59 research outputs found
Square Complex Orthogonal Designs with Low PAPR and Signaling Complexity
Space-Time Block Codes from square complex orthogonal designs (SCOD) have
been extensively studied and most of the existing SCODs contain large number of
zero. The zeros in the designs result in high peak-to-average power ratio
(PAPR) and also impose a severe constraint on hardware implementation of the
code when turning off some of the transmitting antennas whenever a zero is
transmitted. Recently, rate 1/2 SCODs with no zero entry have been reported for
8 transmit antennas. In this paper, SCODs with no zero entry for transmit
antennas whenever is a power of 2, are constructed which includes the 8
transmit antennas case as a special case. More generally, for arbitrary values
of , explicit construction of rate SCODs
with the ratio of number of zero entries to the total number of entries equal
to is reported,
whereas for standard known constructions, the ratio is . The
codes presented do not result in increased signaling complexity. Simulation
results show that the codes constructed in this paper outperform the codes
using the standard construction under peak power constraint while performing
the same under average power constraint.Comment: Accepted for publication in IEEE Transactions on Wireless
Communication. 10 pages, 6 figure
On some special cases of the Entropy Photon-Number Inequality
We show that the Entropy Photon-Number Inequality (EPnI) holds where one of
the input states is the vacuum state and for several candidates of the other
input state that includes the cases when the state has the eigenvectors as the
number states and either has only two non-zero eigenvalues or has arbitrary
number of non-zero eigenvalues but is a high entropy state. We also discuss the
conditions, which if satisfied, would lead to an extension of these results.Comment: 12 pages, no figure
Low-delay, High-rate Non-square Complex Orthogonal Designs
The maximal rate of a non-square complex orthogonal design for transmit
antennas is if is even and if is
odd and the codes have been constructed for all by Liang (IEEE Trans.
Inform. Theory, 2003) and Lu et al. (IEEE Trans. Inform. Theory, 2005) to
achieve this rate. A lower bound on the decoding delay of maximal-rate complex
orthogonal designs has been obtained by Adams et al. (IEEE Trans. Inform.
Theory, 2007) and it is observed that Liang's construction achieves the bound
on delay for equal to 1 and 3 modulo 4 while Lu et al.'s construction
achieves the bound for mod 4. For mod 4, Adams et al. (IEEE
Trans. Inform. Theory, 2010) have shown that the minimal decoding delay is
twice the lower bound, in which case, both Liang's and Lu at al.'s construction
achieve the minimum decoding delay. % when mod 4. For large value of ,
it is observed that the rate is close to half and the decoding delay is very
large. A class of rate-1/2 codes with low decoding delay for all has been
constructed by Tarokh et al. (IEEE Trans. Inform. Theory, 1999). % have
constructed a class of rate-1/2 codes with low decoding delay for all . In
this paper, another class of rate-1/2 codes is constructed for all in which
case the decoding delay is half the decoding delay of the rate-1/2 codes given
by Tarokh et al. This is achieved by giving first a general construction of
square real orthogonal designs which includes as special cases the well-known
constructions of Adams, Lax and Phillips and the construction of Geramita and
Pullman, and then making use of it to obtain the desired rate-1/2 codes. For
the case of 9 transmit antennas, the proposed rate-1/2 code is shown to be of
minimal-delay.Comment: To appear in IEEE Transactions on Information Theor
Entropy power inequality for a family of discrete random variables
It is known that the Entropy Power Inequality (EPI) always holds if the
random variables have density. Not much work has been done to identify discrete
distributions for which the inequality holds with the differential entropy
replaced by the discrete entropy. Harremo\"{e}s and Vignat showed that it holds
for the pair (B(m,p), B(n,p)), m,n \in \mathbb{N}, (where B(n,p) is a Binomial
distribution with n trials each with success probability p) for p = 0.5. In
this paper, we considerably expand the set of Binomial distributions for which
the inequality holds and, in particular, identify n_0(p) such that for all m,n
\geq n_0(p), the EPI holds for (B(m,p), B(n,p)). We further show that the EPI
holds for the discrete random variables that can be expressed as the sum of n
independent identical distributed (IID) discrete random variables for large n.Comment: 18 pages, 1 figur
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