Ravi Teja Sukhavasi

Ravi Teja Sukhavasi, Babak Hassibi

We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime reliable, for a particular binary-input memoryless channel, if at each time, probability of making an error about a source bit that was sent d time instants ago decays exponentially in d. Anytime reliable codes are useful in interactive communication problems and, in particular, can be used to stabilize unstable plants across noisy channels. Schulman proved the existence of such codes which, due to their structure, he called tree codes; however, to date, no explicit constructions and tractable decoding algorithms have been devised. In this paper, we show the existence of anytime reliable "linear" codes with "high probability", i.e., suitably chosen random linear causal codes are anytime reliable with high probability. The key is to consider time-invariant codes (i.e., ones with Toeplitz generator and parity check matrices) which obviates the need to union bound over all times. For the binary erasure channel we give a simple ML decoding algorithm whose average complexity is constant per time iteration and for which the probability that complexity at a given time t exceeds KC^3 decays exponentially in C. We show the efficacy of the method by simulating the stabilization of an unstable plant across a BEC, and remark on the tradeoffs between the utilization of the communication resources and the control performance.

Ravi Teja Sukhavasi, Babak Hassibi

The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in problems of distributed control and networked control systems. Although the work of Schulman and Sahai over the past two decades, and their development of the notions of "tree codes" and "anytime capacity", provides the theoretical framework for studying such problems, there has been scant practical progress in this area because explicit constructions of tree codes with efficient encoding and decoding did not exist. To stabilize an unstable plant driven by bounded noise over a noisy channel one needs real-time encoding and real-time decoding and a reliability which increases exponentially with delay, which is what tree codes guarantee. We prove the existence of linear tree codes with high probability and, for erasure channels, give an explicit construction with an expected encoding and decoding complexity that is constant per time instant. We give sufficient conditions on the rate and reliability required of the tree codes to stabilize vector plants and argue that they are asymptotically tight. This work takes a major step towards controlling plants over noisy channels, and we demonstrate the efficacy of the method through several examples.

Onkar Dabeer, Radhika Gowaikar, Slawomir K. Grzechnik et al.

Autonomous vehicles rely on precise high definition (HD) 3d maps for navigation. This paper presents the mapping component of an end-to-end system for crowdsourcing precise 3d maps with semantically meaningful landmarks such as traffic signs (6 dof pose, shape and size) and traffic lanes (3d splines). The system uses consumer grade parts, and in particular, relies on a single front facing camera and a consumer grade GPS. Using real-time sign and lane triangulation on-device in the vehicle, with offline sign/lane clustering across multiple journeys and offline Bundle Adjustment across multiple journeys in the backend, we construct maps with mean absolute accuracy at sign corners of less than 20 cm from 25 journeys. To the best of our knowledge, this is the first end-to-end HD mapping pipeline in global coordinates in the automotive context using cost effective sensors.