Motivated by the communication through a network employing linear network coding, linear operator channels (LOCs) over finite fields are studied with arbitrarily distributed transfer matrices. Some intrinsic symmetric properties of LOCs are revealed and are used to simplify transition matrix computation and input distribution optimization. Subspace coding for LOCs is studied with the help of th...

In this paper, we propose a general-purpose graphics processing unit (GPGPU) based parallelization technique for random linear network coding (RLNC). RLNC is recognized as a useful tool for enhancing performance of networked systems, and several parallel implementation techniques have been proposed in the literature to overcome its high computation overhead. However, existing parallel methods c...

We consider applying network coding in settings where there is a cost associated with network use. We show that, while minimum-cost multicast problems without network coding are very difficult except in the special cases of unicast and broadcast, finding minimum-cost subgraphs for single multicast connections with network coding can be posed as a linear optimization problem. In particular, we a...

of the Dissertation Generalized ACE Codes and Information Theoretic Results in Network Coding

Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven platforms, these challenges are particular important. In this work, we consider the coding variant Perpetual codes which are sparse, non-uniform and the cod...

Network coding is a recent research topic in wireless networking. By combining multiple packets in a single broadcast transmission, network coding can greatly improve the capacity of multi-hop wireless networks. Packet mixing, when applied with traditional routing, can only be performed at the junctions of the paths determined by the routing module. This limits significantly the coding opportun...

Constant dimension codes are subsets of the finite Grassmann variety. The study of constant dimension codes with good distances have been central in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are characterized that the elements of the code can be viewed as the orbit under a group action. The paper gives a complete characterization of ...

Short message noisy network coding (SNNC) differs from long message noisy network coding (LNNC) in that one transmits many short messages in blocks rather than using one long message with repetitive encoding. Several properties of SNNC are developed. First, SNNC with backward decoding achieves the same rates as SNNC with offset encoding and sliding window decoding for memoryless networks where ...

This paper serves as a tutorial lecture on the use of network coding to provide resource efficient, and agile proactive protection. Network coding, which was introduced in [1], allows intermediate network nodes to form linear combinations of packets received on different input links. The use of network coding results in capacity enhancement. This capacity enhancement is used to provide protecti...