211 research outputs found
On additive MDS codes over small fields
Let be a additive MDS code which is linear over . We prove that if and of the projections of are linear over then is linear over . We use this geometrical theorem, other geometric arguments and some computations to classify all additive MDS codes over for . We also classify the longest additive MDS codes over which are linear over . In these cases, the classifications not only verify the MDS conjecture for additive codes, but also confirm there are no additive non-linear MDS codes which perform as well as their linear counterparts. These results imply that the quantum MDS conjecture holds for .Peer ReviewedPostprint (published version
The equivalence of linear codes implies semi-linear equivalence
The version of record is available online at: 10.1007/s10623-022-01055-xWe prove that if two linear codes are equivalent then they are semi-linearly equivalent. We also prove that if two additive MDS codes over a field are equivalent then they are additively equivalent.Peer ReviewedPostprint (author's final draft
Wet paper codes and the dual distance in steganography
In 1998 Crandall introduced a method based on coding theory to secretly embed
a message in a digital support such as an image. Later Fridrich et al. improved
this method to minimize the distortion introduced by the embedding; a process
called wet paper. However, as previously emphasized in the literature, this
method can fail during the embedding step. Here we find sufficient and
necessary conditions to guarantee a successful embedding by studying the dual
distance of a linear code. Since these results are essentially of combinatorial
nature, they can be generalized to systematic codes, a large family containing
all linear codes. We also compute the exact number of solutions and point out
the relationship between wet paper codes and orthogonal arrays
Additive MDS codes
We prove that an additive code over a finite field which has a few projections
which are equivalent to a linear code is itself equivalent to a linear code, providing the code is not too short.Postprint (published version
Media-Based MIMO: A New Frontier in Wireless Communications
The idea of Media-based Modulation (MBM), is based on embedding information
in the variations of the transmission media (channel state). This is in
contrast to legacy wireless systems where data is embedded in a Radio Frequency
(RF) source prior to the transmit antenna. MBM offers several advantages vs.
legacy systems, including "additivity of information over multiple receive
antennas", and "inherent diversity over a static fading channel". MBM is
particularly suitable for transmitting high data rates using a single transmit
and multiple receive antennas (Single Input-Multiple Output Media-Based
Modulation, or SIMO-MBM). However, complexity issues limit the amount of data
that can be embedded in the channel state using a single transmit unit. To
address this shortcoming, the current article introduces the idea of Layered
Multiple Input-Multiple Output Media-Based Modulation (LMIMO-MBM). Relying on a
layered structure, LMIMO-MBM can significantly reduce both hardware and
algorithmic complexities, as well as the training overhead, vs. SIMO-MBM.
Simulation results show excellent performance in terms of Symbol Error Rate
(SER) vs. Signal-to-Noise Ratio (SNR). For example, a LMIMO-MBM is
capable of transmitting bits of information per (complex) channel-use,
with SER at dB (or SER
at dB). This performance is achieved using a single transmission
and without adding any redundancy for Forward-Error-Correction (FEC). This
means, in addition to its excellent SER vs. energy/rate performance, MBM
relaxes the need for complex FEC structures, and thereby minimizes the
transmission delay. Overall, LMIMO-MBM provides a promising alternative to MIMO
and Massive MIMO for the realization of 5G wireless networks.Comment: 26 pages, 11 figures, additional examples are given to further
explain the idea of Media-Based Modulation. Capacity figure adde
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