On the Existence of Universally Decodable Matrices

Details On the Existence of Universally Decodable Matrices On the Existence of Universally Decodable Matrices

2006-01-14

arxiv.org/abs/cs/0601066v1

Computer Science

Information Theory

Scientific paper

Universally decodable matrices (UDMs) can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $N$ and a prime power $q$. The main result of this paper is that the simple condition $L \leq q+1$ is both necessary and sufficient for $(L,N,q)$-UDMs to exist. The existence proof is constructive and yields a coding scheme that is equivalent to a class of codes that was proposed by Rosenbloom and Tsfasman. Our work resolves an open problem posed recently in the literature.

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