Adriaan J. De Lind Van Wijngaarden

On the Performance of Network Coding with Protection Cycles

A meshed network with N transport paths can be effectively protected against single link failures using network coding and protection cycles (p-cycles). This so called 1+N protection scheme provides instantaneous recovery from single link failures. The performance of this scheme has thus far been considered for a network with unit traffic demands, and the reported results were based on simulations. In this paper, we give an analytical upper bound on the required transport capacity for 1+N protection in full-meshed networks with unit traffic demands. Next, we consider networks with uniform and exponentially distributed traffic demands, and derive more realistic bounds for the achievable network performance of 1+N protection in full-meshed networks.We will show analytically that the gains decrease significantly relative to a unit-traffic demand distribution, independent of the protection mechanism used.

On the Construction of Integer Codes with Minimal Signal Point Constellations

We consider the class of integer codes that are capable of correcting single errors in a two-dimensional lattice (H. Morita et al., 2003). Integer codes, defined over integer rings, allow the correction of single errors with distance 1. In this paper, we extend our previous results (H. Morita et al., 2003). We will detail the derivation of an upper bound on the code size and give constructions that attain this bound. Next, several coding algorithms are presented that efficiently transform binary information into a sequence of symbols that are associated with signal points in a two-dimensional lattice. The proposed decoding algorithms can correct any single error with distance 1 in the given signal point constellation and restore the binary information. We will present a systematic technique to design signal point constellations that support the constructed integer codes and that are optimal in terms of the total Mannheim and Euclidean distance