Multishot Codes for Network Coding: Bounds and a Multilevel Construction

TL;DR

This paper investigates multishot subspace codes for network coding, providing bounds and a multilevel construction to improve communication reliability over multiple uses of the subspace channel.

Contribution

It introduces the concept of multishot subspace codes, establishes bounds, and proposes a multilevel construction based on block-coded modulation.

Findings

Derived lower and upper bounds for code sizes.

Proposed a multilevel code construction method.

Enhanced understanding of multishot coding capabilities.

Abstract

The subspace channel was introduced by Koetter and Kschischang as an adequate model for the communication channel from the source node to a sink node of a multicast network that performs random linear network coding. So far, attention has been given to one-shot subspace codes, that is, codes that use the subspace channel only once. In contrast, this paper explores the idea of using the subspace channel more than once and investigates the so called multishot subspace codes. We present definitions for the problem, a motivating example, lower and upper bounds for the size of codes, and a multilevel construction of codes based on block-coded modulation.