15 10 0241-00-004g Ldpc Code Performance and Complexity

8/8/2019 15 10 0241-00-004g Ldpc Code Performance and Complexity

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Q. Wang [USTB]Slide 1Submission Slide 1

Project: IEEE P802.15 Working Group forWireless Personal Area NetworksProject: IEEE P802.15 Working Group forWireless Personal Area Networks

(WPANs)(WPANs)

Submission Title: LDPCCode Performance and Complexity Comparing with Convolutional and

RS Code

Date Submitted: [01 Sept 2009]

Source: [Qin Wang ] Company [University of Science & Technology Beijing]

Address: [30 Xueyuan Road, Beijing 100083, China]

Voice:[[+8610-62334781], FAX: [], E-Mail:[[email protected]]

Re: Contribution to 15.4g FSK-PHY

Abstract:Analysis of the performance and complexity ofLDPC to the convolutional and RS codes

being considered for FEC.

Purpose: Contribution to the CPP merged PHY

Notice: This document has been prepared to assist the IEEE P802.15. It is offered as a basis

for discussion and is not binding on the contributing individual(s) or organization(s). The materialin this document is subject to change in form and content after further study. The contributor(s)

reserve(s) the right to add, amend or withdraw material contained herein.

Release: The contributor acknowledges and accepts that this contribution becomes the property

of IEEE and may be made publicly available by P802.15.


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Q. Wang [USTB]Slide 2Submission

LDPCCode Performance and Complexity

Co

mparing withCo

nvo

lutio

nal and RSCode


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Background

Simulation Methodology

Simulation Results

Packet Error Rate (PER) vs. SNR

LDPC

C

onvolutional coding gain difference vs. Block size Impact of estimated SNR

Computational complexity comparison between LDPC code and RScode

Summary and Conclusions

References

Outline


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Sept 2009 doc.: IEEE 802. 15-10-0241-00-004g


Background

Advanced coding candidates: BCH Code, Reed-Solomon Code, ConvolutionalCode, Turbo Code, Low Density Parity Check (LDPC) Code, etc.

Contribution IEEE 802.11-03/865 [1] introduced Low-Density Parity-Check(LDPC) codes as candidate codes for 802.11n applications. It showedpotential advantages of those codes over existing convolutional codes used in802.11a/g.

We compare the performance of example LDPC codes with the ConvolutionalCode in 802.11n, including Various frame lengths

Various code rates

Impact of estimated SNR

We compare the Computational Complexity of the LDPC with the RS code inDVB-C.

In this report, the performance comparison under AWGN channel is addressedonly. In the next related submission, emphasis will be on performancecomparison under other channel model.


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Simulation Methodology - General

Modulation BPSK

BPS

K

Coding Rate (R) 1/2 2/3

PHY model with BPSK constellation. Simulation included:

Channels simulated:

AWGN channel. This implementation utilized the MATLAB code.

Simulation scenario assumed:

All packets detected, ideal synchronization, no frequency offset

Ideal front end, Nyquist sampling frequency

Simulation Methodology - General


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General FEC:

Code lengths: 648, 1296 bits, chosen based on 802.11n standard [2]

Code rates: 1/2, 2/3 (as in 802.11n)

Convolutional codes:

Viterbi decoding algorithm

LDPC codes:

Iterative Sum-Product decoding algorithm (BP) with 20 iterations

Concatenated codewords for longer packets

Simulation Methodology - FEC


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Channel Model: AWGN

Modulation: BPSK

Simulation Results: PER vs. SNR

0 1 2 3 4 5 6 7 8 9 1010

-5

10-4

10-3

10-2

10-1

100

SNR (dB)

PER

Pack et Error Rate (PER) vs. SNR under AW GN Channel

LDPC Code wi th pac ket length 648, coding rate 1/2LDPC Code wi th pac ket length 648, coding rate 2/3

LDPC Code wi th pac ket length 1296, coding rate 1/2

LDPC Code wi th pac ket length 1296, coding rate 2/3

Convolut ional Code wi th pac ket length 648, coding rate 1/2





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Simulation Results:(LDPC_coding_gain Convolutional_Coding_Gain) vs. Block Size

Modulation: BPSKCode rate: 1/2

Channel model: AWGNCoding gain difference measured at PER of 10-2

0 200 400 600 800 1000 1200 14002. 5

3

3. 5

4

4. 5

5

5. 5

6

6. 5

Block s ize (b its )

Coding

gain

difference

(dB)

LDPC-Convolutional Coding gain difference at PER of 10 -2 vs. block size


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Simulation Results: Impact of estimated SNR

-2 0 2 4 6 8 10 12 14 1610

-4

10-3

10-2

10-1

100

10log10(Est-SNR/Ideal-SNR)

BER

w i

i

l SN R Es t im

to r

w ith non-i

l SN R Es t im

to r

x-axis indicates:

SNRideal

SNRestimated

_

_log10 10!V

Where ideal_SNR denotes the

variable used to generate AWGN

and estimated_SNR denotes the

variable got by SNR estimation

algorithm.

Modulation type: BPSK

Coding rate: 1/2

Impact ofestimated SNR

Code length after encoder: 1944


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Complexity Comparison between LDPC Code and RS Cod

According to reference [3], the decoding complexity for one iteration of the

BP decoding is:

Addition operation:Multiplication operation:

where N is the code length ofLDPC code; J is the number ofones in each

column.

)13( JN

)23(4 JN

According to reference [4], the decoding complexity for RS decoding is:

Addition and multiplication operation in Galois Field:

where t is correct ability of RS code; n is code length; u is the number of

errors for one packet.

222)1(2 unutunt

Conclusion: The computational complexity ofLDPCCode increases

linearly with incensement of block size as that of RS Code.

For both LDPC decoder and RS decoder, the implementation complexity heavily

depends on the decoding algorithm, e.g. BP/log-BP/min-sum for LDPC and

architecture & logic design. Thus, we only discuss the computational complexity in

terms of big-O.


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LDPC codes offer considerable performance advantages over the existingconvolutional codes.

With the proper designLDPC

codes can be made flexible enough in terms ofcoding rate and block size, so as to satisfy demands of 802.15.4g applications.

The decoding algorithm ofLDPC presented here is not sensitive to the accuracyof SNR estimating.

The computational complexity ofLDPCCode increases linearly withincensement of block size as that of RS Code.

Summary and Conclusions


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References

[1] IEEE 802.11-03/865r1, LDPC FEC for IEEE 802.11n Applications, EricJacobson, Intel, November 2003.

[2] IEEE Std 802.11n/D2.00, Part 11: Wireless LAN Medium Access Control(MAC) and Physical Layer (PHY) Specifications, Enhancements forHigherThroughput.

[3] Marc P. C. Fossorier, Miodrag Mihaljevic, Reduced Complexity IterativeDecoding ofLow-Density Parity Check Codes Based on BeliefPropagation,IEEE Transactions on Communications, Vol. 47, No. 5, May, 1999.

[4] Hao Yongjie, Jiang jianguo, Improved Time-domain Decoding Algorithm ofRS Code, Computer Engineering, Vol. 34, No. 14, July 2008.

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15 10 0241-00-004g Ldpc Code Performance and Complexity

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