On Majorana representations of the group 32:23^2{:}2 of 3C-pure type and the corresponding vertex operator algebras

In this article, we study Griess algebras and vertex operator subalgebras generated by Ising vectors in a moonshine type VOA such that the subgroup generated by the corresponding Miyamoto involutions has the shape $3^2{:}2$ and any two Ising vectors generate a 3C subVOA $U_{3C}$. We show that such a Griess algebra is uniquely determined, up to isomorphisms. The structure of the corresponding vertex operator algebra is also discussed. In addition, we give a construction of such a VOA inside the lattice VOA $V_{E_8^3}$, which gives an explicit example for Majorana representations of the group $3^2{:}2$ of 3C-pure type

GTD-based transceivers for decision feedback and bit loading

We consider new optimization problems for transceivers with DFE receivers and linear precoders, which also use bit loading at the transmitter. First, we consider the MIMO QoS (quality of service) problem, which is to minimize the total transmitted power when the bit rate and probability of error of each data stream are specified. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It is shown that under some multiplicative majorization conditions there exists a custom GTD-based transceiver which achieves the minimal power. The problem of maximizing the bit rate subject to the total power constraint and given error probability is also considered in this paper. It is shown that the GTD-based systems also give the optimal solutions to the bit rate maximization problem

MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization

This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zero-forcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities for the symbol streams. The precoder and DFE matrices are optimized jointly with bit allocation. It is shown that the generalized triangular decomposition (GTD) introduced by Jiang, Li, and Hager offers an optimal family of solutions. The optimal linear transceiver (which has a linear equalizer rather than a DFE) with optimal bit allocation is a member of this family. This shows formally that, under optimal bit allocation, linear and DFE transceivers achieve the same minimum power. The DFE transceiver using the geometric mean decomposition (GMD) is another member of this optimal family, and is such that optimal bit allocation yields identical bits for all symbol streams—no bit allocation is necessary—when the specified error probabilities are identical for all streams. The QR-based system used in VBLAST is yet another member of the optimal family and is particularly well-suited when limited feedback is allowed from receiver to transmitter. Two other optimization problems are then considered: a) minimization of power for specified set of bit rates and error probabilities (the QoS problem), and b) maximization of bit rate for fixed set of error probabilities and power. It is shown in both cases that the GTD yields an optimal family of solutions

Generalized Triangular Decomposition in Transform Coding

A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang This family includes the Karhunen-Loeve transform (KLT) and the generalized version of the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to that of the KLT and the PLT. Even though the original PLT introduced by Phoong is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes, the GTD-based family includes members that are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT, which has the unit noise-gain property. Other special cases of the GTD-TC are the geometric mean decomposition (GMD) and the bidiagonal decomposition (BID) transform coders. The GMD-TC in particular has the property that the optimum bit allocation is a uniform allocation; this is because all its transform domain coefficients have the same variance, implying thereby that the dynamic ranges of the coefficients to be quantized are identical

Joint optimization of transceivers with decision feedback and bit loading

The transceiver optimization problem for MIMO channels has been considered in the past with linear receivers as well as with decision feedback (DFE) receivers. Joint optimization of bit allocation, precoder, and equalizer has in the past been considered only for the linear transceiver (transceiver with linear precoder and linear equalizer). It has also been observed that the use of DFE even without bit allocation in general results in better performance that linear transceivers with bit allocation. This paper provides a general study of this for transceivers with the zero-forcing constraint. It is formally shown that when the bit allocation, precoder, and equalizer are jointly optimized, linear transceivers and transceivers with DFE have identical performance in the sense that transmitted power is identical for a given bit rate and error probability. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It will be shown that a broad class of GTD-based systems solve the optimal DFE problem with bit allocation. The special case of a linear transceiver with optimum bit allocation will emerge as one of the many solutions

ON THE EQUIVALENCE OF IMPORT TARIFF AND QUOTA: THE CASE OF RICE IMPORT IN TAIWAN

This paper extends the existing theory on the equivalence of import tariff and quota. If the equivalence is defined on the domestic price level (weak equivalence), then either the zero conjectural variation for domestic country or a perfectly competitive market will be sufficient to support this equivalence. If the equivalence is defined both on the same domestic price level as well as tariff rate (strong equivalence), then the conditions are that either domestic country acts as a Cournot competitor and foreign country is a price taker, or both domestic and foreign country are price takers. An empirical spatial-equilibrium trade model is constructed to simulate the impacts of import tariff and quota. Using Taiwan¡¦s rice import as an example, the empirical results show that if Taiwan switches from the quota system to tariff system, the domestic rice price as well as total social welfare can be increased given the same import volume.International Relations/Trade,