Dirty paper code design using nested trellis

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Dirty Paper Code design based on

nested lattice codeand

Performance analysisBy:

Krishna Prasad Phelu

(067/MSI/609)

(102139)

1

Date: 13 November, 2011.


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Presentation outlines

Background

Problem definition

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Motivation

Figure: channel coding with side information.

Multi-terminal communication networks is one of

the fields of interest nowadays.

Channel coding with the side information (CCSI)

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Motivation: CCSI

1

log( )2

X

S Z

PC

P P

Capacity with side information (S) not known to both

encoder and decoder.

Capacity with S known to both encoder and decoder.

1

log( )2

X

Z

PC

P

Costa[1] proved in 1983 with S known only to encoder

1log( )

2

X

Z

PC

P

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Objective

To research on the DPC (dirty paper code), a special

case of CCSI.

To design DPC based on nested lattice code using

TCM/TCQ scheme.

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Problem definition

Power constraint on X:2

1

1 n

i X

i

X Pn

Received signal, Y=X+S+Z.

S is not known at the decoder but known non-casually

at encoder.

(0, )Z

Z N P Noise:

Figure: DPC channel.

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Problem definitionCont

Tx can not simply pre-subtract S from X.

Tx: X =X-S.Rx: Y = X + S + Z = X + Z

Direct pre-subtraction have sever power penalty.

power of X: E[X2]=PX+PS

PS can be much higher than PX

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Tomlinson-Harashima Precoding

(THP) 1D implementation of Dirty paper coding problem

Mod- operation is performed on X=(X-S)

Tx: X mod =(X-S) mod .

X is limited to interval

[0, )X If THP has no power penalty.

Equivalent to scalar quantization

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Figure: Power penalty due to direct pre-subtraction for same signal.

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Dirty paper coding (DPC)

Consider an entire sequence of S for higher

dimensional mod operation

Joint source and channel code design problem.

Zamir et al [4] proposed a practical nested code

scheme for joint source and channel code design.

TCQ/TCM is used.

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DPC using TCQ/TCM

X

X Z

P

P P

Figure: DPC Encoder using TCQ/TCM scheme.

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DPC using TCQ/TCM Contd

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C2 is the channel code (TCM)

C1 concatenated with C2 serves as a source code

(TCQ)

TCQ uses Viterbi algorithm to quantize S to U


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H is syndrome former of code C1. We use the viterbi decoder for decoding code from

C2

Figure: DPC Decoder using TCQ/TCM.

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Figure: A TCQ/TCM encoder (rate 1/2/3 encoder).

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The trellis structure change

depending on the data bits.

difference between the Viterbi

algorithm and nested code

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SF and ISF of C1 can be designed and implemented

using following sequential circuit.

Figure: Syndrome former of code C1 Figure: ISF of code C1

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[ ,1]T TH D 1( ) [0,1]TH


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Figure: DPC system simulation using TCQ/TCM scheme.

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Figure: DPC performance.

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Figure: Capacity gain that can be achieved with DPC.

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Recommendation

For better performance of DPC

Use convolutional codes with very high constraint

lengths

TCQ/TTCM scheme

Turbo-like TCQ/TTCM scheme

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Conclussion

DPC is efficient interference pre-cancelation scheme at

transmitter.

DPC can be used to achieve channel capacity limit,

without power penalty in Multi-terminal

communication networks (like MIMO).

DPC can be designed using nested code scheme.

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References:[1] M. Costa, Writing on dirty paper, IEEE Transactions on Information

Theory, vol. It-29, pp. 439-441, May 1983.

[2] Y. Sun, Y. Yang, A. D. Liveris, V. Stankovic, and Z. Xiong, "Near-Capacity Dirty- Paper Code Design: A Source-Channel CodingApproach", IEEE Transactions on Information Theory, vol. 55, no. 7,

July 2009.[3] Yong Sun, "Source-channel coding for robust image transmission and

for dirty paper coding", Ph.D. dissertation, Office of Graduate Studies ofTexas A&M University, Dec 2005.

[4] R. Zamir, S. Shamai, and U. Erez, Nested linear/lattice codes for

structured multiterminalbinning, IEEE Trans. Inform. Theory, vol. 48,pp. 1250-1276, June 2002.

[5] J. Chou, S. Pradhan, and K. Ramchandran, Turbo coded trellis-basedconstructions for data embedding: channel coding with sideinformation, in Proc. 35thAsilomar Conf. Signals, Systems andComputers, Pacific Grove, CA, November 2001, vol. 1, pp. 305309.

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References:[6] Y. Sun, M. Uppal, A. Liveris, S. Cheng, V. Stankovic, and Z. Xiong,

Nested turbo codes for the Costa problem, IEEE Trans.Communications, Vol. 56, pp. 1- 12,Janaury 2008.

[7] M. A. Uppal, " Code design for multiple-input multiple-output broadcastchannel, MSc Thesis, Texas A&M University, August 2006.

[8] P. Bhagawat, W. Wang, M. Uppal, G. Choi, Z. Xiong, M. Yeary and A.Harris, An FPGA Implementation of Dirty Paper Precoder, ICC 2007proceeding.

[9] W. Yu, D. Varodayan, and J. Cioffi, Trellis and convolutional precodingfor transmitter-based interference pre-subtraction, IEEE Trans.Commun., vol. 53, no. 7, pp. 12201230, Jul. 2005

[10] Zhenyu Tu, Jing Li, Blum, R.S., Compression of a Binary Sourcewith Side Information Using Parallelly Concatenated ConvolutionalCodes, vol. 1 pp. 46-50, January 2005.

[11] www.wikipedia.com/ dirty paper coding.

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Dirty paper code design using nested trellis

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