Fast tracker performance using the new 'variable resolution associative memory' for ATLAS

The Fast Tracker (FTK) for the ATLAS trigger is a 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 at each level-1 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 probability for a track to match at least one pattern in the bank. To optimize the efficiency the easiest way is to increase the road size, keeping the number of patterns low and the system cheap. But this has a bad performance at high luminosity, where large roads are sensitive to the combinatoric effect, pushing on the contrary to use smaller roads and more patterns and making the system extremely expensive. We propose an elegant solution to this problem: the 'variable resolution patterns'. Each detector layer within a pattern will be able to use the optimal width. Using 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. We will show how this reduces the number of fake roads, while keeping the efficiency high and avoiding excessive bank size due to the reduced width.