2 research outputs found
Delays and the Capacity of Continuous-time Channels
Any physical channel of communication offers two potential reasons why its
capacity (the number of bits it can transmit in a unit of time) might be
unbounded: (1) Infinitely many choices of signal strength at any given instant
of time, and (2) Infinitely many instances of time at which signals may be
sent. However channel noise cancels out the potential unboundedness of the
first aspect, leaving typical channels with only a finite capacity per instant
of time. The latter source of infinity seems less studied. A potential source
of unreliability that might restrict the capacity also from the second aspect
is delay: Signals transmitted by the sender at a given point of time may not be
received with a predictable delay at the receiving end. Here we examine this
source of uncertainty by considering a simple discrete model of delay errors.
In our model the communicating parties get to subdivide time as microscopically
finely as they wish, but still have to cope with communication delays that are
macroscopic and variable. The continuous process becomes the limit of our
process as the time subdivision becomes infinitesimal. We taxonomize this class
of communication channels based on whether the delays and noise are stochastic
or adversarial; and based on how much information each aspect has about the
other when introducing its errors. We analyze the limits of such channels and
reach somewhat surprising conclusions: The capacity of a physical channel is
finitely bounded only if at least one of the two sources of error (signal noise
or delay noise) is adversarial. In particular the capacity is finitely bounded
only if the delay is adversarial, or the noise is adversarial and acts with
knowledge of the stochastic delay. If both error sources are stochastic, or if
the noise is adversarial and independent of the stochastic delay, then the
capacity of the associated physical channel is infinite
Continuous Time Channels with Interference
Khanna and Sudan \cite{KS11} studied a natural model of continuous time
channels where signals are corrupted by the effects of both noise and delay,
and showed that, surprisingly, in some cases both are not enough to prevent
such channels from achieving unbounded capacity. Inspired by their work, we
consider channels that model continuous time communication with adversarial
delay errors. The sender is allowed to subdivide time into an arbitrarily large
number of micro-units in which binary symbols may be sent, but the symbols
are subject to unpredictable delays and may interfere with each other. We model
interference by having symbols that land in the same micro-unit of time be
summed, and we study -interference channels, which allow receivers to
distinguish sums up to the value . We consider both a channel adversary that
has a limit on the maximum number of steps it can delay each symbol, and a more
powerful adversary that only has a bound on the average delay.
We give precise characterizations of the threshold between finite and
infinite capacity depending on the interference behavior and on the type of
channel adversary: for max-bounded delay, the threshold is at
D_{\text{max}}=\ThetaM \log\min{k, M})), and for average bounded delay the
threshold is at .Comment: 7 pages. To appear in ISIT 201