Convolutional Codes with Maximum Column Sum Rank for Network Streaming
Information Theory
2016-04-19 v2 math.IT
Abstract
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.
Cite
@article{arxiv.1506.03792,
title = {Convolutional Codes with Maximum Column Sum Rank for Network Streaming},
author = {Rafid Mahmood and Ahmed Badr and Ashish Khisti},
journal= {arXiv preprint arXiv:1506.03792},
year = {2016}
}
Comments
14 pages, presented in part at ISIT 2015, accepted to IEEE Transactions on Information Theory