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Contact:
Marcus Greferath
School of Math. Sciences
University College Dublin
Belfield, Dublin 4, Ireland
Phone:
+353-1-716-2588 (UCD)
+353-85-153-0951 (mobile)
Joachim Rosenthal
Institut of Mathematics
University of Zurich
Winterthurerstrasse 190
8057 Zurich, Switzerland
Phone:
+41-44-63 55884 (office)
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ITW 2010 Dublin
IEEE Information Theory Workshop
Dublin, August 30 - September 3, 2010
Coding and decoding
Tue 31 Aug, 16.20-17.40, Room 2
Contributed session
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Brian L. Luke and Phillip E. Pace
Computation of the Robust Symmetrical Number System Dynamic Range
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Abstract:
The robust symmetrical number system (RSNS) is a number theoretic
transform formed using N ≥ 2 integer sequences and ensures that
two successive RSNS vectors (paired terms from all N sequences)
differ by only one integer -- integer Gray code property. The
dynamic range M of the RSNS is defined as the greatest
length of combined sequences that contain no ambiguities or repeated
paired terms. For all but a select few RSNS sequences there is no
closed-form solution to compute the dynamic range and its position.
This paper presents an efficient algorithm for computing the dynamic
range and its position. The dynamic range is shown to satisfy
M < Pf where Pf is the RSNS fundamental period Pf = 2 N ∏ mi.
It then follows that M < M where M = ∏ mi is
the dynamic range of the residue number system. An example is
presented to demonstrate the algorithm. The efficiency of the
algorithm is examined by comparing the speed of computation to a
naive search algorithm (using MATLAB on a PC).
Tue 31 Aug, 16.20-16.40, Room 2
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Kohtaro Tadaki
Properties of Optimal Prefix-Free Machines as Instantaneous Codes
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Abstract:
The optimal prefix-free machine U is a universal decoding
algorithm used to define the notion of program-size complexity
H(s) for a finite binary string s. Since the set of all halting
inputs for U is chosen to form a prefix-free set, the optimal
prefix-free machine can be regarded as an instantaneous code for
noiseless source coding scheme. In this paper, we investigate the
properties of optimal prefix-free machines as instantaneous codes.
In particular, we investigate the properties of the set U-1(s)
of codewords associated with a symbol s. Namely, we investigate
the number of codewords in U-1(s) and the distribution of
codewords in U-1(s) for each symbol s, using the toolkit of
algorithmic information theory.
Tue 31 Aug, 16.40-17.00, Room 2
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Oscar Moreno and José Ortiz-Ubarri
Group Permutable Constant Weight Codes
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Abstract:
Improvements to the Johnson Bound for Optical Orthogonal Codes have
been used to prove the optimality of double-periodic arrays with row
and column length relatively prime. In our work we produce families
of double-periodic arrays where the row and column length are not
relatively prime. In this work we introduce the concept of group
permutable constant weight codes and non-binary group permutable
constant weight codes. We present improvements to the Johnson Bound
to bound the cardinality of the families of double-periodic arrays
whose row and column length are not relatively prime. We present
some families of group permutable constant weight codes and prove
the optimality of these families.
Tue 31 Aug, 17.00-17.20, Room 2
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Khumbo Kumwenda and Eric Mwambene
Codes from graphs related to the categorical product of triangular graphs and Kn
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Abstract:
For any prime p and n ≥ 3, we examine p-ary linear codes
generated by incidence matrices of two classes of graphs, Hn and
Γn where Hn-1 is an induced subgraph of
Γn. Γn is a subgraph of the union of the categorical
product of triangular graphs Tn and complete graphs Kn, and
complements of triangular graphs Tn and Kn, where
the union of graphs is as defined in [Diestel, 1997]. For the codes
of Hn, we exhibit permutation decoding sets of order n for full
error correction. Their size is only twice the lower bound due to
Gordon. We also consider partial permutation decoding
for the binary codes from Γn.
Tue 31 Aug, 17.20-17.40, Room 2
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