5,540 research outputs found
Constructions of Optimal and Near-Optimal Multiply Constant-Weight Codes
Multiply constant-weight codes (MCWCs) have been recently studied to improve
the reliability of certain physically unclonable function response. In this
paper, we give combinatorial constructions for MCWCs which yield several new
infinite families of optimal MCWCs. Furthermore, we demonstrate that the
Johnson type upper bounds of MCWCs are asymptotically tight for fixed weights
and distances. Finally, we provide bounds and constructions of two dimensional
MCWCs
Multiply Constant-Weight Codes and the Reliability of Loop Physically Unclonable Functions
We introduce the class of multiply constant-weight codes to improve the
reliability of certain physically unclonable function (PUF) response. We extend
classical coding methods to construct multiply constant-weight codes from known
-ary and constant-weight codes. Analogues of Johnson bounds are derived and
are shown to be asymptotically tight to a constant factor under certain
conditions. We also examine the rates of the multiply constant-weight codes and
interestingly, demonstrate that these rates are the same as those of
constant-weight codes of suitable parameters. Asymptotic analysis of our code
constructions is provided
Filter Bank Fusion Frames
In this paper we characterize and construct novel oversampled filter banks
implementing fusion frames. A fusion frame is a sequence of orthogonal
projection operators whose sum can be inverted in a numerically stable way.
When properly designed, fusion frames can provide redundant encodings of
signals which are optimally robust against certain types of noise and erasures.
However, up to this point, few implementable constructions of such frames were
known; we show how to construct them using oversampled filter banks. In this
work, we first provide polyphase domain characterizations of filter bank fusion
frames. We then use these characterizations to construct filter bank fusion
frame versions of discrete wavelet and Gabor transforms, emphasizing those
specific finite impulse response filters whose frequency responses are
well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas
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