A Unified Construction of Space–Time Codes With Optimal Rate–Diversity Tradeoff

Lu, Hsiao-feng; Kumar, P. Vijay

doi:10.1109/tit.2005.846403

Cited by 151 publications

(129 citation statements)

References 30 publications

Supporting

Mentioning

129

Contrasting

Order By: Relevance

“…Further applications of codes in the rank metric include cryptography [11], [19], space-time coding [20], [21] and distributed storage systems [28], [29].…”

Section: Introductionmentioning

confidence: 99%

Some Gabidulin Codes Cannot Be List Decoded Efficiently at any Radius

Raviv

Wachter-Zeh

2016

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proven, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove two bounds on the list size in decoding certain Gabidulin codes. The first bound is an existential one, showing that exponentially-sized lists exist for codes with specific parameters. The second bound presents exponentially-sized lists explicitly, for a different set of parameters. Both bounds rule out the possibility of efficiently list decoding several families of Gabidulin codes for any radius beyond half the minimum distance. Such a result was known so far only for non-linear rank-metric codes, and not for Gabidulin codes. Using a standard operation called lifting, identical results also follow for an important class of constant dimension subspace codes.

show abstract

“…Further applications of codes in the rank metric include cryptography [11], [19], space-time coding [20], [21] and distributed storage systems [28], [29].…”

Section: Introductionmentioning

confidence: 99%

Some Gabidulin Codes Cannot Be List Decoded Efficiently at any Radius

Raviv

Wachter-Zeh

2016

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…In order to exploit the transmit diversity, several SpaceTime Block Codes (STBC) have been proposed in the literature [1,12,14,26,27,33,38,40,55]. Space-Time Trellis Codes (STTC) have also been extensively studied in the literature developing from [56].…”

Section: Introductionmentioning

confidence: 99%

Cyclic Division Algebras: A Tool for Space-Time Coding

Oggier

Belfiore

Viterbo

2007

FNT in Communications and Information Theory

View full text Add to dashboard Cite

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space-Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank.Extensive work has been done on Space-Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space-Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes.The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space-Time block codes.

show abstract

“…Not only can such finite codes be used in essence to build all space-time codes (see [12], [15], [18], [19], [20], and [21] for some constructions), they are interesting mathematical objects in their own right, with a long pedigree. Gabidulin [10] employed finite column distance and finite rank codes for studying crisscross errors in data storage.…”

Section: Introductionmentioning

confidence: 99%

Duality theory for space-time codes over finite fields

Grant¹,

Varanasi²

2008

Advances in Mathematics of Communications

View full text Add to dashboard Cite

Abstract. We further the study of the duality theory of linear space-time codes over finite fields by showing that the only finite linear temporal correlated codes with a duality theory are the column distance codes and the rank codes. We introduce weight enumerators for both these codes and show that they have MacWilliams-type functional equations relating them to the weight enumerators of their duals. We also show that the complete weight enumerator for finite linear sum-of-ranks codes satisfies such a functional equation. We produce an analogue of Gleason's Theorem for linear finite rank codes. Finally, we relate the duality matrices of n × n linear rank codes and length n vector codes under the Hamming metric.

show abstract

A Unified Construction of Space–Time Codes With Optimal Rate–Diversity Tradeoff

Cited by 151 publications

References 30 publications

Some Gabidulin Codes Cannot Be List Decoded Efficiently at any Radius

Some Gabidulin Codes Cannot Be List Decoded Efficiently at any Radius

Cyclic Division Algebras: A Tool for Space-Time Coding

Duality theory for space-time codes over finite fields

Contact Info

Product

Resources

About