Rate regions for coherent and noncoherent multisource network error correction

In this paper we derive capacity regions for network error correction with both known and unknown topologies (coherent and non-coherent network coding) under a multiple-source multicast transmission scenario. For the multiple-source non-multicast scenario, given any achievable network code for the error-free case, we construct a code with a reduced rate region for the case with errors

Network codes with deadlines

We investigate the effect of decoding deadlines on network coding capacity, specifically, the capacity curve of a network as a function of the allowed delay from the time a set of bits is transmitted by the source to the time it is fully decoded by the sinks. We show that scalar linear codes are not optimal even for multicast when the data has deadlines. In fact, infinite blocklength is required in general in order to achieve the optimal performance of linear block codes in these scenarios. We study the case of two types of data, where the first type has a tighter deadline than the other. We find for an interesting family of networks the optimal linear convolutional codes. We formulate a code design criterion for general networks with two data types. Finally, as an alternative approach, we show that the problem of multicast with deadlines can be transformed into a non-multicast problem without deadlines in an extended network. Using that approach, we find an upper bound on the complexity of checking the feasibility of the problem

A Novel Decoder for Unknown Diversity Channels Employing Space-Time Codes

We suggest new decoding techniques for diversity channels employing space time codes (STC) when the channel coefficients are unknown to both transmitter and receiver. Most of the existing decoders for unknown diversity channels employ training sequence in order to estimate the channel. These decoders use the estimates of the channel coefficients in order to perform maximum likelihood (ML) decoding. We suggest an efficient implementation of the generalized likelihood ratio test (GLRT) algorithm that improves the performance with only slight increase in complexity. We also suggest an energy weighted decoder (EWD) that shows additional improvement without further increase in the computational complexity.</p

On Noncoherent Correction of Network Errors and Erasures with Random Locations

Abstract—We consider the problem of correcting errors and erasures with network coding. Unlike existing works which consider performance limits for worst-case locations of given numbers of errors and erasures, we consider the performance of given (not necessarily optimal) coding and forwarding strategies for given (not necessarily worst-case) models of error and erasure locations. Our approach characterizes decoding success in terms of the rank of certain matrices corresponding to useful and erroneous information received at the sink nodes. We use this approach to analyze random coding and forwarding strategies on a family of simple networks with random error and erasure locations, and show that the relative performance of the strategies depends on the erasure and error probabilities. I

Coding for the deterministic network model

Abstract—The capacity of multiuser networks has been a longstanding problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. For wireless multicast relay networks, they have shown that the capacity for the deterministic model is equal to the minimal rank of the incidence matrix of a certain cut between the source and any of the sinks. Their proposed code construction, however, is not guaranteed to be efficient and may potentially involve an infinite block length. We propose an efficient linear code construction for the deterministic wireless multicast relay network model. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, for a layered network, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent. I

A systematic approach to network coding problems using conflict graphs

We present a new approach to network coding problems that could lead to a systematic method for deciding solvability of a given network. The approach is based on a graph theoretic formulation of the problem. The constraints at each node in the network are represented using hyperedges in a ‘conflict’ hypergraph. This representation reduces the solvability question to that of finding a stable set with certain properties in a hypergraph. The approach is sufficiently general to allow even non-linear codes by suitably modifying the conflict graph. We also demonstrate the use of the conflict graph idea in the context of a multicast crossbar switch. Using examples, we show that the rate region of a multicast switch strictly improves with network coding at the inputs, and derive an outer bound on the rate region when intra-session network coding is allowed