Exact Worst Case TCAM Rule Expansion

In recent years, hardware-based packet classification has became an essential component in many networking devices. It often relies on ternary content-addressable memories (TCAMs), which can compare in parallel the packet header against a large set of rules. Designers of TCAMs often have to deal with unpredictable sets of rules. These result in highly variable rule expansions, and can only rely on heuristic encoding algorithms with no reasonable guarantees. In this paper, given several types of rules, we provide new upper bounds on the TCAM worst case rule expansions. In particular, we prove that a W-bit range can be encoded in W TCAM entries, improving upon the previously known bound of 2W - 5. We further prove the optimality of this bound of W for prefix encoding, using new analytical tools based on independent sets and alternating paths. Next, we generalize these lower bounds to a new class of codes called hierarchical codes that includes both binary codes and Gray codes. Last, we propose a modified TCAM architecture that can use additional logic to significantly reduce the rule expansions, both in the worst case and using real-life classification databases.