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Space-Efficient TCAM-based Classification Using Gray Coding

Infocom paper presentation. Space-Efficient TCAM-based Classification Using Gray Coding. Anat Bremler – Barr Interdisciplianry Center. Danny Hendler Ben-Gurion University. Talk outline. Definitions Problem definition, prior art The Short Range Gray Encoding Algorithm

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Space-Efficient TCAM-based Classification Using Gray Coding

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  1. Infocom paper presentation Space-Efficient TCAM-based Classification Using Gray Coding Anat Bremler – Barr Interdisciplianry Center Danny Hendler Ben-Gurion University

  2. Talk outline • Definitions • Problem definition, prior art • The Short Range Gray Encoding Algorithm • Experimental results • Future work

  3. Packet Classification

  4. ACL ID ACL11 ACL11 ACL11 ACL11 ACL11 ACL11 ACL11 117.57.3.2 Sourceaddr 127.*.*.* 128.32.0.0 128.32.0.0 95.14.5.1 117.57.3.2 128.32.0.0 136 80 55 34-36 >1024 >1024 Sourceport ≤ 1024 32.12.1.1 46.2.67.11 32.*.*.* 95.12.3.3 Destaddr 32.*.*.* 32.12.1.1 32.12.1.1 15 25 ≤ 1024 15-18 80 80 Destport 80 TCP TCP Protocol TCP UDP TCP TCP UPD Action Allow Allow Allow Log Log Deny Deny searchkey f Packet Classification header payload ACL database

  5. Search key 0011101101010000010100111110110 Ternary content-addressable memory • Associative memory: parallel comparisons against all entries • Fixed-width entries • Ternary digits: 0 / 1 / X (don’t care) • Only first match is returned TCAM 1 0011101101010XX00X01001111XXXX 11X00X00001110X0X101000110XXXX 2 3 10XX010100X0XX0100011010X01000 4 001110XXXXXXXXXXXXXXXXXXXXXXX ... 1 1110XX010X01X0010101010X0XXXXX Width of W digits

  6. TCAM 1 0011101101010XX00X01001111XXXX 11X00X00001110X0X101000110XXXX 2 3 10XX010100X0XX0100011010X01000 4 001110XXXXXXXXXXXXXXXXXXXXXXX ... 1110XX010X01X0010101010X0XXXXX TCAM: pros, cons, usage • Pros • High throughput • Deterministic throughput • Cons • Higher cost (~X30 than SRAM) • Higher power consumption • Usage • Over 6M deployed devices (2004) • Used in multi-gigabit systems with >10K rules • May support 128K entries of 144- bit, 133M searches/second.

  7. How can we efficiently represent range rules by TCAM entries? The problem: TCAM range representation Match-type rule field value matching key-field exact 00111011011011000000 001110110110110000000 001110110110110000000 prefix 001***************** range >1024 2012

  8. 0 1 000 001 010 011 100 101 110 111 [1,6] TCAM entries: 001, 01*, 10*, 110 Basic approach: prefix expansion Representing [1,6] • Prefix expansion is inefficient • A range over W-bits may expand to 2W-2 entries • For 2 range-fields, may expand to (2W-2)2 • Expansion factor of up to 6 on real-world databases !!!

  9. XXXXX XXXXX XXXXX XXXXX ... XXXXX Extra bits(typically 36) Prior art: use of extra bits TCAM 1 0011101101010XX00X01001111XXXX 2 11X00X00001110X0X101000110XXXX 3 10XX010100X0XX0100011010X01000 4 001110XXXXXXXXXXXXXXXXXXXXXXX ... 1110XX010X01X0010101010X0XXXXX • Hierarchical database dependent encoding [Liu2002], [Lunteren and Engbersen2003] • Database-Independent Range Pre-Encoding [Venkatachary,Lakshminarayanan, Rangarajan2005]

  10. XXXXX XXXXX XXXXX XXXXX ... XXXXX Prior art: database-dependent encoding Key idea: allocate an extra bit to commonly occurring ranges. TCAM Example Source-port ≥ 1024 1 0011101101010XX00X01001111XXXX 2 11X00X00001110X0X101000110XXXX 3 10XX010100X0XX0100011010X01000 Representing a rule Set the assigned extra bit to 1 Set all other extra bits to X 11010010101XXXXXXXXXXXXXXXXXX 4 001110XXXXXXXXXXXXXXXXXXXXXXX 1 ... 1110XX010X01X0010101010X0XXXXX Generating the search key If source-port within range set extra bit to 1 Otherwise set extra bit to 0

  11. Fence encoding(w-bit words) Range Encoding = i 02w-i-11i ≥ i x2w-i-11i < i 02w-ixi-1 [i,j] 02w-1-jXj-i1i Prior art: database-independent range –pre-encoding (DIRPE) Key idea: Use extra bits for independent encoding, use general ternary values rather than prefixes. Number i is encoded by: 02w-1-i1i • Fence encoding • Expansion 1 • Requires 2w-1 bits What if we have a smaller number of bits?

