Hua Chieh Li

Algebraic identification for optimal nonorthogonality 4/spl times/4 complex space-time block codes using tensor product on quaternions

The design potential of using quaternionic numbers to identify a 4/spl times/4 real orthogonal space-time block code has been exploited in various communication articles. Although it has been shown that orthogonal codes in full-rate exist only for 2 Tx-antennas in complex constellations, a series of complex quasi-orthogonal codes for 4 Tx-antennas is still proposed to have good performance recently. This quasi-orthogonal scheme enables the codes to reach the optimal nonorthogonality, which can be measured by taking the expectation over all transmit signals of the ratios between the powers of the off-diagonal and diagonal components. This correspondence extends the quaternionic identification to the above encoding methods. Based upon tensor product for giving the quaternionic space a linear extension, a complete necessary and sufficient condition for identifying any given complex quasi-orthogonal code with the extended space is generalized by considering every possible two-dimensional R-algebra.

On heights of p-ADIC dynamical systems

When we consider the properties of the iterates of a noninvertible endomorphism of a formal group, all the roots of iterates of the endomorphism are simple and the full commuting family contains both invertible and noninvertible series. Experimental evidence seems to suggest that for an invertible series to commute with a noninvertible series with only simple roots of iterates, two such commuting power series must be endomorphisms of a single formal group. Lubin proposed four conjectures to support this conjecture. In this paper, we provide answers to these four conjectures.

Deriving new quasi-orthogonal space-time block codes and relaxed designing viewpoints with full transmit diversity

It has been shown that a complex orthogonal design that provides full diversity and full transmission rate is not possible for more than two transmit antennas. The paper presents a new class of quasi-orthogonal space-time block codes using a group-theoretic method. The new designs can achieve full diversity for quadrature phase-shift-keying modulation, like the system using rotated constellations. Based upon the analysis of the new codes, a relaxed designing viewpoint for full diversity is proposed for arbitrary signal constellations.

P-ADIC POWER SERIES WHICH COMMUTE UNDER COMPOSITION

When two noninvertible series commute to each other, they have same set of roots of iterates. Most of the results of this paper will be concerned with the problem of which series commute with a given noninvertible series. Our main theorem is a generalization of Lubin’s result about isogenies of formal

p -Typical Dynamical Systems and Formal Groups

By using the idea of logarithm, we give an effective method to decide whether a stable series is an endomorphism of a formal group or not. We also give examples that contradict Lubins conjecture.

Generally Dimensional and Constellation Expansion Free Space–Time Block Codes for QAM With Full Diversity

This correspondence presents new rate-1 space-time block codes (STBCs) attending full diversity over every quadrature amplitude modulation (QAM) constellation when the number of Tx antennas is a power of two. From the simulation results, our design performs very closely to the quasi-orthogonal code with constellation rotation over 4-QAM and 16-QAM in the case of four Tx antennas over quasi-static Rayleigh fading channels. Moreover, the proposed codes would not cause any constellation expansion over QAM symbols in contrast with the quasi-orthogonal codes with constellation rotations

Generally Explicit Space–Time Codes With Nonvanishing Determinants for Arbitrary Numbers of Transmit Antennas

Nonvanishing determinants have emerged as an attractive criterion enabling a space-time code achieve the optimal diversity-multiplexing gains tradeoff. It seems that cyclic division algebras play the most crucial role in designing a space-time code with nonvanishing determinants. In this paper, we explicitly construct space-time codes for arbitrary numbers of transmit antennas that achieve nonvanishing determinants and the optimal diversity-multiplexing gains tradeoff over Z [i]. Unlike previous methods usually arising a field compositum for two or more fields, our scheme, which only requires one simple extension, constitutes a much more efficient and feasible advancement whether in theory or practice.

When is a p-adic power series an endomorphism of a formal group?

If f(x) is a noninvertible endomorphism of a formal group, then we have that f(x) commutes with an invertible series and O[[x]] is Galois over O[[fn(x)]] for all n ∈N. We shall prove that the converse of this statement is also true.

An improved 8 × 8 approximately universal code with the large normalized diversity product

When an approximately universal code is designed with cyclic division algebras, the normalized diversity product can be intrinsically increased by a small integer non-norm element. While 2 + i has been the smallest integer non-norm element in all known 8 × 8 designs over QAM, this paper presents another new 8 × 8 code with the smaller non-norm element 1 + i over QAM.

Space-time block codes which can be identified as rings: Twisted group algebras of small groups

In this paper, we give a general criterion to determine when a complex space-time block code has a ring structure and then we provide a complete list of complex space-time block codes which have ring structures up to size 4.