36 research outputs found
Interactive Coding Resilient to an Unknown Number of Erasures
We consider distributed computations between two parties carried out over a noisy channel that may erase messages. Following a noise model proposed by Dani et al. (2018), the noise level observed by the parties during the computation in our setting is arbitrary and a priori unknown to the parties.
We develop interactive coding schemes that adapt to the actual level of noise and correctly execute any two-party computation. Namely, in case the channel erases T transmissions, the coding scheme will take N+2T transmissions using an alphabet of size 4 (alternatively, using 2N+4T transmissions over a binary channel) to correctly simulate any binary protocol that takes N transmissions assuming a noiseless channel. We can further reduce the communication to N+T by relaxing the communication model and allowing parties to remain silent rather than forcing them to communicate in every round of the coding scheme.
Our coding schemes are efficient, deterministic, have linear overhead both in their communication and round complexity, and succeed (with probability 1) regardless of the number of erasures T
Adaptive Protocols for Interactive Communication
How much adversarial noise can protocols for interactive communication
tolerate? This question was examined by Braverman and Rao (IEEE Trans. Inf.
Theory, 2014) for the case of "robust" protocols, where each party sends
messages only in fixed and predetermined rounds. We consider a new class of
non-robust protocols for Interactive Communication, which we call adaptive
protocols. Such protocols adapt structurally to the noise induced by the
channel in the sense that both the order of speaking, and the length of the
protocol may vary depending on observed noise.
We define models that capture adaptive protocols and study upper and lower
bounds on the permissible noise rate in these models. When the length of the
protocol may adaptively change according to the noise, we demonstrate a
protocol that tolerates noise rates up to . When the order of speaking may
adaptively change as well, we demonstrate a protocol that tolerates noise rates
up to . Hence, adaptivity circumvents an impossibility result of on
the fraction of tolerable noise (Braverman and Rao, 2014).Comment: Content is similar to previous version yet with an improved
presentatio
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
Noisy Beeping Networks
We introduce noisy beeping networks, where nodes have limited communication
capabilities, namely, they can only emit energy or sense the channel for
energy. Furthermore, imperfections may cause devices to malfunction with some
fixed probability when sensing the channel, which amounts to deducing a noisy
received transmission. Such noisy networks have implications for
ultra-lightweight sensor networks and biological systems.
We show how to compute tasks in a noise-resilient manner over noisy beeping
networks of arbitrary structure. In particular, we transform any algorithm that
assumes a noiseless beeping network (of size ) into a noise-resilient
version while incurring a multiplicative overhead of only in its
round complexity, with high probability. We show that our coding is optimal for
some tasks, such as node-coloring of a clique.
We further show how to simulate a large family of algorithms designed for
distributed networks in the CONGEST() model over a noisy beeping network.
The simulation succeeds with high probability and incurs an asymptotic
multiplicative overhead of in the
round complexity, where is the maximal degree of the network. The
overhead is tight for certain graphs, e.g., a clique. Further, this simulation
implies a constant overhead coding for constant-degree networks