23,284 research outputs found
A Counterexample to Cover's 2P Conjecture on Gaussian Feedback Capacity
We provide a counterexample to Cover's conjecture that the feedback capacity
of an additive Gaussian noise channel under power constraint
be no greater than the nonfeedback capacity of the same channel under
power constraint , i.e., .Comment: 2 pages, submitted to IEEE Transactions on Information Theor
Structural Properties of Index Coding Capacity Using Fractional Graph Theory
The capacity region of the index coding problem is characterized through the
notion of confusion graph and its fractional chromatic number. Based on this
multiletter characterization, several structural properties of the capacity
region are established, some of which are already noted by Tahmasbi, Shahrasbi,
and Gohari, but proved here with simple and more direct graph-theoretic
arguments. In particular, the capacity region of a given index coding problem
is shown to be simple functionals of the capacity regions of smaller
subproblems when the interaction between the subproblems is none, one-way, or
complete.Comment: 5 pages, to appear in the 2015 IEEE International Symposium on
Information Theory (ISIT
On Critical Index Coding Problems
The question of under what condition some side information for index coding
can be removed without affecting the capacity region is studied, which was
originally posed by Tahmasbi, Shahrasbi, and Gohari. To answer this question,
the notion of unicycle for the side information graph is introduced and it is
shown that any edge that belongs to a unicycle is critical, namely, it cannot
be removed without reducing the capacity region. Although this sufficient
condition for criticality is not necessary in general, a partial converse is
established, which elucidates the connection between the notion of unicycle and
the maximal acylic induced subgraph outer bound on the capacity region by
Bar-Yossef, Birk, Jayram, and Kol.Comment: 5 pages, accepted to 2015 IEEE Information Theory Workshop (ITW),
Jeju Island, Kore
The Approximate Capacity of the MIMO Relay Channel
Capacity bounds are studied for the multiple-antenna complex Gaussian relay
channel with t1 transmitting antennas at the sender, r2 receiving and t2
transmitting antennas at the relay, and r3 receiving antennas at the receiver.
It is shown that the partial decode-forward coding scheme achieves within
min(t1,r2) bits from the cutset bound and at least one half of the cutset
bound, establishing a good approximate expression of the capacity. A similar
additive gap of min(t1 + t2, r3) + r2 bits is shown to be achieved by the
compress-forward coding scheme.Comment: 8 pages, 5 figures, submitted to the IEEE Transactions on Information
Theor
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