20 research outputs found
On the Gap between Scalar and Vector Solutions of Generalized Combination Networks
We study scalar-linear and vector-linear solutions to the generalized
combination network. We derive new upper and lower bounds on the maximum number
of nodes in the middle layer, depending on the network parameters. These bounds
improve and extend the parameter range of known bounds. Using these new bounds
we present a general lower bound on the gap in the alphabet size between
scalar-linear and vector-linear solutions.Comment: 6 pages, 1 figures, accepted by ISIT 2020, revised according to the
review
Low-Power Cooling Codes with Efficient Encoding and Decoding
A class of low-power cooling (LPC) codes, to control simultaneously both the
peak temperature and the average power consumption of interconnects, was
introduced recently. An -LPC code is a coding scheme over wires
that (A) avoids state transitions on the hottest wires (cooling), and (B)
limits the number of transitions to in each transmission (low-power).
A few constructions for large LPC codes that have efficient encoding and
decoding schemes, are given. In particular, when is fixed, we construct LPC
codes of size and show that these LPC codes can be modified to
correct errors efficiently. We further present a construction for large LPC
codes based on a mapping from cooling codes to LPC codes. The efficiency of the
encoding/decoding for the constructed LPC codes depends on the efficiency of
the decoding/encoding for the related cooling codes and the ones for the
mapping
Robust Positioning Patterns with Low Redundancy
A robust positioning pattern is a large array that allows a mobile device to
locate its position by reading a possibly corrupted small window around it. In
this paper, we provide constructions of binary positioning patterns, equipped
with efficient locating algorithms, that are robust to a constant number of
errors and have redundancy within a constant factor of optimality. Furthermore,
we modify our constructions to correct rank errors and obtain binary
positioning patterns robust to any errors of rank less than a constant number.
Additionally, we construct -ary robust positioning sequences robust to a
large number of errors, some of which have length attaining the upper bound.
Our construction of binary positioning sequences that are robust to a
constant number of errors has the least known redundancy amongst those explicit
constructions with efficient locating algorithms. On the other hand, for binary
robust positioning arrays, our construction is the first explicit construction
whose redundancy is within a constant factor of optimality. The locating
algorithms accompanying both constructions run in time cubic in sequence length
or array dimension.Comment: Extended Version of SODA 2019 Pape