Space-Efficient TCAM-based Classification Using Gray Coding

1. Space-Efficient TCAM-based Classification Using Gray Coding Authors:Anat Bremler-Barr and Danny Hendler Publisher: IEEE INFOCOM 2007 Present:Chen-Yu Lin Date: Dec,3, 2008

2. Outline • Introduction • Related works • SRGE: Efficient Encoding of Short Ranges • Hybrid SRGE • Experimental results and comparative analysis

3. Introduction • TCAMs are not well-suited for representing rules that contain range fields. • The resulting range expansion can be dramatically reduce TCAM utilization. • Observation : The majority of real-life database ranges are short. • 60% unique length • 40% length less than 20 • This paper present a novel algorithm called Short Range Gray Encoding (SRGE). • SRGE encodes range borders as binary reflected gray codes and represents the resulting range by a minimal set of ternary string. • To the best of our knowledge, SRGE is the first algorithm that significantly reduces range expansion without resorting to use of extra bits. • To further improve TCAM utilization, we use extra bits by employing hybrid-SRGE scheme.

4. Related works (1/3) • Extended TCAM • Implements range matching directly in hardware. • This is a long-term solution. • It seems changing the ternary nature of TCAM entries. • Issues of TCAM range representation • Prefix expansion • Database dependent range encoding • Database independent range encoding

5. Related works (2/3) • Prefix expansion • A traditional technique for range representation. • The worst case expansion ratio for W-bit fields is 2W-2. • For example : 2-bit . 1 2

6. Related works (3/3) • Database dependent range encoding • Use the extra bits available in TCAM entries for encoding ranges that occur in the database more efficiently. • The encoding of a range may depend on the number of occurrences of the range in the database. • [6][7] proposed hierarchical encoding schemes, however, that may reduce the expansion of range rules considerably complicates the task of incrementally updating. • Our hybrid-SRGE scheme encodes the vast majority of ranges without using extra bits and use dependent encoding only for a very small number of ranges. • Database independent range encoding • Encode each range independently of the distribution of ranges in the database.

7. SRGE (1/9) • Gray code • A binary encoding of a contiguous range of integers such that the codes of any two adjacent numbers differ by a single bit. • SRGE uses a specific Gray code called binary-reflected Gray code (BRGC). • This reflection property of BRGC allows our algorithm to minimize the size of range cover sets.

8. SRGE (2/9) 0101 1011 p 6 14 SRGE example: range [6 - 14]

9. SRGE (3/9) 0100 1100 p pr pl 6 14 SRGE example: range [6 - 14]

10. SRGE (4/9) Prefixes1 = {010*} Prefixes1 = {*10*} S’ SRGE example: range [6 - 14]

11. SRGE (5/9) 1110 1010 P’ pr’ pl’ S’ SRGE example: range [6 - 14]

12. SRGE (6/9) Prefixes2 = {101*, 1001} Prefixes2 = {1*1*, 1*01} P’ pr’ pl’ S’ SRGE example: range [6 - 14]

13. SRGE (7/9) Prefixes1 Prefixes2

14. SRGE (8/9)

15. SRGE (9/9) • The ternary strings in the cover set produced by the SRGE-cover procedure may overlap each other. • Although some of the entries representing a range may overlap, the SRGE algorithm only requires a single TCAM lookup. • If a key falls inside a range R, then the lookup will return the first matching entry that belongs to the cover of R.

16. Hybrid – SRGE (1/2) • The size of TCAM entries is typically larger than the size of classification rules. • This leaves a number of extra bits. • To further improve TCAM utilization • Use these extra bits by employing a database dependent hybrid – SRGE. • The high-level idea is to assign a single extra bit to each of the ranges whose TCAM entries consumption is highest under SRGE encoding. • X : # extra bits available in every TCAM entry. • Hybrid – SRGE procedures: • Compute a list of unique ranges that occur in the database. • Sorted in decreasing order of the overall number of redundant entries. • The first X ranges in the list is dealt with by using a standard database-dependent encoding.

17. Hybrid – SRGE (2/2) • The well known range ≤ 1024 is the heaviest range under SRGE. • Hybrid-SRGE assigns the first extra bit (bit 1) to the heaviest range. • Each entry that contains a source port field with the range ≤ 1024 is set to 1, else set to *. • Example: 0*1 Applied dependent encoding *10 Gray code representation

18. Experimental result & analysis (1/6) • We evaluate the efficiency of the hybrid-SRGE scheme on 2 databases. • real-life • The collection of 126 separate files • Total 223K rules which contain 280 unique ranges. • Prefix expansion resulted in an expansion factor of 2.6 • ~ 26% of rules contained range fields. • Random database

19. Experimental result & analysis (2/6) • More than 60% of the unique ranges have length less than 20. • 22% of the total number of unique ranges have length 2.

20. Experimental result & analysis (3/6) • Notation definitions: • D : a classification database • n(D) : # rules in D • nE(D) : # TCAM entries required to represent D using scheme E • FE (D) : D’s database expansion factor using E • r(D) : # range rules in D • nrE (D) : # TCAM entries required to represent all of D’s range rules using encoding scheme E. • FRE (D) : D’s range redundancy factor • Database expansion factor • Range redundancy factor

21. Experimental result & analysis (4/6) • Evaluation SRGE on random databases • A perfect encoding scheme will achieve a database expansion factor of 1. • Will also have a range encoding redundancy factor of 0. 16% 5.5% 5

22. Experimental result & analysis (5/6) • Evaluation hybrid-SRGE on real-life databases • Our tests show that the hybrid-SRGE scheme success in reducing database expansion caused by range rules from a factor of 2.3 to a factor of only 1.03.

23. Experimental result & analysis (6/6) • For each range, we calculate its contribution as follows: • # times it appears * # entries required to represent it 92%