doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 1 LDPC vs. Convolutional Codes: Performance and Complexity Comparison March 2004 Aleksandar Purkovic, Sergey Sukobok, Nina Burns Nortel Networks (contact:

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 2 Background Codes used for comparison Candidate LDPC code details Methodology Performance/Complexity comparison Summary and Conclusions References Outline

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 3 Several advanced coding candidates so far at the n: –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 a/g) with two other codes: –Candidate LDPC codes –More complex (256-state) convolutional code Background

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 4 Following codes were compared in terms of performance and complexity: –64-state (6 delay elements) convolutional codes (IEEE a/g) – CC6 –256-state (8 delay elements) convolutional codes (ETSI EN ) – 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) Codes used for comparison

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 5 Algebraic construction of the parity check matrix: –Based on the  -rotation approach first described in [11] –Extended for code rates up to 7/8; other code rates (<7/8) achieved by shortening –Longer blocks encoded by concatenating Parity check matrix Candidate LDPC codes details Building blocks (examples): Parity check matrix is expandable by replacing each non-zero element by a small permutation matrix

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 6 Performance evaluation –PHY model based on the a 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 (add’s, xor’s, 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 Methodology

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 7 Performance/Complexity Comparison: 40-byte packets

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 8 Performance/Complexity Comparison: 1000-byte packets

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 9 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. Summary and Conclusions

doc.: IEEE /xxxxr0 Submission March 2004 Aleksandar Purkovic et al, Nortel NetworksSlide 10 References [1] IEEE n, “Turbo Codes for IEEE n,” Brian Edmonston et al,.January 2004 [2] IEEE /312r0, “Towards IEEE HDR in the Enterprise,” Sebastien Simoens et al, Motorola, May 2002 [3] IEEE /708r0,”MIMO-OFDM for High Throughput WLAN: Experimental Results,” Alexei Gorokhov et al, Philips, November 2002 [4] IEEE /0014r1,”Different Channel Coding Options for MIMO-OFDM n,” Ravi Mahadevappa et al, Realtek, January 2004 [5] IEEE /865r1, “LDPC FEC for IEEE n Applications”, Eric Jacobson, Intel, November [6] IEEE /0071r1, “LDPC vs. Convolutional Codes for n Applications: Performance Comparison,” Aleksandar Purkovic et al, Nortel, January 2004 [7] IEEE /232r0, “Extended Data Rate a, Marcos Tzannes et al,” March 2002 [8] IEEE /96r0, “On The Use Of Reed Solomon Codes For n,” Xuemei Ouyang, Philips, January 2004, [9] IEEE /0207r0, “Simplifying MAC FEC Implementation and Related Issues,” Jie Liang et al, TI, March 2002 [10] IEEE /239r0, “MAC FEC Performance,” Sean Coffey et al, TI, March 2002 [11] R. Echard et al, “The  -rotation low-density parity check codes,” In Proc. GLOBECOM 2001, pp , Nov [12] IEEE Std a-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 /940r1, “TGn Channel Models”, TGn Channel Models Special Committee, November [14] Laurent Schumacher, “WLAN MIMO Channel Matlab program,” January 2004, version 3.3.