4-bit CRC for 1 MHz and 2 MHz modes July 2012 doc.: IEEE 11-12/0800r1 4-bit CRC for 1 MHz and 2 MHz modes Date: 2012-07-16 Authors: Name Affiliations Address Phone email Ron Murias Monisha Ghosh Frank La Sita InterDigital Communications 781 Third Ave King of Prussia, PA +1 403 889 1200 ron@murias.ca Submission 1 Ron Murias, InterDigital Communications

July 2012 doc.: IEEE 11-12/0800r1 Abstract This document proposes a correction for the 4-bit CRC used on the 1 MHz and 2 MHz SIG field. Submission 2 Ron Murias, InterDigital Communications

Overview July 2012 doc.: IEEE 11-12/0800r1 Document IEEE 802.11-12/0596r0 proposed using the 4 LSBs of the 8-bit CRC used in 802.11ac with generator x8 + x2 + x +1. Simulation results presented indicate an error floor in the false positive probability. 0596r0 Motion 1 was accepted during the May 2012 meeting: “to use the 4 LSB of the 11n HTSIG field 8-bit CRC for the 4-bit CRC in 11ah 2MHz and 1MHz SIG(A) fields, and use the same 11n HTSIG field 8-bit CRC in SIGB field of the >=2MHz long preamble” Codeword weight analysis shows that taking the 4 LSBs of the 8-bit generator results in a code with minimum distance of 1. There are 3 single bit error patterns that cannot be detected by this CRC when used with either a 26-bit SIG (1 MHz) or a 38-bit SIG (2 MHz). Clearly this is not a good choice for a CRC: even the1-bit parity check used in 802.11a can detect all single bit errors. Options investigated: Use the optimal generator polynomial for a 4-bit CRC: x4 + x + 1. This may not be acceptable to the group since it is a different generator polynomial even though the performance is better. Search for a different combination of 4 bits other than the 4 LSBS that can detect all single-bit errors. i.e. have minimum distance of 2. Submission 3 Ron Murias, InterDigital Communications

Generator Matrix For x4 + x +1 with 26 information bits July 2012 doc.: IEEE 11-12/0800r1 Generator Matrix For x4 + x +1 with 26 information bits Message Bits c3c2c1c0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 The parity bits c3c2c1c0 do not have the all zero combination. Minimum distance of this code is 2. Submission 4 Ron Murias, InterDigital Communications

Generator Matrix For x8 + x2 + x +1 with 26 information bits July 2012 doc.: IEEE 11-12/0800r1 Message Bits c7c6c5c4c3c2c1c0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 There are three combinations of the LSB parity bits c7c6c5c4 that are all-zero. Hence, the corresponding parity check matrix has three all-zero columns. Minimum distance of this code is 1. There are two combinations of the MSB parity bits c3c2c1c0 that are all-zero: Hence, the corresponding parity check matrix has two all-zero columns. Minimum distance of this code is 1. Submission 5 Ron Murias, InterDigital Communications

July 2012 doc.: IEEE 11-12/0800r1 Hamming Weight (HW) Analysis for x8 + x2 + x +1 with 26 information bits CRC Bits HW = 1 HW = 2 HW = 3 HW = 4 HW = 5 c7c6c5c4 3 28 254 1663 8839 c3c2c1c0 15 280 1785 8736 2 24 247 1687 8969 c5c2c1c0 31 1658 9029 c5c3c2c0 34 1635 c5c4c1c0 27 265 1670 8879 c5c4c2c0 252 1657 8976 c5c4c3c1 29 264 8890 c6c3c1c0 35 246 1648 8992 c6c3c2c1 260 1662 8930 c6c4c3c1 263 1646 8901 c6c5c2c0 33 259 1640 8909 c6c5c3c2 32 1645 8925 c7c4c2c1 248 9018 c7c4c3c0 c7c4c3c1 c7c5c2c0 255 8949 c7c5c4c1 266 1629 8874 c7c6c3c2 262 1674 8896 Specification Framework Proposal (4 LSBs) Generator: x4 + x + 1 4 MSBs Possible alternative Submission 6 Ron Murias, InterDigital Communications

Hamming Weight (HW) Analysis for x8 + x2 + x +1 with 38 information bits July 2012 doc.: IEEE 11-12/0800r1 CRC Bits HW = 1 HW = 2 HW = 3 HW = 4 HW = 5 c7c6c5c4 3 52 707 6932 53267 c3c2c1c0 39 765 7101 52761 51 697 6947 53377 c5c3c2c0 65 692 6867 53564 c5c4c2c0 58 711 6942 53325 c6c4c3c1 56 720 6938 53292 c6c5c2c0 62 704 6894 53426 c6c5c3c2 717 6906 53339 c7c4c2c1 699 6865 53501 c7c5c4c1 60 721 6876 53323 Specification Framework Proposal (4 LSBs) Generator: x4 + x + 1 4 MSBs Possible alternative The 7 puncture patterns above are a subset of the 16 patterns for the case when 26 information bits are used. These 7 patterns were simulated to pick a common pattern for both 1 MHz and 2 MHz options. Submission 7 Ron Murias, InterDigital Communications

False Positive Results with 1 MHz SIG July 2012 doc.: IEEE 11-12/0800r1 Best choices: c5c3c2c0 and c7c4c2c1 Submission 8 Ron Murias, InterDigital Communications

False Positive Results with 2 MHz SIG July 2012 doc.: IEEE 11-12/0800r1 Best choices: c5c4c2c0 and c7c4c2c1 Submission 9 Ron Murias, InterDigital Communications

July 2012 doc.: IEEE 11-12/0800r1 Conclusion If 802.11ah requires a 4-bit CRC derived from the 8-bit generator polynomial currently being used in 802.11ac, there are better (with minimum distance greater than 1) puncturing choices than using the 4 LSBs. For the 1 MHz SIG with 26 information bits, of the 70 possible combinations, there are 16 that have minimum distance 2 and hence can guarantee detection of all single bit-errors. Simulation results indicate that the combination c7c4c2c1 has a false positive performance about 1 dB better than the current proposal and is very close to the optimal 4-bit CRC. For the 2 MHz SIG with 38 information bits, of the 70 possible combinations, there are 7 that have minimum distance 2 and hence can guarantee detection of all single bit-errors. Simulation results indicate that the combination c7c4c2c1 has a false positive performance very close to the optimal 4-bit CRC. Submission 10 Ron Murias, InterDigital Communications

July 2012 doc.: IEEE 11-12/0800r1 Straw Polls Straw Poll #1 Do you agree that there are better (i.e. minimum distance greater than 1) puncturing choices than using the 4 LSBs, If 802.11ah requires a 4-bit CRC derived from the 8-bit generator polynomial currently being used in 802.11ac? Y: N: A:

July 2012 doc.: IEEE 11-12/0800r1 Straw Polls Straw Poll #2 Do you agree that, for both 1 MHz SIG and 2 MHz SIG, there exist some combinations that have minimum distance 2 and hence can guarantee detection of all single bit-errors? Y: N: A:

July 2012 doc.: IEEE 11-12/0800r1 Straw Polls Straw Poll #3 Do you agree that the group should consider a better combination, e.g., c7c4c2c1, than the 4 LSBs, for both 1 Mhz and 2 Mhz SIG field 4-bit CRC? Y: N: A: