Hua Chieh Li
National Taiwan Normal University
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Featured researches published by Hua Chieh Li.
IEEE Transactions on Information Theory | 2005
Ming Yang Chen; Hua Chieh Li; Soo-Chang Pei
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.
Proceedings of the American Mathematical Society | 2002
Hua Chieh Li
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.
international conference on communications | 2005
Ming Yang Chen; Chiang Yu Chen; Hua Chieh Li; Soo-Chang Pei; John M. Cioffi
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.
Transactions of the American Mathematical Society | 1997
Hua Chieh Li
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
Compositio Mathematica | 2002
Hua Chieh Li
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.
IEEE Transactions on Information Theory | 2007
Ming Yang Chen; Chiang Yu Chen; Hua Chieh Li; Soo-Chang Pei; Hsuan-Jung Su
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
IEEE Transactions on Information Theory | 2009
Hua Chieh Li; Ming Yang Chen
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.
Proceedings of the American Mathematical Society | 1996
Hua Chieh Li
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.
international symposium on information theory | 2010
Ming Yang Chen; Hua Chieh Li; John M. Cioffi
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.
Applicable Algebra in Engineering, Communication and Computing | 2007
Hua Chieh Li
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.