1. Q. Wang [USTB], B. Rolfe [BCA]
doc.: IEEE g
Sept 2009
Project: IEEE P Working Group for Wireless Personal Area Networks (WPANs)
Submission Title: LDPC Code 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 , China]
Voice:[[ ], FAX: [],
Re: Contribution to 15.4g FSK-PHY
Abstract: Analysis of the performance and complexity of LDPC 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 P It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in 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 P
Q. Wang [USTB], B. Rolfe [BCA]

2. LDPC Code Performance and Complexity Comparing with Convolutional and RS Code

3. Outline Background Simulation Methodology Simulation Results
Packet Error Rate (PER) vs. SNR
LDPC – Convolutional coding gain difference vs. Block size
Impact of estimated SNR
Computational complexity comparison between LDPC code and RS code
Summary and Conclusions
References

4. Background
Advanced coding candidates: BCH Code, Reed-Solomon Code, Convolutional Code, Turbo Code, Low Density Parity Check (LDPC) Code, etc.
Contribution IEEE /865 [1] introduced Low-Density Parity-Check (LDPC) codes as candidate codes for n applications. It showed potential advantages of those codes over existing convolutional codes used in a/g.
We compare the performance of example LDPC codes with the Convolutional Code in n, including
Various frame lengths
Various code rates
Impact of estimated SNR
We compare the Computational Complexity of the LDPC with the RS code in DVB-C.
In this report, the performance comparison under AWGN channel is addressed only. In the next related submission, emphasis will be on performance comparison under other channel model.

5. Simulation Methodology - General Simulation Methodology - General
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
Modulation
BPSK
Coding Rate (R)
1/2
2/3

6. Simulation Methodology - FEC
General FEC:
Code lengths: 648, 1296 bits, chosen based on n standard [2]
Code rates: 1/2, 2/3 (as in n)
Convolutional codes:
Viterbi decoding algorithm
LDPC codes:
Iterative Sum-Product decoding algorithm (BP) with 20 iterations
Concatenated codewords for longer packets

7. Simulation Results: PER vs. SNR
Channel Model: AWGN
Modulation: BPSK

8. IEEE / k
September 2003
Simulation Results:
(LDPC_coding_gain– Convolutional_Coding_Gain) vs. Block Size
Modulation: BPSK
Code rate: 1/2
Channel model: AWGN
Coding gain difference measured at PER of 10-2
Brian Johnson, Nortel Networks

9. Simulation Results: Impact of estimated SNR
x-axis indicates:
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
Code length after encoder:
1944

10. Complexity Comparison between LDPC Code and 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.
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 of LDPC code; J is the number of ones in each
column.
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.
Conclusion: The computational complexity of LDPC Code increases linearly with incensement of block size as that of RS Code.

11. Summary and Conclusions
IEEE / k
September 2003
Summary and Conclusions
LDPC codes offer considerable performance advantages over the existing convolutional codes.
With the proper design LDPC codes can be made flexible enough in terms of coding rate and block size, so as to satisfy demands of g applications.
The decoding algorithm of LDPC presented here is not sensitive to the accuracy of SNR estimating.
The computational complexity of LDPC Code increases linearly with incensement of block size as that of RS Code.
Brian Johnson, Nortel Networks

12. IEEE / k
September 2003
References
[1] IEEE /865r1, “LDPC FEC for IEEE n Applications”, Eric Jacobson, Intel, November 2003.
[2] IEEE Std n/D2.00, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Enhancements for Higher Throughput.
[3] Marc P. C. Fossorier, Miodrag Mihaljevic, “Reduced Complexity Iterative Decoding of Low-Density Parity Check Codes Based on Belief Propagation”, IEEE Transactions on Communications, Vol. 47, No. 5, May, 1999.
[4] Hao Yongjie, Jiang jianguo, “Improved Time-domain Decoding Algorithm of RS Code”, Computer Engineering, Vol. 34, No. 14, July 2008.
Brian Johnson, Nortel Networks