Communication over Finite-Field Matrix Channels

Abstract

This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random network coding. The model assumes that n packets of length m are transmitted over the network, and up to t erroneous packets are randomly chosen and injected into the network. Upper and lower bounds on capacity are obtained for any channel parameters, and asymptotic expressions are provided in the limit of large field or matrix size. A simple coding scheme is presented that achieves capacity in both limiting cases. The scheme has decoding complexity O(n^2 m) and a probability of error that decreases exponentially both in the packet length and in the field size in bits. Extensions of these results for coherent network coding are also presented.

24 pages, to be published at the IEEE Transactions on Information Theory

References in corpus (3)

• A Rank-Metric Approach to Error Control in Random Network Coding
• On Metrics for Error Correction in Network Coding
• Coding for Network Coding

Cited by in corpus (8)

• Batched Sparse Codes
• Rank Minimization over Finite Fields: Fundamental Limits and Coding-Theoretic Interpretations
• Communication over Finite-Chain-Ring Matrix Channels
• Subspace Properties of Network Coding and their Applications
• On the Capacity of Non-Coherent Network Coding
• On the Capacity of Multiplicative Finite-Field Matrix Channels
• On the hardness of code equivalence problems in rank metric
• Layering of Communication Networks and a Forward-Backward Duality