5,438 research outputs found
Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which
is conjectured to be a universally optimal code. We show that this scheme has a
generalization in terms of Kerdock codes, as well as in terms of maximal real
mutually unbiased bases. These schemes also related to extremal line-sets in
Euclidean spaces and Barnes-Wall lattices. D. de Caen and E. R. van Dam
constructed two infinite series of formally dual 3-class association schemes.
We explain this formal duality by constructing two dual abelian schemes related
to quaternary linear Kerdock and Preparata codes.Comment: 16 page
QPSK Block-Modulation Codes for Unequal Error Protection
Unequal error protection (UEP) codes find applications in broadcast channels, as well as in other digital communication systems, where messages have different degrees of importance. Binary linear UEP (LUEP) codes combined with a Gray mapped QPSK signal set are used to obtain new efficient QPSK block-modulation codes for unequal error protection. Several examples of QPSK modulation codes that have the same minimum squared Euclidean distance as the best QPSK modulation codes, of the same rate and length, are given. In the new constructions of QPSK block-modulation codes, even-length binary LUEP codes are used. Good even-length binary LUEP codes are obtained when shorter binary linear codes are combined using either the well-known |u¯|u¯+v¯|-construction or the so-called construction X. Both constructions have the advantage of resulting in optimal or near-optimal binary LUEP codes of short to moderate lengths, using very simple linear codes, and may be used as constituent codes in the new constructions. LUEP codes lend themselves quite naturally to multistage decoding up to their minimum distance, using the decoding of component subcodes. A new suboptimal two-stage soft-decision decoding of LUEP codes is presented and its application to QPSK block-modulation codes for UEP illustrated
Low Correlation Sequences over the QAM Constellation
This paper presents the first concerted look at low correlation sequence
families over QAM constellations of size M^2=4^m and their potential
applicability as spreading sequences in a CDMA setting.
Five constructions are presented, and it is shown how such sequence families
have the ability to transport a larger amount of data as well as enable
variable-rate signalling on the reverse link.
Canonical family CQ has period N, normalized maximum-correlation parameter
theta_max bounded above by A sqrt(N), where 'A' ranges from 1.8 in the 16-QAM
case to 3.0 for large M. In a CDMA setting, each user is enabled to transfer 2m
bits of data per period of the spreading sequence which can be increased to 3m
bits of data by halving the size of the sequence family. The technique used to
construct CQ is easily extended to produce larger sequence families and an
example is provided.
Selected family SQ has a lower value of theta_max but permits only (m+1)-bit
data modulation. The interleaved 16-QAM sequence family IQ has theta_max <=
sqrt(2) sqrt(N) and supports 3-bit data modulation.
The remaining two families are over a quadrature-PAM (Q-PAM) subset of size
2M of the M^2-QAM constellation. Family P has a lower value of theta_max in
comparison with Family SQ, while still permitting (m+1)-bit data modulation.
Interleaved family IP, over the 8-ary Q-PAM constellation, permits 3-bit data
modulation and interestingly, achieves the Welch lower bound on theta_max.Comment: 21 pages, 3 figures. To appear in IEEE Transactions on Information
Theory in February 200
Codes for Key Generation in Quantum Cryptography
As an alternative to the usual key generation by two-way communication in
schemes for quantum cryptography, we consider codes for key generation by
one-way communication. We study codes that could be applied to the raw key
sequences that are ideally obtained in recently proposed scenarios for quantum
key distribution, which can be regarded as communication through symmetric
four-letter channels.Comment: IJQI format, 13 pages, 1 tabl
Convolutional and tail-biting quantum error-correcting codes
Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to
4096 states and minimum distances up to 10 are constructed as stabilizer codes
from classical self-orthogonal rate-1/n F_4-linear and binary linear
convolutional codes, respectively. These codes generally have higher rate and
less decoding complexity than comparable quantum block codes or previous
quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same
rate and error-correction capability and essentially the same decoding
algorithms are derived from these convolutional codes via tail-biting.Comment: 30 pages. Submitted to IEEE Transactions on Information Theory. Minor
revisions after first round of review
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