The Capacity of Random Linear Coding Networks as Subspace Channels

TL;DR

This paper models noncoherent random linear coding networks as subspace channels, deriving a capacity lower bound using a symmetric DMC approach and subspace coding, independent of network topology.

Contribution

It introduces a subspace channel model for RLCNs and derives a capacity lower bound using a novel basis selection method, without assuming specific network structures.

Findings

Derived a capacity lower bound for noncoherent RLCNs

Introduced a symmetric DMC model via basis selection

Showed subspace coding achieves the capacity bound

Abstract

In this paper, we consider noncoherent random linear coding networks (RLCNs) as a discrete memoryless channel (DMC) whose input and output alphabets consist of subspaces. This contrasts with previous channel models in the literature which assume matrices as the channel input and output. No particular assumptions are made on the network topology or the transfer matrix, except that the latter may be rank-deficient according to some rank deficiency probability distribution. We introduce a random vector basis selection procedure which renders the DMC symmetric. The capacity we derive can be seen as a lower bound on the capacity of noncoherent RLCNs, where subspace coding suffices to achieve this bound.