680 research outputs found
Error Correcting Codes for Distributed Control
The problem of stabilizing an unstable plant over a noisy communication link
is an increasingly important one that arises in applications of networked
control systems. Although the work of Schulman and Sahai over the past two
decades, and their development of the notions of "tree codes"\phantom{} 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 decoding delay, which is what tree codes
guarantee. We prove that linear tree codes occur with high probability and, for
erasure channels, give an explicit construction with an expected decoding
complexity that is constant per time instant. We give novel 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 an
important step towards controlling plants over noisy channels, and we
demonstrate the efficacy of the method through several examples.Comment: 39 page
Searching with Measurement Dependent Noise
Consider a target moving with a constant velocity on a unit-circumference
circle, starting from an arbitrary location. To acquire the target, any region
of the circle can be probed for its presence, but the associated measurement
noise increases with the size of the probed region. We are interested in the
expected time required to find the target to within some given resolution and
error probability. For a known velocity, we characterize the optimal tradeoff
between time and resolution (i.e., maximal rate), and show that in contrast to
the case of constant measurement noise, measurement dependent noise incurs a
multiplicative gap between adaptive search and non-adaptive search. Moreover,
our adaptive scheme attains the optimal rate-reliability tradeoff. We further
show that for optimal non-adaptive search, accounting for an unknown velocity
incurs a factor of two in rate.Comment: Information Theory Workshop (ITW) 201
Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem
In this paper, we propose an open-loop unequal-error-protection querying
policy based on superposition coding for the noisy 20 questions problem. In
this problem, a player wishes to successively refine an estimate of the value
of a continuous random variable by posing binary queries and receiving noisy
responses. When the queries are designed non-adaptively as a single block and
the noisy responses are modeled as the output of a binary symmetric channel the
20 questions problem can be mapped to an equivalent problem of channel coding
with unequal error protection (UEP). A new non-adaptive querying strategy based
on UEP superposition coding is introduced whose estimation error decreases with
an exponential rate of convergence that is significantly better than that of
the UEP repetition coding introduced by Variani et al. (2015). With the
proposed querying strategy, the rate of exponential decrease in the number of
queries matches the rate of a closed-loop adaptive scheme where queries are
sequentially designed with the benefit of feedback. Furthermore, the achievable
error exponent is significantly better than that of random block codes
employing equal error protection.Comment: To appear in IEEE Transactions on Information Theor
Error Exponents for Variable-length Block Codes with Feedback and Cost Constraints
Variable-length block-coding schemes are investigated for discrete memoryless
channels with ideal feedback under cost constraints. Upper and lower bounds are
found for the minimum achievable probability of decoding error as
a function of constraints R, \AV, and on the transmission rate,
average cost, and average block length respectively. For given and \AV,
the lower and upper bounds to the exponent are
asymptotically equal as . The resulting reliability
function, , as a
function of and \AV, is concave in the pair (R, \AV) and generalizes
the linear reliability function of Burnashev to include cost constraints. The
results are generalized to a class of discrete-time memoryless channels with
arbitrary alphabets, including additive Gaussian noise channels with amplitude
and power constraints
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