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Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we obtain refined versions of the Hamming bound, the Singleton bound and the Gilbert-Varshamov bound for coherent network… (More)

Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and terminals. For example, some network coding schemes require the computational and/or storage capacities of an… (More)

BATS codes are proposed for communication through networks with linear network coding, and can be regarded as a matrix generalization of Raptor codes. In this paper, the performance of finite-length BATS codes is analyzed with respect to both belief propagation (BP) decoding and inactivation decoding. For a fixed number of input symbols and a fixed number… (More)

—Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that results in bounds that are tighter than the corresponding cut-set bounds. We also define the concept of " uncertainty region… (More)

Linear operator channels (LOCs) are motivated by the communications through networks employing random linear network coding (RLNC). Following the recent information theoretic results about LOCs, we propose two coding schemes for LOCs and evaluate their performance. These schemes can be used in networks employing RLNC without constraints on the network size… (More)

—Batched sparse (BATS) codes are proposed for transmitting a collection of packets through communication networks employing linear network coding. BATS codes generalize fountain codes and preserve the properties such as ratelessness and low encoding/decoding complexity. Moreover, the buffer size and the computation capability of the intermediate network… (More)

— In classical algebraic coding theory, the minimum distance of block code completely determines the ability of the code in terms of error correction/detection and erasure correction. We have obtained generalizations of these results for network codes.

SUMMARY In this paper, we first study the error correction and detection capability of codes for a general transmission system inspired by network error correction. For a given weight measure on the error vectors, we define a corresponding minimum weight decoder. Then we obtain a complete characterization of the capability of a code for 1) error correction;… (More)