Ambiguity resistant polynomial matrices

Guangcai Zhou; Xiang Gen Xia

doi:10.1016/S0024-3795(98)10127-1

Ambiguity resistant polynomial matrices

Guangcai Zhou, Xiang Gen Xia^*

^*Corresponding author for this work

University of Delaware

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

An N × K (N ≥ K) ambiguity resistant (AR) matrix G(z) is an irreducible polynomial matrix of size N × K over a field F such that the equation EG(z) = G(Z)V(z) with E an unknown constant matrix and V(z) an unknown polynomial matrix has only the trivial solution E = αI_N, V(z) = αI_K, where α ∈ F. AR matrices have been introduced and applied in modern digital communications as error control codes defined over the complex field. In this paper we systematically study AR matrices over an infinite field F. We discuss the classification of AR matrices, define their normal forms, find their simplest canonical forms, and characterize all (K + 1) × K AR matrices that are the most interesting matrices in the applications,

Original language	English
Pages (from-to)	19-35
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	286
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(98)10127-1
Publication status	Published - 1 Jan 1999
Externally published	Yes

Keywords

Ambiguity resistant matrix
Error control coding
Irreducible matrix
Polynomial matrix

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10.1016/S0024-3795(98)10127-1

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AB - An N × K (N ≥ K) ambiguity resistant (AR) matrix G(z) is an irreducible polynomial matrix of size N × K over a field F such that the equation EG(z) = G(Z)V(z) with E an unknown constant matrix and V(z) an unknown polynomial matrix has only the trivial solution E = αIN, V(z) = αIK, where α ∈ F. AR matrices have been introduced and applied in modern digital communications as error control codes defined over the complex field. In this paper we systematically study AR matrices over an infinite field F. We discuss the classification of AR matrices, define their normal forms, find their simplest canonical forms, and characterize all (K + 1) × K AR matrices that are the most interesting matrices in the applications,

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KW - Error control coding

KW - Irreducible matrix

KW - Polynomial matrix

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Ambiguity resistant polynomial matrices

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Keywords

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