2 research outputs found
Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile
Superregular matrices are a class of lower triangular Toeplitz matrices that
arise in the context of constructing convolutional codes having a maximum
distance profile. These matrices are characterized by the property that no
submatrix has a zero determinant unless it is trivially zero due to the lower
triangular structure. In this paper, we discuss how superregular matrices may
be used to construct codes having a maximum distance profile. We also introduce
group actions that preserve the superregularity property and present an upper
bound on the minimum size a finite field must have in order that a superregular
matrix of a given size can exist over that field.Comment: 20 pages. Replaced on 19/7/2006, because bibtex files were not
included in the original submissio
Convolutional Codes with Maximum Column Sum Rank for Network Streaming
The column Hamming distance of a convolutional code determines the error
correction capability when streaming over a class of packet erasure channels.
We introduce a metric known as the column sum rank, that parallels column
Hamming distance when streaming over a network with link failures. We prove
rank analogues of several known column Hamming distance properties and
introduce a new family of convolutional codes that maximize the column sum rank
up to the code memory. Our construction involves finding a class of
super-regular matrices that preserve this property after multiplication with
non-singular block diagonal matrices in the ground field.Comment: 14 pages, presented in part at ISIT 2015, accepted to IEEE
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