2,623 research outputs found
Capacity of a POST Channel with and without Feedback
We consider finite state channels where the state of the channel is its
previous output. We refer to these as POST (Previous Output is the STate)
channels. We first focus on POST() channels. These channels have binary
inputs and outputs, where the state determines if the channel behaves as a
or an channel, both with parameter . %with parameter We
show that the non feedback capacity of the POST() channel equals its
feedback capacity, despite the memory of the channel. The proof of this
surprising result is based on showing that the induced output distribution,
when maximizing the directed information in the presence of feedback, can also
be achieved by an input distribution that does not utilize of the feedback. We
show that this is a sufficient condition for the feedback capacity to equal the
non feedback capacity for any finite state channel. We show that the result
carries over from the POST() channel to a binary POST channel where the
previous output determines whether the current channel will be binary with
parameters or . Finally, we show that, in general, feedback may
increase the capacity of a POST channel
Finite-State Channels with Feedback and State Known at the Encoder
We consider finite state channels (FSCs) with feedback and state information
known causally at the encoder. This setting is quite general and includes: a
memoryless channel with i.i.d. state (the Shannon strategy), Markovian states
that include look-ahead (LA) access to the state and energy harvesting. We
characterize the feedback capacity of the general setting as the directed
information between auxiliary random variables with memory to the channel
outputs. We also propose two methods for computing the feedback capacity: (i)
formulating an infinite-horizon average-reward dynamic program; and (ii) a
single-letter lower bound based on auxiliary directed graphs called -graphs.
We demonstrate our computation methods on several examples. In the first
example, we introduce a channel with LA and derive a closed-form, analytic
lower bound on its feedback capacity. Furthermore, we show that the mentioned
methods achieve the feedback capacity of known unifilar FSCs such as the
trapdoor channel, the Ising channel and the input-constrained erasure channel.
Finally, we analyze the feedback capacity of a channel whose state is
stochastically dependent on the input.Comment: 39 pages, 10 figures. The material in this paper was presented in
part at the 56th Annual Allerton Conference on Communication, Control, and
Computing, Monticello, IL, USA, October 2018, and at the IEEE International
Symposium on Information Theory, Los Angeles, CA, USA, June 202
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
- …