1,179 research outputs found
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
Weyl Spreading Sequence Optimizing CDMA
This paper shows an optimal spreading sequence in the Weyl sequence class,
which is similar to the set of the Oppermann sequences for asynchronous CDMA
systems. Sequences in Weyl sequence class have the desired property that the
order of cross-correlation is low. Therefore, sequences in the Weyl sequence
class are expected to minimize the inter-symbol interference. We evaluate the
upper bound of cross-correlation and odd cross-correlation of spreading
sequences in the Weyl sequence class and construct the optimization problem:
minimize the upper bound of the absolute values of cross-correlation and odd
cross-correlation. Since our optimization problem is convex, we can derive the
optimal spreading sequences as the global solution of the problem. We show
their signal to interference plus noise ratio (SINR) in a special case. From
this result, we propose how the initial elements are assigned, that is, how
spreading sequences are assigned to each users. In an asynchronous CDMA system,
we also numerically compare our spreading sequences with other ones, the Gold
codes, the Oppermann sequences, the optimal Chebyshev spreading sequences and
the SP sequences in Bit Error Rate. Our spreading sequence, which yields the
global solution, has the highest performance among the other spreading
sequences tested
A class of narrow-sense BCH codes over of length
BCH codes with efficient encoding and decoding algorithms have many
applications in communications, cryptography and combinatorics design. This
paper studies a class of linear codes of length over
with special trace representation, where is an odd prime
power. With the help of the inner distributions of some subsets of association
schemes from bilinear forms associated with quadratic forms, we determine the
weight enumerators of these codes. From determining some cyclotomic coset
leaders of cyclotomic cosets modulo , we prove
that narrow-sense BCH codes of length with designed distance
have the corresponding trace representation, and have the
minimal distance and the Bose distance , where
Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes
Given positive integers and , let denote the maximum size
of a binary code of length and minimum distance . The well-known
Gilbert-Varshamov bound asserts that , where
is the volume of a Hamming sphere of
radius . We show that, in fact, there exists a positive constant such
that whenever . The result follows by recasting the Gilbert- Varshamov bound into a
graph-theoretic framework and using the fact that the corresponding graph is
locally sparse. Generalizations and extensions of this result are briefly
discussed.Comment: 10 pages, 3 figures; to appear in the IEEE Transactions on
Information Theory, submitted August 12, 2003, revised March 28, 200
Deterministic Rateless Codes for BSC
A rateless code encodes a finite length information word into an infinitely
long codeword such that longer prefixes of the codeword can tolerate a larger
fraction of errors. A rateless code achieves capacity for a family of channels
if, for every channel in the family, reliable communication is obtained by a
prefix of the code whose rate is arbitrarily close to the channel's capacity.
As a result, a universal encoder can communicate over all channels in the
family while simultaneously achieving optimal communication overhead. In this
paper, we construct the first \emph{deterministic} rateless code for the binary
symmetric channel. Our code can be encoded and decoded in time per
bit and in almost logarithmic parallel time of , where
is any (arbitrarily slow) super-constant function. Furthermore, the error
probability of our code is almost exponentially small .
Previous rateless codes are probabilistic (i.e., based on code ensembles),
require polynomial time per bit for decoding, and have inferior asymptotic
error probabilities. Our main technical contribution is a constructive proof
for the existence of an infinite generating matrix that each of its prefixes
induce a weight distribution that approximates the expected weight distribution
of a random linear code
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