1. 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:
Authors:
Name
Affiliations
Address
Phone
Ron Murias
Monisha Ghosh
Frank La Sita
InterDigital Communications
781 Third Ave
King of Prussia, PA
Submission 1
Ron Murias, InterDigital Communications

2. 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

3. Overview July 2012 doc.: IEEE 11-12/0800r1
Document IEEE /0596r0 proposed using the 4 LSBs of the 8-bit CRC used in ac 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 a 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

4. 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
The parity bits c3c2c1c0 do not have the all
zero combination.
Minimum distance of this code is 2.
Submission 4
Ron Murias, InterDigital Communications

5. Generator Matrix For x8 + x2 + x +1 with 26 information bits
July 2012
doc.: IEEE 11-12/0800r1
Message Bits c7c6c5c4c3c2c1c0
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

6. 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

7. 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

8. 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

9. 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

10. July 2012
doc.: IEEE 11-12/0800r1
Conclusion
If ah requires a 4-bit CRC derived from the 8-bit generator polynomial currently being used in ac, 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

11. 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 ah requires a 4-bit CRC derived from the 8-bit generator polynomial currently being used in ac? Y: N: A:

12. 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:

13. 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: