1,010 research outputs found
Difference Balanced Functions and Their Generalized Difference Sets
Difference balanced functions from to are closely related
to combinatorial designs and naturally define -ary sequences with the ideal
two-level autocorrelation. In the literature, all existing such functions are
associated with the -homogeneous property, and it was conjectured by Gong
and Song that difference balanced functions must be -homogeneous. First we
characterize difference balanced functions by generalized difference sets with
respect to two exceptional subgroups. We then derive several necessary and
sufficient conditions for -homogeneous difference balanced functions. In
particular, we reveal an unexpected equivalence between the -homogeneous
property and multipliers of generalized difference sets. By determining these
multipliers, we prove the Gong-Song conjecture for prime. Furthermore, we
show that every difference balanced function must be balanced or an affine
shift of a balanced function.Comment: 17 page
Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA
In this paper, we propose a fast decoder algorithm for uniquely decodable
(errorless) code sets for overloaded synchronous optical code-division
multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a
way that the users can uniquely recover the information bits with a very simple
decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML)
decoder, which has a high computational complexity for even moderate code
lengths, the proposed decoder has much lower computational complexity.
Simulation results in terms of bit error rate (BER) demonstrate that the
performance of the proposed decoder for a given BER requires only 1-2 dB higher
signal-to-noise ratio (SNR) than the ML decoder.Comment: arXiv admin note: substantial text overlap with arXiv:1806.0395
New quasi-orthogonal BCH-derived sequences for CDMA applications
European Transactions on Telecommunications, vol. 18Based on two methods recently proposed—the ‘Ranging Criterion’ (RC) and the ‘Generators Ranging Criterion’ (GRC)—new (quasi orthogonal) even BCH-derived sequences are generated which are very attractive for synchronous or quasi-synchronous Code Division Multiple-Access (CDMA) systems.
Numerical results show that the new family of BCH-derived sequences can contain a higher number of quasi-orthogonal sequences with lower correlation values and higher processing gains (PGs) than the spreading sequences typically used in the third generation of mobile communications system, UMTS or in the recent large area synchronised CDMA (LAS-CDMA) technology. It is shown that the even BCHderived
sequences are easily generated by a linear shift register generator, allowing the construction of systems with receiver structures of low complexity as compared with those of quasi-synchronous systems
using low correlation zone sequences, as for instance the LAS-CDMA system
Linear Codes from Some 2-Designs
A classical method of constructing a linear code over \gf(q) with a
-design is to use the incidence matrix of the -design as a generator
matrix over \gf(q) of the code. This approach has been extensively
investigated in the literature. In this paper, a different method of
constructing linear codes using specific classes of -designs is studied, and
linear codes with a few weights are obtained from almost difference sets,
difference sets, and a type of -designs associated to semibent functions.
Two families of the codes obtained in this paper are optimal. The linear codes
presented in this paper have applications in secret sharing and authentication
schemes, in addition to their applications in consumer electronics,
communication and data storage systems. A coding-theory approach to the
characterisation of highly nonlinear Boolean functions is presented
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