100 research outputs found
An Upper Bound on the Capacity of non-Binary Deletion Channels
We derive an upper bound on the capacity of non-binary deletion channels.
Although binary deletion channels have received significant attention over the
years, and many upper and lower bounds on their capacity have been derived,
such studies for the non-binary case are largely missing. The state of the art
is the following: as a trivial upper bound, capacity of an erasure channel with
the same input alphabet as the deletion channel can be used, and as a lower
bound the results by Diggavi and Grossglauser are available. In this paper, we
derive the first non-trivial non-binary deletion channel capacity upper bound
and reduce the gap with the existing achievable rates. To derive the results we
first prove an inequality between the capacity of a 2K-ary deletion channel
with deletion probability , denoted by , and the capacity of the
binary deletion channel with the same deletion probability, , that is,
. Then by employing some existing upper
bounds on the capacity of the binary deletion channel, we obtain upper bounds
on the capacity of the 2K-ary deletion channel. We illustrate via examples the
use of the new bounds and discuss their asymptotic behavior as .Comment: accepted for presentation in ISIT 201
Memory effects can make the transmission capability of a communication channel uncomputable
Most communication channels are subjected to noise. One of the goals of
Information Theory is to add redundancy in the transmission of information so
that the information is transmitted reliably and the amount of information
transmitted through the channel is as large as possible. The maximum rate at
which reliable transmission is possible is called the capacity. If the channel
does not keep memory of its past, the capacity is given by a simple
optimization problem and can be efficiently computed. The situation of channels
with memory is less clear. Here we show that for channels with memory the
capacity cannot be computed to within precision 1/5. Our result holds even if
we consider one of the simplest families of such channels -information-stable
finite state machine channels-, restrict the input and output of the channel to
4 and 1 bit respectively and allow 6 bits of memory.Comment: Improved presentation and clarified claim
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