AUTHOR： ORI ROTTENSTREICH AND ISSAC KESLASSY

PUBLISHER： IEEE INFOCOM 2010

PRESENTER： ZONG-LIN SIE

DATE： 2010/09/15

Worst-Case TCAM Rule Expansion

Outline

Introduction

Background

Range Expansion Guarantees

Experimental Result

Suggested Architectures

Introduction

In this paper , given several type of rules , provide new upper bounds on the TCAM worst-case rule expansions.

For a W-bit range ： previously known upon bound ： 2W-5

TCAMs. this paper’s method provide ： W TCAMs.Also propose a modified TCAM architecture

that uses additional logic to significantly reduce the rule expansion.

Background (1/3)

What is TCAM ？ Ternary Content Addressable Memory.

Packet classification is the core function behind many network application.(routing 、 filtering…)

Hardware-based TCAMs are the standard devices

for high-speed packet classification.

Background (2/3)

What is rule expansion ？ two types of rules ： (1) simple rules ： need single entry per rule. (2) range rules ： might need many entries per

rule. Thus cause rule expansion.

for example ： range[2,4] means 01* and 100 range[1,14] means

0001,001*,01**,10**,11**,1110

Background (3/3)

However , power consumption constitutes a bottleneck for TCAM scaling.

Given same access rate , a TCAM chip consumes up to 30 times more power than equivalent SRAM chip with a software-based solution.

Goal of this paper is to gain a more fundamental understanding of the worst-case number of TCAM entries needed to encode a rule . Provide upper bounds.

Related Work (1/3)

Internal expansion ： only uses entries from within the range . W-bit

field can be encoded in 2W-2 entries for W ≥ 2 . Rule with d fields , can be encoded up to

entries . For instance ： W=3 , single field R = [1,6] needs 2W-2 = 4 entries. (see 111 as default)

Related Work (2/3)

The same way but rely on Gray codes instead of binary codes reduce the worst-case internal range expansion from 2W-2 to 2W-4 for sufficient large W.

Using more complex coding , improve to 2W-5 .

Related Work (3/3)

External encoding ： the same instance , W=3 , R = [1,6] . we encode the range exterior first , and then

the range itself is encoded indirectly. So , only 3 entries!

Range Expansion Guarantees(Model and Notations)

Definition 1(Header) ： is a W-bit string

defined on the d fields . Each sub-string of length

corresponds to field with .Definition 2(Range Rule) ： The range rule in field is defined as an

integer range[r1,r2] . r1≤r2 ,both W-bit integers. if xi match , .

Range Expansion Guarantees(Model and Notations)

Definition 3(TCAM entry) ： A TCAM entry is

composed of a TCAM rule S = ,

where {0,1} are bit values and * stands for don’t-care ,

And an action , where A is a set of actions . A W-

bit string b = matches S , denoted as , if

for all .

Range Expansion Guarantees(Model and Notations)

Ex: R = [1,6] A = {accept ,deny}, ,

Optimal Range Expansion Problem

We want to find a TCAM encoding scheme that minimizes the worst-case TCAM expansion

over all possible ranges R .

Optimal Range Expansion Problem

Then the range expansion f(W) is defined as the best-achievable range expansion for W-bit ranges given all encoding schemes , i.e.

To find the range expansion ,we first characterize the extremal range expansion g(W) , which is defined ：

A range R over is called extremal if R = [0,y] or R = for some arbitrary value of y.

Range Expansion Guarantees

Theorem 1 ： for all W ≥ 1 , the extremal range expansion satisfies the following upper-bound ：

(by induction on

W)

example ： for W=3 , the extremal range R = [0,6]

can encoded with only 2 TCAMs .(111 , ***) This is better than the best internal encoding

(0**,10* ,110) ,which use W=3 TCAMs entries.

Range Expansion Guarantees

Theorem 2 ： for all W≥ 1 , the worst-case range expansion satisfies the following upper-bound ： proof ： by induction on W ≥ 1. (1) for W = 1 , all non-empty ranges are extremal , therefore , the result follows by Theorem 1. for W = 2 , all non-empty and non-extremal ran- ges are either single points , or[1,2] can be enco- ded in 2 TCAMs.

Range Expansion Guarantees

(2) induction step ： Now let W ≥ 3 ,and assume the

claim true until W – 1. Consider any range , and cut it into 4 sub-ranges. , which

and distinguish the following cases ：

Range Expansion Guarantees

case(1) ： if ,

then by induction R can be encoded in at most W-1 entries . case(2) ： Else if

, then this is just a shifted version of the previo- us case and , by lemma 2 ,R can be encoded in at most W-1 entries .

Range Expansion Guarantees

case(3) ： (a) If

is a right –extremal range on , and by lemma 1,can be encoded in g(W-1) TCAM entries . Further by lemma 2 can be encoded in g(W-2) TCAM entries . (b) if can be encoded in g(W-2) TCAM entries , and

in g(W-1) TCAM entries .

Range Expansion Guarantees

Therefore , in both sub-cases , by theorem 1 ,

R can be encoded in up to

TCAM entries . case(4) ： we use 2 different techniques

according to the parity of W .

Range Expansion Guarantees

Range Expansion Guarantees

Range Expansion Guarantees

Exponential Number of TCAM Entries ： Theorem 4 ： For any classification rule R = of d fields , there is an encoding scheme

Linear Number of TCAM Entries Theorem 5 ： Any classification rule R on d fields

can be encoded in at most d ． W TCAM entries

with- out any additional logic.

Range Expansion Guarantees

Example of linear number entries ：

we first negatively encode the four striped regions , using an encoding of four one-dimensional extremal intervals , 4W . And a default positive entry . Total

4W+1 .

Experimental Result

Internal binary-prefix approach 2W-2 = 14.Suggested scheme W = 8.

Suggested Architecture (1/3)

Standard INTERNAL –RRODUCT Assume d=2 ,W=4 ,k=2R1 = [1,14] ×[5,14]R2 = [7,10] ×[2,3]

use 6×5 to encode R1use 3×1 to encode R2total 33 entries

Suggested Architecture (2/3)

Proposed COMBINED-PRODUCT (using complementary to encode , upper

bound W)Assume d=2 ,W=4 ,k=2R1 = [1,14] ×[5,14]R2 = [7,10] ×[2,3]

use 12 to encode R1use 3 to encode R2total 15 entries

Suggested Architecture (3/3)

Proposed COMBINED-SUM (each field of each range is encoded

separately)Assume d=2 ,W=4 ,k=2R1 = [1,14] ×[5,14]R2 = [7,10] ×[2,3]

use 3+4 to encode R1use 3+1 to encode R2total 11 entries

Suggested Architecture