w/ ShapingBICM w/ Shaping


Conclusion

Outline

1 Introduction



4 Implementation

5 Conclusion


Conclusion

Conclusion

The simple constellation-shaping strategy considered in this paper canachieve shaping gains of about 0.6 dB.

This work can be further extended to include LDPC code, which willmake the system fully compatible with DVB-S2 standard

Extrinsic information transfer chart (EXIT chart) can be used tooptimize the parameter of the error correction code


Conclusion Questions


IntroductionConstellation ShapingOptimization ResultsImplementationConclusionQuestions

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