On the Performance of Network Coding with Protection Cycles Martin Belzner Friedrich-Alexander-University Erlangen-Nuremberg Cauerstr. 7/LIT D-91058 Erlangen, Germany Herbert Haunstein Alcatel-Lucent Optics Division Thurn-Und-Taxis-Str. 10 D-90411 Nuremberg, Germany Adriaan J. van Wijngaarden Bell Laboratories, Alcatel-Lucent Math. of Networks and Commun. Dept. 600 Mountain Ave Murray Hill, NJ 07974 Abstract—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. I. I NTRODUCTION Transport networks are designed to maximize the network availability and at the same time minimize the required resources per transported bit and the corresponding capital and operational expenditures. Providers often employ network protection schemes to effectively trade off resources, error pro- tection and error recovery time. Two important techniques are dynamic restoration and pre-provisioning. Dynamic restoration schemes act upon detection of a network error by switching to an alternative transport path. Pre-provisioned protection schemes reserve protection transport resources in advance, and switch, upon detection of a link or node failure, from the affected path onto a pre-determined protection path. One common scheme, typically referred to as 1+1 protection, transmits data in parallel over a working path and a protection path via a disjoint route. This scheme does not require an explicit error detection mechanism, and errors in one of the paths do not result in information loss. Another common approach is to protect N transport paths with M protection paths, in short, an M:N protection scheme. This scheme pre- allocates transport resources, but does not actually use these resources unless a working path fails. It requires a fast error detection mechanism to minimize throughput disruptions prior to switching. In [3], a new concept was introduced that uses network coding and protection cycles (p-cycles) to protect a network with N transport paths against any single link failure. This so called 1+N protection method uses the protection paths to carry encoded information from the transport paths and guarantee nearly instantaneous recovery. The results presented in [3] consider the achievable gains relative to the required transport capacity of 1+N protection relative to 1+1 protection This work was funded in part by the Deutsche Forschungsgemeinschaft (DFG) under grant HU 634/8-1. for unit traffic demands. In this paper, we consider full- meshed networks with more realistic network traffic demand distributions. We concentrate our analysis on full-meshed networks as these are currently being considered as a topology to form the future core transport networks [6] and data centers. We present analytical results for the actual achievable network performance when network coding and p-cycles are used in full-meshed networks with uniform and exponentially distributed data rates for the individual demands between the network nodes, thus providing more realistic results for the actual achievable network performance. While the presented results are given for full-meshed networks with 1+N protection using p-cycles, the basic analytical derivations apply to any 1+N protection mechanism that uses network coding. This paper is structured as follows. Section II briefly reviews the concept of 1+N protection with p-cycles. In Section III, we present analytical results that quantify the achievable resource savings of 1+N protection with p-cycles relative to 1+1 protection in full-meshed transport networks with uniform and exponentially-distributed traffic demands. In Section IV we propose an optimized scheme for 1+N protection with p- cycles to increase the resource savings. II. NETWORK CODING FOR PROTECTION Network coding, introduced in [4], uses the basic concept that multiple independent symbols, e.g., units of information such as bits or packets, can be coded into a single output symbol at a network node in order to reduce the required transport resources. In [3], network coding is used to protect meshed networks with p-cycles that provide fast restoration similar to ring protection mechanisms [5]. The main advantage of a p-cycle over standard ring protection is that it protects all links on the cycle as well as all links that connect two nodes on the cycle. In [2], it was shown that due to these non- cycle links, also referred to as straddling links, the required transport resource redundancy in meshed networks with p- cycles is directly proportional to the inverse of the average node degree of the network. Hence, the additional transport resource requirements for protection paths are minimized in full-meshed networks. In the remainder of this paper we use the term traffic demand to refer to the data rate of the end-to-end traffic between two network nodes. The term information symbol refers to the working path traffic with a given traffic demand between two network nodes. The traffic demand distribution refers to the distribution of all end-to-end data rates in the network between the communicating network nodes. A 1+N 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings