On Finding an Optimal TCAM Encoding Scheme

for Packet Classification

Ori Rottenstreich (Technion, Israel)

Joint work with

Isaac Keslassy (Technion, Israel)

Avinatan Hassidim (Google Israel & Bar-Ilan Univ.)

Haim Kaplan (Tel Aviv Univ.)

Ely Porat (Bar-Ilan Univ.)

Network Structure

2

Accept?

Packet Classification

Action

--------

---- ----

--------

Rule ActionPolicy Database (classifier)

Packet Classification

Forwarding Engine

Incoming Packet

HEADER

Switch

3

TCAM Architecture

Enc

oder

Match lines

0

1

2

3

4

6

5

7

8

9

deny

accept

accept

denydeny

deny

denyaccept

deny

accept

00111011111110000001101001011001000

00111011100100

1110010010011100101011111111111

0011101000011100

0

0

0

1

0

1

0

1

0

1

row 3

Each entry is a word in {0,1,}W

Packet Header

TCAM Array

Source Port

Width W 4

Rule Source address

Source port

Dest.address

Dest.Port

Protocol

Action

Rule 1 123.25.0.0/16 80 255.2.3.4/32 80 TCP Accept

Rule 2 13.24.35.0/24 >1023 255.2.127.4/31 5556 TCP Deny

Rule 3 16.32.223.14 20-50 255.2.3.4/31 50-70 UDP Accept

Rule 4 22.2.3.4 1-6 255.2.3.0/21 20-22 TCP Deny

Range Rules

• Range rule = rule that contains range field Usually source-port or destination-port

• How many entries are required to represent one range field?

5

• Reducing number of TCAM entries by exploiting TCAM

properties• Example: R=[1,6]

TCAM Encoding Example

010 011001 110100 101 111000

0 1 2 3 4 5 6 7

6

Basic encoding

with 6 entries

• Reducing number of TCAM entries by exploiting TCAM

properties• Example: R=[1,6]

TCAM Encoding Example

010 011001 110100 101

001

111000

0 1 2 3 4 5 6 7

6

01* 10* 110

Shorter encoding

with 4 entries

• Reducing number of TCAM entries by exploiting TCAM

properties• Example: R=[1,6]

TCAM Encoding Example

010 011001 110100 101

***

111000

111000

0 1 2 3 4 5 6 7

6

Improved encoding

with only 3 entries

• Definition: An encoding in which in all entries “*”-s appear only as a suffix

• Example: Encoding of the range R = [0,2]

• Property: For a general function F, it is easy to find an optimal prefix encoding

• TCAM enables non-prefix encoding

• Can we use this TCAM property to do better than past algorithms?

Past Work: Prefix Encoding

7

Prefix encoding Non-prefix encoding

[Suri et al. ’03]

Outline

Introduction Optimal Encoding of Extremal Ranges Average Expansion of Extremal Ranges Bounds on the Worst-Case Expansion

8

Given a function F, we define• - The size of a smallest encoding of F. • - The size of a smallest prefix encoding of F.

• Property: For a general function F, the equality

does not necessarily hold.

• Example:

General Functions

9

010 011001000

0 1 2 3 Optimal

encodingOptimal prefix

encoding

Given a range R, does necessarily ?

• Extremal ranges = Ranges that start or end a sub-tree (e.g. [0,2] or [4,6] in tree [0,7])• Real life database: 97% of all rules are extremal ranges

• Theorem: For an extremal range R,

• Corollary: Finding an optimal encoding of extremal ranges is easy

• Open Question: Non–extremal ranges?

Range Functions

10

010 011001 110100 101 111000

0 1 2 3 4 5 6 7

Given a subtree T and a range R, we define

• - The size of a smallest encoding of R∩T with a last entry of

• - The size of a smallest encoding of R∩T with a last entry of

• Example: If and then

• and •

• Property:

Optimal Encoding

11

D

• Illustration of the algorithm for the extremal range R=[0,22]

• Values are calculated recursively for T0,…,T5

• The range R can be encoded in entries:

Algorithm Illustration

1

1

1

0

0

T0 :(1,2)

T1 :(2,2)

T2 :(2,3)

T3:(2,3)

T4:(3,3)

TW=5:(3,4)

0 22 31

R = [0,22] 12

T0 :[22,22]

T1 :[22,23]

T2 :[20,23]

• For simplicity, let’s focus on the simple extremal ranges [0,y]

Another Way to Look at it…

13

1

1

1

0

0

T0 :(1,2)

T1 :(2,2)

T2 :(2,3)

T3:(2,3)

T4:(3,3)

TW=5:(3,4)

0 22 31

R = [0,22]=[00000,10110]

A

(a,a+1)

C

(c+1,c)

B

(b,b)

0 0

1 1

1 0

Deterministic Finite Automaton (DFA)

start

•Theorem: For a range , let be the number of blue transitions of the DFA in the processing of .

Then, .

• For simplicity, let’s focus on the simple extremal ranges [0,y]

Another Way to Look at it…

14

A

(a,a+1)

C

(c+1,c)

B

(b,b)

0 0

1 1

1 0

Deterministic Finite Automaton (DFA)

start

•Theorem: For a range , let be the number of blue transitions of the DFA in the processing of .

Then, .

•Corollary: is affected by the average number of blue transitions (among the first W transitions) in the Markov Chain derived from the DFA.

• For simplicity, let’s focus on the simple extremal ranges [0,y]

Another Way to Look at it…

14

A

(a,a+1)

C

(c+1,c)

B

(b,b)

0 0

1 1

1 0

Deterministic Finite Automaton (DFA)

start1/2 1/2

A

(a,a+1)

C

(c+1,c)

B

(b,b)

1/2 1/2

1/2 1/2 Corresponding Markov Chain

• Theorem: The average range expansion of simple extremal ranges [0,y] satisfies:

• Corollary:

Average Expansion of Simple Extremal Ranges

15

Outline

Introduction Optimal Encoding of Extremal Ranges Average Expansion of Extremal Ranges Bounds on the Worst-Case Expansion

16

Known Our Contribution

1-D Ranges

2-D Ranges

Bounds on the Worst-Case Expansion

17

- Worst-case expansion over all ranges of W bits:

=

=Optimality over all coding schemesfor 1-D ranges

Optimality over all coding schemes for 2-D ranges

Concluding Remarks

• Optimal encoding of extremal ranges

• Formula for the average range expansion of simple extremal ranges

• Tight worst-case bounds r(W) (1-D ranges, all coding schemes) r2(W) (2-D ranges, all coding schemes)

18

Thank You