Convolutional Codes with Maximum Column Sum Rank for Network Streaming

TL;DR

This paper introduces the column sum rank metric for convolutional codes, establishes its properties, and constructs a new family of codes that maximize this metric for network streaming over link failure channels.

Contribution

It defines the column sum rank metric, proves its properties, and constructs convolutional codes that optimize this metric for improved network streaming reliability.

Findings

Maximized column sum rank for convolutional codes

Established rank analogues of known distance properties

Constructed codes using super-regular matrices

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.