  12. Key idea: Divide all (regular plus extra) bits to chunks, encode each by fence encoding W+36 bits XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Chunk1 (k1 bits) Chunk2 (k2 bits) Chunk4 (k4 bits) Chunk3 (k3 bits) Prior art: database-independent range –pre-encoding (cont’d) What if a smaller number of bits is available? Range expansion increases with the number of chunks

  13. An Observation: The problem is equivalent to the DNF expression minimization problem R=[10,11] b1b0 + b1b’0 ≈ b1 The general problem is NP-complete. • “Computing the minimum DNF representation of boolean functions defined by interval” • [Schieber, Geist, Zacks, 2005] • A linear-time algorithm for finding minimum-size DNF expression for any range of binary-coded numbers • Worst-case expansion for binary-encoded numbers is 2W-4 Thanks to Ronny Roth for the observation and the reference to the paper

  14. Talk outline • Definitions • Problem definition, prior art • The Short Range Gray Encoding Algorithm • Experimental results • Open questions

  15. Our solution: Short-Range Gray Encoding (SRGE) Gain without pain: Range expansion reduction can be obtained without the use of extra bits by changing the encoding scheme (SRGE) SRGE can be combined with database-dependent scheme: the Hybrid-SRGE scheme Hybrid-SRGE yields range-expansion of only 1.02 on real databases

  16. An example: covering [1,2] Binary encoding Gray encoding 00 01 10 11 00 01 11 10 Cover set: {01, 10} Cover set: {*1} Our solution: observations • Ranges tend to be small: typically correspond to similar-functionality ports: • 161-162: snmp, snmptrap • 67-68: bootps server, bootps client • 2300-2400: Microsoft DirectX • Binary coding not optimal for small ranges

  17. Obviously, not `our’ Frank Gray 3-bit BRGC: 000 001 011 010 110 111 101 100 0 0 0 0 0 0 0 0 4-bit BRGC: 1 1 1 1 1 1 1 1 Binary Reflected Gray Code Gray code: codewords for consecutive integers differ by single bit 000 001 011 010 110 111 101 100 100 101 111 110 010 011 001 000 Transforming binary  BRGC is quick

  18. Binary Reflected Gray Code (cont’d) 1 0 0 1 0 1 0 1 1 0 0 1 1 0 000 001 011 010 110 111 101 100 It is exactly this reflection property that helps decrease expansion

  19. p The SRGE algorithm Need to find minimum cover of [s,e] using gray coding. Find the least common ancestor p of point s and e s e

  20. pl pr The SRGE algorithm Let pl be the rightmost leaf in p’s left sub-tree Let pr be the leftmost leaf in p’s right sub-tree p s e

  21. The SRGE algorithm First, we handle the smaller of: [s,pl], [e,pr] p s pl pr e

  22. s’ The SRGE algorithm Cover by prefixes the smaller range and its mirror relative to p p s pl pr e We still need to cover the leftover range [s’,e], if it is non-empty

  23. p’ pl’ pr’ The SRGE algorithm • Repeat the previous procedure for the leftover: [s',e] • find their least common ancestor p’ • let pl' be the rightmost leaf in the left sub-tree of p' • let pr' be the leftmost leaf in the right sub-tree of p' p s pr s' e

  24. The SRGE algorithm • Two cases to consider: • |[pr', e]| > |[s', pl']|: • Cover [pr', e] by prefixes • The mirror of [pr', e] (relative to p') covers [s', pl'] p p’ s pr s’ pl’ pr’ e

  25. The SRGE algorithm • |[s', pl']|>|[pr', e']|: • Cover [pr', e] by prefixes. • Cover [s', pl'] by one a single prefix, corresponding to p' left sub-tree p p’ q ql s pr s’ pl’ pr’ e

  26. Hybrid-SRGE • For each unique range, compute total number of redundant entries under SRGE • Deal with the most expensive ranges by using standard database-dependent encoding

  27. Talk outline • Definitions • Problem definition, prior art • The Short Range Gray Encoding Algorithm • Experimental results • Future work

  28. SRGE range-expansion reduction Random ranges

  29. 223K rules with 300 unique ranges Combined from collection of 126 separate databases (firewall, acl-routers, intrusion prevention systems) Results on a real-life database Algorithm Expansion Redundancy Hybrid SRGE 1.03 1.2 Hybrid DIRPE 1.12 NA Prefix expansion 2.6 NA Acknowledgment: Cisco, David Taylor (WHSTL)

  30. Almost 60% of the unique ranges have length less then 20 Approx. 40% of the total number of ranges have length less then 20 Range-length distribution

  31. A small number of ranges cause most expansion

  32. Range expansion bounds The worst-case expansion ratio of SRGE on w-bit words is 2w-4 The worst-case expansion ratio of any range-covering scheme on w-bit words is at least w, regardless of the encoding scheme

  33. Expansion as function of bits number 2w-2 SRGE worst-case expansion is2W-4entries Number of TCAM entries At leastWentries required – regardless of the encoding technique Unknown 1 w Number of bits used 2^w-1

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