1. FTK variable resolution pattern banks
TDAQ Week at SLAC – 11/18/2010
G. Volpi – INFN Frascati, MC Fellowship

2. Associative memory and SS size
Large SS
Small SS
SS size optimization is an hard task, with many variables
Using “large” SS the final AM bank is fully efficient with a limited number of patterns
Using “small” SS, half the “large” SS, the number of patterns increase
Decrease the chance a pattern fires for random hits (noise, tracks fragments, …)
More patterns, more chips, more €€€ or $$$
Current estimate for the number of patterns per region is 25M for 2013, 5M for , up100M for 2018, 386 M after 2020
G. Volpi - FTK Variable resolution banks
/18/2010

3. SS size vs efficiency and road traffic
90%
# of patterns in Amchips (barrel only, 45 f degress)
65M
500M
Pattern size r-f: 24 pixel, 20 SCT 36 pix z
Pattern size r-f: 12 pixel, 10 SCT 36 pix z
(1.2 mm)
(1.6 mm)
(14 mm)
(0.6 mm)
(0.8 mm)
(14 mm)
The output is very different in a real scenario: i.e. using
<# 3E34> = 342k
<# 3E34> = 40k
G. Volpi - FTK Variable resolution banks
/18/2010

4. TSP and variable resolution
Patterns with “large” and “small” SS could be related:
One pattern with large SS contains many patterns with small SS
A tree organization is natural
AM is used to search the 1st step
TSP processor could search within the sub-patterns
TSP banks can be implemented using less expensive devices
Final efficiency depends on the TSP patterns
AM level
TSP level
G. Volpi - FTK Variable resolution banks
/18/2010

5. AM performance and TSP relation
Most simple bank with AM patterns doubling the phi size of TSP pattern: 1 bit/layer
Typical reduction factor 3
Most of the AM patterns have few sub-patterns (1, 2 or 3)
Difference made by fake AM roads, rejected at TSP stage
shows a very small fraction of AM patterns are confirmed at TSP level
A strategy able to reject the AM road with few kids early will have a large effect
G. Volpi - FTK Variable resolution banks
/18/2010

6. Variable resolution AM
We can use don’t care on the least significant bit when we want to match the pattern AM resolution or use all the bits to match TSP resolution
TSP patterns AM
pattern
All patterns with 1 kid are stored at TSP precision
All the layer without DC can ignore the hits in the “wrong” side of the layer DC
G. Volpi - FTK Variable resolution banks
/18/2010

7. DC bits and sub-patterns distributions
Single “kid” AM patterns
Using DC single kid AM patterns are described using the best precision
The number of DC bits in a bank peaks to 1 also for AM patterns with >1 sub-pattern
The distribution shows how the sub-patterns are strongly correlated
The DC bit in the AM chip increases the number of cells used to describe a pattern: from 15  16
The increase is 1/15~7%, the equivalent TSP bank is 3 times bigger
G. Volpi - FTK Variable resolution banks
/18/2010

8. Simulation strategy
The FTK simulation was modified to include the DC bits
Option A only simulation: 3 pixel layers + 4 SCT axial layers
Option B test is ongoing
3 pileup scenarios were studied: 17, 40 and 75 pileup events
For each pile-up scenario a different bank is chosen to try to meet chip development and LHC schedule
The working point for each scenario is decided fixing the TSP size to have an efficiency >=90% and following our experience
For each scenario the extracted numbers are:
Number of roads/processing units at different simulation level using barrel only simulation:
Final numbers assuming16 processing units
G. Volpi - FTK Variable resolution banks
/18/2010

9. AM roads confirmed by DC
Road flux PE
Bank studied using WHbb with 17.6 pileup events.
TSP Total bank size 5 MP
Average number of road at different levels per processing unit: 384283423
Strong reduction using DC, about 5.
Most of the DC roads are confirmed by the TSP (74%)
Often AM roads have more than 1 TSP roads
Barrel only
Median
95% of events
50% of events
TSP roads
AM board output
AM roads confirmed at TSP level
AM roads confirmed by DC
G. Volpi - FTK Variable resolution banks
/18/2010

10. Road flux 40 PE Barrel only
Bank studied using WHbb with 40 pileup events.
TSP Total bank size 100 MP
The number of roads at the different levels per processing unit:
14780260015532286
The DC suppression factor 5.6
Barrel only
G. Volpi - FTK Variable resolution banks
/18/2010

11. Roads flux 75 PE Barrel only
Bank studied using WHbb with 75 pileup events.
TSP Total bank size 384 MP
Number of roads at the different levels per processing unit:
21400330017702380
DC reduction factor 6.5
Barrel only
G. Volpi - FTK Variable resolution banks
/18/2010

12. Summary tables Average number of roads/units* AM AM w/ DC AM w/ TSP
17.6 evts
5040
959
709
1060
40 evts
37000
6500
3880
5720
75 evts
53500
8250
4430
5950
No DC in old AM chip
To be compared with a limit of 8000 output roads.
The 75 pileup events exceed that limit indeed at that time (2020) a more powerful chip should be used: 8L and maybe better use of DC with more bits/layer
* the number are corrected x2.5 to include the traffic in the endcaps. 16 processing units are assumed
G. Volpi - FTK Variable resolution banks
/18/2010

13. Conclusions
The use of DC bits gives the opportunity to strongly reduce the number of roads
DC does most of the work of the TSP
Is the TSP really necessary?
Use of variable resolution patterns for option A showed promising results
Further optimizations are possible
The number of roads confirmed by he DC is within the required limit
Variable resolution and DC are generic, test using the same algorithm in FTK option B ongoing
G. Volpi - FTK Variable resolution banks
/18/2010

14. Backup slides G. Volpi - FTK Variable resolution banks
/18/2010

15. Combination flux Barrel only, correction factor 2.5 to apply
The flux of the combinations is also largely effected the DC.
The average number of combinations is (x103):
92.311.69.17.2
Barrel only, correction factor 2.5 to apply
G. Volpi - FTK Variable resolution banks
/18/2010

16. Combination flux Barrel only, correction factor 2.5 to apply
The flux of the combinations is also largely effected the DC.
The average number of combinations is (x103):
15719.912.89.58
Barrel only, correction factor 2.5 to apply
G. Volpi - FTK Variable resolution banks
/18/2010

17. Fit combinations flux The average numbers of combinations are (x103):
23728.516.312.7
accounts for the hits in the unused part of the AM pattern.
TSP can use only the standard DC mask.
Could a dynamic DC mask reduce the fits’ number?e
G. Volpi - FTK Variable resolution banks
/18/2010