Encoding Short Ranges in TCAM Without Expansion: Efficient Algorithm and Applications

Yotam HarcholThe Hebrew University of Jerusalem, Israel

Joint work with:

This research was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no 259085.

Anat Bremler-Barr David Hay Yacov Hel-OrIDC Herzliya,

IsraelHebrew University,

IsraelIDC Herzliya,

Israel

To appear in ACM SPAA 2016

TCAM – Ternary Content Addressable Memory

• TCAM is an associative memory module– Useful for parallel multidimensional prefix lookup

• Each entry may consist of 0, 1, and * bits

• Widely used in high-speed networking devices

2

P1

P2

Drop

P3

SRAM

011101001110001011

00110****110001***0111*****1100010**00*******110******01*******11000****

TCAM

1

0

1

2

3

4

5

0

1

2

3

4

5

Example: 2-dimensional IP lookup:

Source IP Dest. IP

What about ranges?(e.g., port numbers)

Range Encoding in Binary Representation

• Can ternary encode only certain intervals

• Or we need more than one entry (expansion)

• Exponential space blow-up when using multiple range fields3

00000

10001

20010

30011

40100

50101

60110

70111

81000

91001

101010

111011

121100

131101

141110

151111

01**

0***

00**

????

011*100*

????

0101011*100*1010

Encoding Short Ranges

• Ranges of arbitrary length – infeasible without expansion

• Ranges with bounded length – feasible!

• Useful for:– Short TCP/UDP ranges (>60% of the ranges in real life)

– QoS mechanisms (IP ToS/DSCP)

– Packet size classification (by categories)

– Timestamps and counters

– IP spoofing detection (using IP TTL)

– SDX – AS numbering

• Also useful for applications outside the networking domain4

Range Encoding on TCAM: Two Approaches

Lower bound for w-bits field without expansion: 2w-1 bits per range [Lakshminarayanan et al., 2005]

5

fenc([x, y]) = *1**1001**10

**1*10**101*

*1**100***1*

DBfenc( , [x, y]) = *1**100*10**1*10*01*

Database-independent encoding:

Database-dependent encoding:

Easy to update

Compact codes

Both schemes require expansion for a feasible code length

[Lakshminarayanan et al., 2005], [Bremler Barr et al., 2007]

[Liu, 2002], [Van Lunteren & Engbersen, 2003], [Chang & Su, 2007] , [Che et al., 2008], [Bremler Barr et al., 2009], [Rottenstreich & Keslassy, 2010], [Rottenstreich et al., 2013], [Kogan et al., 2014]

RENÉ – Range Encoding with No Expansion

6

fenc([x, y]) = *1**1001**10

Database independent - easy to update

No row expansion

Near-optimal TCAM space usage

Encoding function for short ranges:

Useful for packet classification applications

Useful for high dimensional nearest neighbor search

Binary-Reflected Gray Code (BRGC)

Hamming distance between each two adjacent points = 1

7

0

0

0

0

0

0 0 0

1

1

1 1

1 1 1 1

00000

10001

20011

30010

40110

50111

60101

70100

1

0 0

0

1 1

81100

91101

101111

111110

121010

131011

141001

151000

0 0 0 01 1 1 1

0

0

0

0

0 0 0

1

1 1

1 1 1 1

0000

1001

2011

3010

4110

5111

6101

7100

0

0 0

1

1 1

000

101

211

310

0 1

0 1

Build recursively by reflecting binary code:

Range Encoding withBinary-Reflected Gray Code

• With ternary BRGC we can encode some of the ranges of length h=2k (k∈N)

• What about other (red) ranges?

8

00**

00000

1

0001

20011

3

0010

40110

5

0111

60101

7

0100

81100

9

1101

101111

11

1110

121010

13

1011

141001

15

1000

01** 11** 10**

0*1* *10* 1*1* *00**00**

Layers

• Layer: a set of disjoint consecutive ranges

• Two (blue) layers can be encoded with a BRGC-based ternary word

– Other (red) layers need more bits

9

00** 01** 11** 10**

0*1* *10* 1*1* *00**00**

00000

1

0001

20011

3

0010

40110

5

0111

60101

7

0100

81100

9

1101

101111

11

1110

121010

13

1011

141001

15

1000

Cover Ranges

• Cover range of R: the smallest blue range that fully contains R

– In red layers: No two consecutive ranges in the same layer are fully contained in a cover range

Given the cover range, one bit is enough to differentiate ranges in the same layer

10

R

0***cover(R)

0 1 0

00000

1

0001

20011

3

0010

40110

5

0111

60101

7

0100

81100

9

1101

101111

11

1110

121010

13

1011

141001

15

1000

Single Bit Range Index

• Red ranges require different encoding

• Add one bit for each red layer– Bit value alternates between ranges in the same layer

– Bits of other red layers are set to *

– For blue layers, these bits are always *

11

00000

1

0001

20011

3

0010

40110

5

0111

60101

7

0100

81100

9

1101

101111

11

1110

121010

13

1011

141001

15

1000

0* 1* 0* 1* 0*

*1 *1*0*0 *0

** ******

** ****** **

0* 1* 0* 1* 0*

*1 *1*0*0 *0

Encoding Scheme for Ranges

• Encoding of a single range of length h=2k is:

• Value encoding is now:

12

Ternary BRGCBit of

L1. . .

