1. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 1 Generalized Puncturing to Eliminate Pad Bits in MIMO-OFDM 802.11n Ravi Mahadevappa, ravi@realtek-us.com Stephan ten Brink, stenbrink@realtek-us.com Realtek Semiconductors, Irvine, CA

2. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 2 Pad Bits in 802.11a More Pad Bits in 802.11n Ways to Eliminate Pad Bits Expected Gains by Eliminating Pad Bits Generalized Puncturing Overview

3. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 3 Excerpt from 802.11a PHY Standard Pad Bits in 802.11a pad bits are zeros and ignored at receiver …

4. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 4 In 802.11a, max. number of coded bits per OFDM symbol is N CBPS = 48*6 = 288 In a possible 802.11n system, owing to higher order modulation (e.g. 256QAM) and multiple transmit antennas (e.g. N T =3), the number of bits per OFDM symbol will be several times larger than in 802.11a –Coded bits per OFDM symbol: N CBPS = 48*M*N T Say, max. 256QAM, M=8 bits per symbol Max. number of transmit antennas N T =4 N CBPS = 1536 bits –Other example: M=6 (64QAM), N T =3, N CBPS = 864 Moreover, space/time codes might require the number of OFDM symbols to be an integer multiple of 2 (or 3, or 4), and thus, potentially more pad bits needed Another possible reason for more pad bits: Interleaving over several OFDM symbols (e.g. over 6 OFDM symbols) More Pad Bits in 802.11n

5. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 5 Instead of padding N PAD useless zero-bits, transmit useful information (code redundancy) –Repeat a fragment of length N PAD of the message Disadvantage: requires buffering, uneven distribution of redundancy –Adapt (i.e. reduce) the code rate R=K/N to new code rate R n =K/(N+N PAD ) Evenly distribute the added redundancy, all message bits benefit For convolutional codes, use a simple, generalized puncturing scheme to implement the new code rate R n From code rate R and message length (conveyed in SIGNAL-field of packet preamble), new code rate R n can be computed by receiver (from number of pad bits N PAD ); no need for additional signaling of new code rate Ways to Eliminate Pad Bits

6. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 6 Typical Example: –Message length (info bits) N Li = 6000bits –Code rate R=3/4, coded message length N Lc =8000 –64QAM, M=6, N T =3, N CBPS = 48*M*N T = 864 –N PAD = N CBPS - (N LC modulo N CBPS ) = 640 –New code rate R n = 6000/(8000+640) = 0.69444… Expected Gains by Eliminating Pad Bits

7. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 7 From rate 3/4 to rate 0.69444 by generalized puncturing For the 3x4 example, gain is about 1.2dB, simply by using coded bits instead of zero pad bits Expected Gains by Eliminating Pad Bits

8. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 8 Let the mother code rate be R m (in 802.11a: R m =1/2, convolutional code) R is the code rate originally selected by the transmitter –drawn from discrete set of code rates, e.g. R=1/2, 2/3, 3/4, 7/8, for protection/data rate trade-off For R m <=R n <=R: –some of the punctured bits need to be “unpunctured” to reduce the code rate from R to R n For R n <R m : –All punctured bits need to be unpunctured; moreover, some bits need to be repeated Generalized Puncturing

9. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 9 One very simple implementation (out of many): –Coded message length n (encoded using mother code rate R m ) –New coded message length n_new=n+n_pad Mother code rate Rm new code rate Rn=Rm*n/n_new –Routine returns a repetition/puncturing pattern specifying number of repetitions (or ‘0’, if to puncture) of the bits of the original coded message of length n (indices from 1 to n) –MATLAB: function rep_pct_pattern = gen_puncture(n_new,n) new_seq = ceil((1:n)*n_new/n); rep_pct_pattern = diff([0 new_seq]); A Generalized Puncturing Scheme

10. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 10 Let the mother code rate be R m =1/2, with coded outputs (c 1,c 2 ) per input bit Rate 3/4, puncturing as usual: c 1 : 10110110110110110110110110110110110110110110110110… c 2 : 11011011011011011011011011011011011011011011011011… Rate 0.69444… = 6000/8640: c 1 : 11111010111101010111101011111101011110101011110101… c 2 : 10101111010111111010111101010111101011111101011110… Rate 0.41666… (below mother code rate R m, repetitions needed): c 1 : 21111211112111121111211112111121111211112111121111… c 2 : 11211112111121111211112111121111211112111121111211… Generalized Puncturing Examples

11. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 11 To make the packet length a multiple of the length of a single OFDM symbol N CBPS, pad bits (“dummy bits”) are used in 802.11a With increasing data rate in MIMO-OFDM 802.11n, there will be more pad bits on average Replacing pad bits by coded (redundant) bits improves performance without using extra resources (bandwidth); it comes for free A simple generalized puncturing scheme was presented to perform this task Summary

12. doc.: IEEE 802.11-04/298r0 Submission March 2004 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 12 Some References [1]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