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 $2^a$ transmit antennas whenever $a+1$ is a power of 2, are constructed which includes the 8 transmit antennas case as a special case. More generally, for arbitrary values of $a$, explicit construction of $2^a\times 2^a$ rate $\frac{a+1}{2^a}$ SCODs with the ratio of number of zero entries to the total number of entries equal to $1-\frac{a+1}{2^a}2^{\lfloor log_2(\frac{2^a}{a+1}) \rfloor}$ is reported, whereas for standard known constructions, the ratio is $1-\frac{a+1}{2^a}$. 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 $n$ transmit antennas is $1/2+\frac{1}{n}$ if $n$ is even and $1/2+\frac{1}{n+1}$ if $n$ is odd and the codes have been constructed for all $n$ 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 $n$ equal to 1 and 3 modulo 4 while Lu et al.'s construction achieves the bound for $n=0,1,3$ mod 4. For $n=2$ 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 $n=2$ mod 4. For large value of $n$, 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 $n$ 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 $n$. In this paper, another class of rate-1/2 codes is constructed for all $n$ 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