Worst-Case TCAM Rule Expansion AUTHOR： ORI ROTTENSTREICH AND ISSAC KESLASSY PUBLISHER： IEEE INFOCOM 2010 PRESENTER： ZONG-LIN SIE DATE： 2010/09/15

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. 1.講出TCAM high-speed的原因(parallel)。

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 , . Match if r1 <= xi <= r2

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=2 R1 = [1,14] ×[5,14] R2 = [7,10] ×[2,3] use 6×5 to encode R1 use 3×1 to encode R2 total 33 entries

Suggested Architecture (2/3) Proposed COMBINED-PRODUCT (using complementary to encode , upper bound W) Assume d=2 ,W=4 ,k=2 R1 = [1,14] ×[5,14] R2 = [7,10] ×[2,3] use 12 to encode R1 use 3 to encode R2 total 15 entries

Suggested Architecture (3/3) Proposed COMBINED-SUM (each field of each range is encoded separately) Assume d=2 ,W=4 ,k=2 R1 = [1,14] ×[5,14] R2 = [7,10] ×[2,3] use 3+4 to encode R1 use 3+1 to encode R2 total 11 entries

Suggested Architecture