Diversity coding

Abstract: We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.

Abstract: Multilevel diversity coding was introduced in recent work by Roche (1992) and Yeung (1995). In a multilevel diversity coding system, an information source is encoded by a number of encoders. There is a set of decoders, partitioned into multiple levels, with each decoder having access to a certain subset of the encoders. The reconstructions of the source by decoders within the same level are identical and are subject to the same distortion criterion. Inspired by applications in computer communication and fault-tolerant data retrieval, we study a multilevel diversity coding problem with three levels for which the connectivity between the encoders and decoders is symmetrical. We obtain a single-letter characterization of the coding rate region and show that coding by superposition is optimal for this problem. Generalizing to a symmetrical problem with an arbitrary number of levels, we derive a tight lower bound on the coding rate sum.

Abstract: Link failures in wide area networks are common. To recover from such failures, a number of methods such as SONET rings, protection cycles, and source rerouting have been investigated. Two important considerations in such approaches are the recovery time and the needed spare capacity to complete the recovery. Usually, these techniques attempt to achieve a recovery time less than 50 ms. In this paper we introduce an approach that provides link failure recovery in a hitless manner, or without any appreciable delay. This is achieved by means of a method previously introduced, named diversity coding. We present an algorithm for the design of an overlay network to achieve hitless recovery from single link failures in arbitrary networks via diversity coding. This algorithm is designed to minimize spare capacity for recovery. We compare the spare capacity performance of this algorithm against conventional techniques from the literature via simulations. Based on these results, we conclude that the spare capacity requirements of the proposed technique are favorably comparable to existing techniques, while its recovery time performance is much better, since it can provide hitless recovery.

Abstract: An error-control-based approach, called diversity coding, that provides nearly instantaneous self-healing digital communication networks is presented. This is achieved by constructing an error-correcting code across logically independent channels and by treating link failures within the framework of an erasure channel model. Diversity coding is more efficient than previous approaches to self-healing communication networks since it is nearly instantaneous, is transparent to the end user, minimizes the required extra capacity, and does not need rerouting, resynchronization, or a feedback channel. It is applicable to both circuit-switched and packet-switched networks and to a wide variety of network topologies. Diversity coding can be extended to provide protection from short-duration environmental disruptions, such as multipath fading in radio networks and polarization dispersion in fiber-optic networks, or, in conjunction with previous error detection schemes, to provide forward error correction for random and burst errors. >