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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)
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)
In this paper, performance of finite-length batched sparse (BATS) codes with belief propagation (BP) decoding is analyzed. For fixed number of input symbols and fixed number of batches, a recursive formula is obtained to calculate the exact probability distribution of the stopping time of the BP decoder. When the number of batches follows a Poisson(More)
Cut-set bounds are not, in general, tight for all classes of network communication problems. In this paper, we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, which results in bounds that are tighter than the corresponding cut-set bounds. We also define the concept of “uncertainty(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)