Structured LDPC Codes as an Advanced Coding Scheme for 802.11n

1. Structured LDPC Codes as an Advanced Coding Scheme for 802.11n September 2004 Aleksandar Purkovic, Sergey Sukobok, Nina Burns, Levent Demirekler, Zhaoyun Huang Nortel Networks (contact: apurkovi@nortelnetworks.com) Aleksandar Purkovic et al, Nortel Networks

2. Background • Several advanced coding candidates so far at the 802.11n: • Turbo codes, [1], [2], [3], [4] • LDPC codes, [5], [6], [4], [16] • Convolutional codes, [4] • Trellis Coded Modulation, [7] • Concatenated Reed-Solomon/convolutional codes, [8] • MAC level FEC (Reed-Solomon), [9], [10] • This submission introduces a partial proposal to include structured LDPC codes as an advanced coding scheme for 802.11n Aleksandar Purkovic et al, Nortel Networks

3. Motivation for choosing structured LDPC codes • LDPC codes have matured and become a strong advanced coding candidate due to a significant activity in the coding community, especially during the last several years • LDPC codes are proved to achieve coding gains comparable to turbo codes • Benefits of LDPC codes as a serious advanced coding candidate were introduced to the 802.11n in the past ([5], [6], [16]) • Main problem associated with the LDPC decoder design is usually requirement for highly irregular hardware interconnectivity • Considerable effort has been invested in finding effective hardware architectures in order to benefit from the sparseness of the LDPC parity check matrix • LDPC codes based on a structured parity check matrix greatly reduce decoding hardware bottlenecks with tolerable performance penalty • LDPC parity check matrices with lower (upper) triangular segments enable efficient encoding, eliminating another obstacle, typically associated with implementation of LDPC codes Aleksandar Purkovic et al, Nortel Networks

4. Construction of the structured LDPC parity check matrix based on –rotation • This construction is based on the -rotation (rotation of a square permutation matrix) approach, first described in [11] • Example, base rate 1/2 matrix: H = [Hd|Hp] • Permutation matrices B, C, D, are obtained by 90o, 180o, 270o counterclockwise rotations of the permutation matrix A, respectively Aleksandar Purkovic et al, Nortel Networks

5. General form of the base parity check matrix • Notations: K – information block length, N – codeword length, M – number of parity check bits (M = N-K) • H = [Hd,q|…|Hd,3|Hd,2|Hd,1|Hp] = [Hd|Hp] • Hd,i, (i=1,2,…,q) matrices combined create an MxK matrix, Hd, which corresponds to the “data” bits of the codeword. Design of this matrix ensures high coding gain. • Maximum code rate: R = q/(q+1) • Hp is an MxM “dual diagonal” matrix, which corresponds to the “parity” bits of the codeword. Its “dual diagonal” form enables efficient encoding. Expansion of the base parity check matrix • If there is a need to accommodate larger blocks, base parity check matrix may be expanded L times (L is a small integer) • Hp expansion: each “0” replaced by 0LxL(all-zero); each “1” replaced by ILxL(identity). • Hd expansion: each “0” replaced by 0LxL; each “1” replaced by ILxLrotated (s) times to the right. Shift value, s, can be determined by: s = (rc)mod(L), where r and c are row and column indexes of the “1” to be replaced, respectively. Encoding • Systematic (canonical) encoding • Dual diagonal structure of Hp enables simple recursive derivation of parity check bits Aleksandar Purkovic et al, Nortel Networks

6. Candidate LDPC code details • Base matrix of the size (MxN)=(332x2656), corresponding to the maximum code rate of 7/8, is completely specified by the following set of parameters: [m, a1, b1, a2, b2, a3, b3, a4, b4, a5, b5, a6, b6, a7, b7] = [83,5,8,2,48,7,51,3,30,3,23,17,16,9,8] • Each pair (ai, bi) defines A,i, which in turn completely specifies sub-matrix Hd,i. • Parity check matrix can be symbolically shown as: Aleksandar Purkovic et al, Nortel Networks

7. Performance evaluation methodology • PHY model based on the 802.11a spec. [12]; code rate 7/8 added. • Simulation environment • Partial compliance with CC59 and CC67 • One spatial stream, 20MHz configuration • AWGN channel • Fading Channel Model D with power delay profile as defined in [13], NLOS, without simulation of Doppler spectrum. This implementation utilizes reference Matlab code [14]. • Simulation scenario assumed: • Ideal channel estimation • All packets detected, ideal synchronization, no frequency offset • Ideal front end, Nyquist sampling frequency • K = 1000 bytes, minimum 100 frame errors, down to PER of 10-2 • Code specific • Convolutional codes: Viterbi decoding algorithm • LDPC codes: • Iterative Sum-Product decoding algorithm with maximum of 20 iterations • Concatenated codewords • Channel interleaver was not used (no need for it) Aleksandar Purkovic et al, Nortel Networks

8. Simulation results AWGN Channel D Aleksandar Purkovic et al, Nortel Networks

9. Summary and conclusions • Family of structured LDPC codes has been designed for the 802.11n application. • Design objectives: • Performance improvement over existing convolutional codes • Simple encoding algorithm • Coverage of a broad range of information packet lengths and code rates • Support for additional code rates higher than the current maximum (3/4) • Enable efficient decoder hardware implementation • These structured LDPC codes are designed to be “architecture aware”, [15], and can overcome most of the implementation issues, associated with practical implementations so far. • LDPC codes presented in this contribution can be further refined to fit better 802.11n standard as it shapes up, especially considering various MIMO schemes. Aleksandar Purkovic et al, Nortel Networks

10. [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 802.11-03/940r4, “TGn Channel Models”, TGn Channel Models Special Committee, May 2004. [14] Laurent Schumacher, “WLAN MIMO Channel Matlab program,” January 2004, version 3.3. [15] M.M.Mansour and N.R.Shanbhag, “High-Throughput LDPC Decoders,” IEEE Trans. On VLSI Systems, vol. 11, No 6, pp. 976-996, December 2003 [16] IEEE 802.11-04/3371r0, “LDPC vs. Convolutional Codes : Performance and Complexity Comparison,” Aleksandar Purkovic et al, Nortel, March 2004 References Aleksandar Purkovic et al, Nortel Networks