Fast Tracker Performance using the new ”Variable Resolution Associative Memory” for ATLAS

The Fast Tracker (FTK) for the ATLAS trigger is the only state-of-the-art online processor that tackles and solves the full track reconstruction problem at a hadron collider. We describe an important advancement for the Associative Memory device (AM). The AM is a VLSI processor for pattern recognition based on Content Addressable Memory (CAM) architecture. Pattern matching is carried out by finding track candidates in coarse resolution ”roads”. A large AM bank stores all trajectories of interest, called ”patterns”, for a given detector resolution. The AM extracts roads compatible with a given event during detector read-out. Two important variables characterize the quality of the AM bank: its ”coverage” and the level of fake roads. The coverage, which describes the geometric efficiency of a bank, is defined as the fraction of tracks that match at least one pattern in the bank. Given a certain road size, the coverage of the bank can be increased just adding patterns to the bank, while the number of fakes unfortunately is roughly proportional to the number of patterns in the bank. Moreover, as the luminosity increases, the fake rate increases rapidly. To counter that, we must reduce the width of our roads. If we decrease the road width using the current technology, the system will become very large and extremely expensive. We propose an elegant solution to this problem: the ”variable resolution patterns”. Each pattern and each detector layer within a pattern will be able to use the optimal width, but we will use a ”don’t care” feature (inspired from ternary CAMs) to increase the width when that is more appropriate. In other words we can use patterns of variable shape. As a result we reduce the number of fake roads, while keeping the efficiency high and avoiding excessive bank size due to the reduced width.