LDPC vs. Convolutional Codes: Performance and Complexity Comparison

1
LDPC vs. Convolutional Codes Performance and
Complexity Comparison

• March 2004
• Aleksandar Purkovic, Sergey Sukobok, Nina Burns
• Nortel Networks
• (contact apurkovi_at_nortelnetworks.com)

2
Outline

• Background
• Codes used for comparison
• Candidate LDPC code details
• Methodology
• Performance/Complexity comparison
• Summary and Conclusions
• References

3
Background

• Several advanced coding candidates so far at the
  802.11n
• Turbo codes, 1, 2, 3, 4
• LDPC codes, 5, 6, 4
• Convolutional codes, 4
• Trellis Coded Modulation, 7
• Concatenated Reed-Solomon/convolutional codes,
  8
• MAC level FEC (Reed-Solomon), 9, 10
• This submission compares in terms of
  performance/complexity existing 64-state
  convolutional codes (from 802.11a/g) with two
  other codes
• Candidate LDPC codes
• More complex (256-state) convolutional code

4
Codes used for comparison

• Following codes were compared in terms of
  performance and complexity
• 64-state (6 delay elements) convolutional codes
  (IEEE 802.11a/g) CC6
• 256-state (8 delay elements) convolutional codes
  (ETSI EN 301 958 ) CC8
• LDPC codes (based on algebraic construction)
• Figure below outlines performance of the
  considered codes for a medium packet size of 200
  bytes (floating-point simulation results)

5
Candidate LDPC codes details

• Algebraic construction of the parity check
  matrix
• Based on the p-rotation approach first described
  in 11
• Extended for code rates up to 7/8 other code
  rates (lt7/8) achieved by shortening
• Longer blocks encoded by concatenating
• Parity check matrix

• Building blocks (examples)

• Parity check matrix is expandable by replacing
  each non-zero element by a small permutation
  matrix

6
Methodology

• Performance evaluation
• PHY model based on the 802.11a spec, 12
• QPSK, rate 1/2, packet length 40 bytes
• QPSK, rate 3/4, packet length 1000 bytes
• Channels simulated
• AWGN channel
• Fading Channel Model D with power delay profile
  as defined in 13, NLOS, without simulation of
  Doppler spectrum. This implementation utilized
  the reference Matlab code 14.
• Simulation scenario assumed
• Ideal channel estimation
• All packets detected, ideal synchronization, no
  frequency offset
• Ideal front end, Nyquist sampling frequency
• Complexity estimation
• Number of elementary operations (adds, xors,
  etc.), RAM, ROM
• Soft information represented with 8 bits
• Convolutional codes Viterbi decoding algorithm
• LDPC codes
• Iterative Min-Sum decoding algorithm with maximum
  of 20 iterations
• Concatenated codewords for longer packets

7
Performance/Complexity Comparison 40-byte packets
8
Performance/Complexity Comparison 1000-byte
packets
9
Summary and Conclusions

• Comparison in terms of performance and complexity
  of LDPC and two convolutional codes was presented
  in this contribution.
• More advanced codes (LDPC and CC8) do perform
  better at the cost of reasonable increase in
  complexity.
• LDPC codes have an inherent feature which
  eliminates need for the channel interleaver
  (5,6) this offsets somewhat increased
  complexity.
• Decoder of LDPC codes has embedded feature of
  exiting from the iteration loop once a codeword
  has been found, which means that the average
  number of iterations is less than the maximum.
  This in turns has positive effect on the power
  consumption.

10
References

• 1 IEEE 802.11-04-0003-00-000n, Turbo Codes for
  IEEE 802.11n, Brian Edmonston et al, .January
  2004
• 2 IEEE 802.11-02/312r0, Towards IEEE802.11 HDR
  in the Enterprise, Sebastien Simoens et al,
  Motorola, May 2002
• 3 IEEE 802.11-02/708r0,MIMO-OFDM for High
  Throughput WLAN Experimental Results, Alexei
  Gorokhov et al, Philips, November 2002
• 4 IEEE 802.11-04/0014r1,Different Channel
  Coding Options for MIMO-OFDM 802.11n, Ravi
  Mahadevappa et al, Realtek, January 2004
• 5 IEEE 802.11-03/865r1, LDPC FEC for IEEE
  802.11n Applications, Eric Jacobson, Intel,
  November 2003.
• 6 IEEE 802.11-04/0071r1, LDPC vs.
  Convolutional Codes for 802.11n Applications
  Performance Comparison, Aleksandar Purkovic et
  al, Nortel, January 2004
• 7 IEEE 802.11-01/232r0, Extended Data Rate
  802.11a, Marcos Tzannes et al, March 2002
• 8 IEEE 802.11-04/96r0 , On The Use Of Reed
  Solomon Codes For 802.11n, Xuemei Ouyang,
  Philips, January 2004,
• 9 IEEE 802.11-02/0207r0, Simplifying MAC FEC
  Implementation and Related Issues, Jie Liang et
  al, TI, March 2002
• 10 IEEE 802.11-02/239r0, MAC FEC Performance,
  Sean Coffey et al, TI, March 2002
• 11 R. Echard et al, The p-rotation low-density
  parity check codes, In Proc. GLOBECOM 2001, pp.
  980-984, Nov. 2001
• 12 IEEE Std 802.11a-1999, Part 11 Wireless LAN
  Medium Access Control (MAC) and Physical Layer
  (PHY) Specifications, High-speed Physical Layer
  in the 5 GHz Band
• 13 IEEE 802.11-03/940r1, TGn Channel Models,
  TGn Channel Models Special Committee, November
  2003.
• 14 Laurent Schumacher, WLAN MIMO Channel
  Matlab program, January 2004, version 3.3.