7,706 research outputs found
On Throughput and Decoding Delay Performance of Instantly Decodable Network Coding
In this paper, a comprehensive study of packet-based instantly decodable
network coding (IDNC) for single-hop wireless broadcast is presented. The
optimal IDNC solution in terms of throughput is proposed and its packet
decoding delay performance is investigated. Lower and upper bounds on the
achievable throughput and decoding delay performance of IDNC are derived and
assessed through extensive simulations. Furthermore, the impact of receivers'
feedback frequency on the performance of IDNC is studied and optimal IDNC
solutions are proposed for scenarios where receivers' feedback is only
available after and IDNC round, composed of several coded transmissions.
However, since finding these IDNC optimal solutions is computational complex,
we further propose simple yet efficient heuristic IDNC algorithms. The impact
of system settings and parameters such as channel erasure probability, feedback
frequency, and the number of receivers is also investigated and simple
guidelines for practical implementations of IDNC are proposed.Comment: This is a 14-page paper submitted to IEEE/ACM Transaction on
Networking. arXiv admin note: text overlap with arXiv:1208.238
Symmetry-assisted adversaries for quantum state generation
We introduce a new quantum adversary method to prove lower bounds on the
query complexity of the quantum state generation problem. This problem
encompasses both, the computation of partial or total functions and the
preparation of target quantum states. There has been hope for quite some time
that quantum state generation might be a route to tackle the {\sc Graph
Isomorphism} problem. We show that for the related problem of {\sc Index
Erasure} our method leads to a lower bound of which matches
an upper bound obtained via reduction to quantum search on elements. This
closes an open problem first raised by Shi [FOCS'02].
Our approach is based on two ideas: (i) on the one hand we generalize the
known additive and multiplicative adversary methods to the case of quantum
state generation, (ii) on the other hand we show how the symmetries of the
underlying problem can be leveraged for the design of optimal adversary
matrices and dramatically simplify the computation of adversary bounds. Taken
together, these two ideas give the new result for {\sc Index Erasure} by using
the representation theory of the symmetric group. Also, the method can lead to
lower bounds even for small success probability, contrary to the standard
adversary method. Furthermore, we answer an open question due to \v{S}palek
[CCC'08] by showing that the multiplicative version of the adversary method is
stronger than the additive one for any problem. Finally, we prove that the
multiplicative bound satisfies a strong direct product theorem, extending a
result by \v{S}palek to quantum state generation problems.Comment: 35 pages, 5 figure
Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel
In this paper, faulty successive cancellation decoding of polar codes for the
binary erasure channel is studied. To this end, a simple erasure-based fault
model is introduced to represent errors in the decoder and it is shown that,
under this model, polarization does not happen, meaning that fully reliable
communication is not possible at any rate. Furthermore, a lower bound on the
frame error rate of polar codes under faulty SC decoding is provided, which is
then used, along with a well-known upper bound, in order to choose a
blocklength that minimizes the erasure probability under faulty decoding.
Finally, an unequal error protection scheme that can re-enable asymptotically
erasure-free transmission at a small rate loss and by protecting only a
constant fraction of the decoder is proposed. The same scheme is also shown to
significantly improve the finite-length performance of the faulty successive
cancellation decoder by protecting as little as 1.5% of the decoder.Comment: Accepted for publications in the IEEE Transactions on Communication
The Zero-Undetected-Error Capacity Approaches the Sperner Capacity
Ahlswede, Cai, and Zhang proved that, in the noise-free limit, the
zero-undetected-error capacity is lower bounded by the Sperner capacity of the
channel graph, and they conjectured equality. Here we derive an upper bound
that proves the conjecture.Comment: 8 Pages; added a section on the definition of Sperner capacity;
accepted for publication in the IEEE Transactions on Information Theor
Grassmannian Frames with Applications to Coding and Communication
For a given class of uniform frames of fixed redundancy we define
a Grassmannian frame as one that minimizes the maximal correlation among all frames . We first analyze
finite-dimensional Grassmannian frames. Using links to packings in Grassmannian
spaces and antipodal spherical codes we derive bounds on the minimal achievable
correlation for Grassmannian frames. These bounds yield a simple condition
under which Grassmannian frames coincide with uniform tight frames. We exploit
connections to graph theory, equiangular line sets, and coding theory in order
to derive explicit constructions of Grassmannian frames. Our findings extend
recent results on uniform tight frames. We then introduce infinite-dimensional
Grassmannian frames and analyze their connection to uniform tight frames for
frames which are generated by group-like unitary systems. We derive an example
of a Grassmannian Gabor frame by using connections to sphere packing theory.
Finally we discuss the application of Grassmannian frames to wireless
communication and to multiple description coding.Comment: Submitted in June 2002 to Appl. Comp. Harm. Ana
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