Supporting document for C80216m-09/1720r4
IEEE 802.16 Presentation Submission Template (Rev. 9)
Document Number: IEEE S802.16m-09/1720r3
Date Submitted:
2009-09-24
Source:
Huaning Niu, Rongzhen Yang, Guangjie Li, Alexei Davydov, Yuan Zhu, Jong-Kae (JK) Fwu, Hujun Yin, Yang-seok Choi
[email protected]
Intel Corporation
Venue:.
IEEE 802.16m-09/0028r1: “802.16m/D1 letter ballot document”
Target topic: P802.16M/D1 - 15.3.9.3.1.4
Purpose:
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Current Proposed Equations for 16m
Indexing method from Intel (C80216m-09_1720r4.doc):
M 1
r
Si  1
i 0
i 1
Si is selected subband indices
Indexing method from Samsung (C80216m-09_2132r4.doc):
 N k 

iS ( x)   xk 
k 1
 M  wk 
k 1
N
and
 N k 
N
k 1
iS ( x )   xk  M  x 

j

k 1
j 1


wk   x j
j 1
x is selected subband bitmap
Equation (4) in the paper:
T. M. Cover, “Enumerative source encoding,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 73-77, January 1973
Relationships Between Two Proposed Equations:
they are equivalent to each other in mathematics
Intel Equation
Samsung Equation
 N k 
M 1 N  s
k 1
k
iS ( x )   xk  M  x 
r

j


k 1
k 0 M  k
j 1

 Remove all “xk=0” items
N
M 1
r

and minus 1
Transformed
By Bitmap Reverse Order
i 0
Si  1
i 1
Example Result (N=4, M=2):
Input Location Bitmap
Intel Index
Samsung Index
Intel Index by Bitmap Reverse Order
1100
5
1
0
1010
4
2
1
1001
3
4
3
0110
2
3
2
0101
1
5
4
0011
0
6
5
• Mathematically equivalent: can be transformed each other, i.e the
exact same performance can be got for indexing and reverse indexing
algorithm design

 N 
1
,

,
  
• Samsung index value result in the range of 

 M 
Performance Comparison: Exactly same
(reference to the algorithms in C80216m-09_1720r4.doc and C80216m-09_2132r4.doc)
Average nchoosek operations per reverse indexing, two examples:
N = 24
M
4
3
2
Intel Method
19.8095
18.6136
16.5797
Optimized Reference Method
19.8095
18.6136
16.5797
Gain
0%
0%
0%
M
4
3
2
Intel Method
9.9556
9.45
8.4848
Optimized Reference Method
9.9556
9.45
8.4848
Gain
0%
0%
0%
N = 12
Other Comparisons
Samsung Equation
 N k 
k 1

iS ( x )   xk  M  x 

j

k 1
j 1


N
Intel Equation
M 1
r
i 0
Si  1
i 1
• We prefer Intel equation because it is obviously neat in
equation expression.
• In addition, Samsung equation is not preferred because:
– Indexing value start at “1” instead of “0”
– Bitmap input instead of subband index input
– N loop comparing to M loop, and one inner
accumulation.
Conclusion
• The text in C80216m-09/1720 (its latest
version) is recommended as the subband
indexing method of IEEE 802.16m