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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)

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)

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)

—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)

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed… (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)

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)

—Slotted ALOHA can benefit from physical-layer network coding (PNC) by decoding one or multiple linear combinations of the packets simultaneously transmitted in a timeslot, forming a system of linear equations. Different systems of linear equations are recovered in different timeslots. A message decoder then recovers the original packets of all the users by… (More)