29,257 research outputs found
Extrinsic Jensen-Shannon Divergence: Applications to Variable-Length Coding
This paper considers the problem of variable-length coding over a discrete
memoryless channel (DMC) with noiseless feedback. The paper provides a
stochastic control view of the problem whose solution is analyzed via a newly
proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS)
divergence. It is shown that strictly positive lower bounds on EJS divergence
provide non-asymptotic upper bounds on the expected code length. The paper
presents strictly positive lower bounds on EJS divergence, and hence
non-asymptotic upper bounds on the expected code length, for the following two
coding schemes: variable-length posterior matching and MaxEJS coding scheme
which is based on a greedy maximization of the EJS divergence.
As an asymptotic corollary of the main results, this paper also provides a
rate-reliability test. Variable-length coding schemes that satisfy the
condition(s) of the test for parameters and , are guaranteed to achieve
rate and error exponent . The results are specialized for posterior
matching and MaxEJS to obtain deterministic one-phase coding schemes achieving
capacity and optimal error exponent. For the special case of symmetric
binary-input channels, simpler deterministic schemes of optimal performance are
proposed and analyzed.Comment: 17 pages (two-column), 4 figures, to appear in IEEE Transactions on
Information Theor
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
Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
This paper studies the difficulty of discriminating between an arbitrary
quantum channel and a "replacer" channel that discards its input and replaces
it with a fixed state. We show that, in this particular setting, the most
general adaptive discrimination strategies provide no asymptotic advantage over
non-adaptive tensor-power strategies. This conclusion follows by proving a
quantum Stein's lemma for this channel discrimination setting, showing that a
constant bound on the Type I error leads to the Type II error decreasing to
zero exponentially quickly at a rate determined by the maximum relative entropy
registered between the channels. The strong converse part of the lemma states
that any attempt to make the Type II error decay to zero at a rate faster than
the channel relative entropy implies that the Type I error necessarily
converges to one. We then refine this latter result by identifying the optimal
strong converse exponent for this task. As a consequence of these results, we
can establish a strong converse theorem for the quantum-feedback-assisted
capacity of a channel, sharpening a result due to Bowen. Furthermore, our
channel discrimination result demonstrates the asymptotic optimality of a
non-adaptive tensor-power strategy in the setting of quantum illumination, as
was used in prior work on the topic. The sandwiched Renyi relative entropy is a
key tool in our analysis. Finally, by combining our results with recent results
of Hayashi and Tomamichel, we find a novel operational interpretation of the
mutual information of a quantum channel N as the optimal type II error exponent
when discriminating between a large number of independent instances of N and an
arbitrary "worst-case" replacer channel chosen from the set of all replacer
channels.Comment: v3: 35 pages, 4 figures, accepted for publication in Communications
in Mathematical Physic
Joint source-channel coding with feedback
This paper quantifies the fundamental limits of variable-length transmission
of a general (possibly analog) source over a memoryless channel with noiseless
feedback, under a distortion constraint. We consider excess distortion, average
distortion and guaranteed distortion (-semifaithful codes). In contrast to
the asymptotic fundamental limit, a general conclusion is that allowing
variable-length codes and feedback leads to a sizable improvement in the
fundamental delay-distortion tradeoff. In addition, we investigate the minimum
energy required to reproduce source samples with a given fidelity after
transmission over a memoryless Gaussian channel, and we show that the required
minimum energy is reduced with feedback and an average (rather than maximal)
power constraint.Comment: To appear in IEEE Transactions on Information Theor
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