Bit ofLh/2-1

w bits h-2 bits

Bit ofLh-1

Bit ofLh/2+1

. . .Blue ranges: BRGC(R)

Red ranges: BRGC(cover(R))

BRGCBit of

L1. . .

Bit ofLh/2-1

w bits h-2 bits

Bit ofLh-1

Bit ofLh/2+1

. . .

Toy Example

13

Optimization

• For ranges of length h=2k

k-1 LSBs of the BRGC part are always *

• Code can be shorten to w-log(h)+h-1 bits

14

00000|00

1

0001|10

20011|10

3

0010|11

40110|11

5

0111|01

60101|01

7

0100|00

81100|00

9

1101|10

101111|10

11

1110|11

121010|11

13

1011|01

141001|01

15

1000|00

00**|** 01**|** 11**|** 10**|**

0***|1* *1**|0* 1***|1* *0**|0**0**|0*

0*1*|** *10*|** 1*1*|** *00*|***00*|**

0***|*1 *1**|*0 1***|*1 *0**|*0*0**|*0

00000|00

1

0001|10

20011|10

3

0010|11

40110|11

5

0111|01

60101|01

7

0100|00

81100|00

9

1101|10

101111|10

11

1110|11

121010|11

13

1011|01

141001|01

15

1000|00

00**|** 01**|** 11**|** 10**|**

0***|1* *1**|0* 1***|1* *0**|0**0**|0*

0*1*|** *10*|** 1*1*|** *00*|***00*|**

0***|*1 *1**|*0 1***|*1 *0**|*0*0**|*0

Encoding Multiple Range Lengths

• For ranges of length 3, intersect two ranges of length 4:

15

00*|**

0000|00

1

000|10

2001|10

3

001|11

4011|11

5

011|01

6010|01

7

010|00

8110|00

9

110|10

10111|10

11

111|11

12101|11

13

101|01

14100|01

15

100|00

01*|** 11*|** 10*|**

0**|1* *1*|0* 1**|1*

0*1|** *10|** 1*1|**

0**|*1 *1*|*0 1**|*1

*0*|0*

*00|**

*0*|*0*0*|*0

*00|**

*0*|0*

5 7

01*|**

*1*|0*

4 7

5 8

01*|** Π *1*|0* = 01*|0*

We present the conjunction operator Π:

For two ranges R1, R2: tcode(v) ≈ tcode(R1) Π tcode(R2) if and only if v∈R1 ∩ R2

(also: tcode(R1) Π tcode(R2) = ⊥ R1 ∩ R2 = ∅)

(⊥ means ‘undefined’, and if ai Π bi = ⊥ then a Π b = ⊥)

Theoretical Bound

16

TCA

M b

its

use

d p

er r

ange

fie

ld(l

og 2

scal

e)

Maximal range length(log2 scale)

For w=16

The Nearest Neighbor Search Problem

• Input:- A set of data points- A query point (or a series of those)

(points are in a discrete space)

• Output:Data point closest to the query point

• The Curse of Dimensionality: Hard problem for high dimensions(even over 10 or so)

17

The Nearest Neighbor Search Problem

• Encode cubes on data points

– Given a query point, single TCAM lookup returns the smallest cube that contains it

– No TCAM entry expansion in high dimension

18

DataQuery

The Nearest Neighbor Search Problem

• Or instead, save TCAM space

– Encode cubes on the query point

– Query TCAM with growing cubes

– Find first data point to match

19

DataQuery

Experiment on a Real TCAM

• Currently - no evaluation board for TCAM

• Instead, we used a commodity network switch with a TCAM– Switch has 48 ports of 1Gbps each (1.5 Million packet per second)

– TCAM is 192 bits wide

20

00*1**001***011***01*1**00*1**00*1**00****0***1*0****1

Src. MAC Dest. MAC Src. IP Dest. IP

OpenFlowflow_mod

Queriesas packets

OpenFlowCounters

d-Dimensional Cube Representation:

Single port:1.5 Million Queries

Per Second!

1st dimension 2nd dimension 3rd dimension 4th dimension 5th dimension 6th dimension 7th dimension

Conclusions

21

Database independent - easy to update

No row expansion

Near-optimal TCAM space usage

Encoding function for short ranges:

Useful for packet classification applications

Useful for high dimensional nearest neighbor search

fenc([x, y]) = *1**1001**10

Questions?

Thank you.

22