694 research outputs found
Constructing practical Fuzzy Extractors using QIM
Fuzzy extractors are a powerful tool to extract randomness from noisy data. A fuzzy extractor can extract randomness only if the source data is discrete while in practice source data is continuous. Using quantizers to transform continuous data into discrete data is a commonly used solution. However, as far as we know no study has been made of the effect of the quantization strategy on the performance of fuzzy extractors. We construct the encoding and the decoding function of a fuzzy extractor using quantization index modulation (QIM) and we express properties of this fuzzy extractor in terms of parameters of the used QIM. We present and analyze an optimal (in the sense of embedding rate) two dimensional construction. Our 6-hexagonal tiling construction offers ( log2 6 / 2-1) approx. 3 extra bits per dimension of the space compared to the known square quantization based fuzzy extractor
Optimal Linear and Cyclic Locally Repairable Codes over Small Fields
We consider locally repairable codes over small fields and propose
constructions of optimal cyclic and linear codes in terms of the dimension for
a given distance and length. Four new constructions of optimal linear codes
over small fields with locality properties are developed. The first two
approaches give binary cyclic codes with locality two. While the first
construction has availability one, the second binary code is characterized by
multiple available repair sets based on a binary Simplex code. The third
approach extends the first one to q-ary cyclic codes including (binary)
extension fields, where the locality property is determined by the properties
of a shortened first-order Reed-Muller code. Non-cyclic optimal binary linear
codes with locality greater than two are obtained by the fourth construction.Comment: IEEE Information Theory Workshop (ITW) 2015, Apr 2015, Jerusalem,
Israe
Information Spectrum Approach to the Source Channel Separation Theorem
A source-channel separation theorem for a general channel has recently been
shown by Aggrawal et. al. This theorem states that if there exist a coding
scheme that achieves a maximum distortion level d_{max} over a general channel
W, then reliable communication can be accomplished over this channel at rates
less then R(d_{max}), where R(.) is the rate distortion function of the source.
The source, however, is essentially constrained to be discrete and memoryless
(DMS). In this work we prove a stronger claim where the source is general,
satisfying only a "sphere packing optimality" feature, and the channel is
completely general. Furthermore, we show that if the channel satisfies the
strong converse property as define by Han & verdu, then the same statement can
be made with d_{avg}, the average distortion level, replacing d_{max}. Unlike
the proofs there, we use information spectrum methods to prove the statements
and the results can be quite easily extended to other situations
Hiding State in CλaSH Hardware Descriptions
Synchronous hardware can be modelled as a mapping from input and state to output and a new state, such mappings are referred to as transition functions. It is natural to use a functional language to implement transition functions. The CaSH compiler is capable of translating transition functions to VHDL. Modelling hardware using multiple components is convenient. Components in CaSH can be considered as instantiations of functions. To avoid packing and unpacking state when composing components, functions are lifted to arrows. By using arrows the chance of making errors will decrease as it is not required to manually (un)pack the state. Furthermore, the Haskell do-syntax for arrows increases the readability of hardware designs. This is demonstrated using a realistic example of a circuit which consists of multiple components
A New Achievable Rate Region for Multiple-Access Channel with States
The problem of reliable communication over the multiple-access channel (MAC)
with states is investigated. We propose a new coding scheme for this problem
which uses quasi-group codes (QGC). We derive a new computable single-letter
characterization of the achievable rate region. As an example, we investigate
the problem of doubly-dirty MAC with modulo- addition. It is shown that the
sum-rate bits per channel use is achievable using the new scheme.
Whereas, the natural extension of the Gel'fand-Pinsker scheme, sum-rates
greater than are not achievable.Comment: 13 pages, ISIT 201
On covering expander graphs by Hamilton cycles
The problem of packing Hamilton cycles in random and pseudorandom graphs has
been studied extensively. In this paper, we look at the dual question of
covering all edges of a graph by Hamilton cycles and prove that if a graph with
maximum degree satisfies some basic expansion properties and contains
a family of edge disjoint Hamilton cycles, then there also
exists a covering of its edges by Hamilton cycles. This
implies that for every and every there exists
a covering of all edges of by Hamilton cycles
asymptotically almost surely, which is nearly optimal.Comment: 19 pages. arXiv admin note: some text overlap with arXiv:some
math/061275
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