37,082 research outputs found
Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding
We study coding schemes for error correction in interactive communications.
Such interactive coding schemes simulate any -round interactive protocol
using rounds over an adversarial channel that corrupts up to
transmissions. Important performance measures for a coding scheme are its
maximum tolerable error rate , communication complexity , and
computational complexity.
We give the first coding scheme for the standard setting which performs
optimally in all three measures: Our randomized non-adaptive coding scheme has
a near-linear computational complexity and tolerates any error rate with a linear communication complexity. This improves over
prior results which each performed well in two of these measures.
We also give results for other settings of interest, namely, the first
computationally and communication efficient schemes that tolerate adaptively, if only one party is required to
decode, and if list decoding is allowed. These are the
optimal tolerable error rates for the respective settings. These coding schemes
also have near linear computational and communication complexity.
These results are obtained via two techniques: We give a general black-box
reduction which reduces unique decoding, in various settings, to list decoding.
We also show how to boost the computational and communication efficiency of any
list decoder to become near linear.Comment: preliminary versio
Information theoretic approach to interactive learning
The principles of statistical mechanics and information theory play an
important role in learning and have inspired both theory and the design of
numerous machine learning algorithms. The new aspect in this paper is a focus
on integrating feedback from the learner. A quantitative approach to
interactive learning and adaptive behavior is proposed, integrating model- and
decision-making into one theoretical framework. This paper follows simple
principles by requiring that the observer's world model and action policy
should result in maximal predictive power at minimal complexity. Classes of
optimal action policies and of optimal models are derived from an objective
function that reflects this trade-off between prediction and complexity. The
resulting optimal models then summarize, at different levels of abstraction,
the process's causal organization in the presence of the learner's actions. A
fundamental consequence of the proposed principle is that the learner's optimal
action policies balance exploration and control as an emerging property.
Interestingly, the explorative component is present in the absence of policy
randomness, i.e. in the optimal deterministic behavior. This is a direct result
of requiring maximal predictive power in the presence of feedback.Comment: 6 page
Coding for interactive communication correcting insertions and deletions
We consider the question of interactive communication, in which two remote
parties perform a computation while their communication channel is
(adversarially) noisy. We extend here the discussion into a more general and
stronger class of noise, namely, we allow the channel to perform insertions and
deletions of symbols. These types of errors may bring the parties "out of
sync", so that there is no consensus regarding the current round of the
protocol.
In this more general noise model, we obtain the first interactive coding
scheme that has a constant rate and resists noise rates of up to
. To this end we develop a novel primitive we name edit
distance tree code. The edit distance tree code is designed to replace the
Hamming distance constraints in Schulman's tree codes (STOC 93), with a
stronger edit distance requirement. However, the straightforward generalization
of tree codes to edit distance does not seem to yield a primitive that suffices
for communication in the presence of synchronization problems. Giving the
"right" definition of edit distance tree codes is a main conceptual
contribution of this work
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