We consider a directed acyclic network with three sources and three terminals such that each source independently generates one symbol from a given field F and each terminal wants to receive the sum (over F ) of the source symbols. Each link in the network is considered to be error-free and delay-free and can carry one symbol from the field in each use. We call such a network a 3-source 3-termi...

Network coding is a collection of techniques in which a node is allowed to combine, encode and send one or more packets as a single encoded packet instead of sending individually. It improves throughput, packet delivery ratio and efficiency of the system. The inherent broadcasting nature of wireless mediums helps us to adopt network coding very easily. At the same time, as it reduces the number...

In the traditional information transmission through a network, an intermediate node was only allowed to duplicate input information and output the duplication. In contrast, in the transmission with the network coding, an intermediate node is able to code the input information from multiple links and outputs the coded information. The multicast using the network coding can achieve higher informa...

I Recent studies have shown that non-linear prediction can be implemented with neural networks, and non-linear predictors will on average achieve about 2 3 improvement in prediction gain over conventional linear predictors. In this paper, we take the advantage of non-linear prediction with neural network, apply it to predictive speech coding and attempt to improve the speech coding performance....

In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to linear network error correction coding, i.e., linear network error correction multicast/broadcast/dispersion codes. We further propose the (weakly, strongly) exte...

In this work, we propose buffer-aided physical-layer network coding (PLNC) techniques for cooperative direct-sequence code-division multiple access systems. In the proposed buffer-aided PLNC schemes, a relay pair selection algorithm is employed to obtain the relay pair and the packets in the buffer entries with the best performance and the associated link combinations used for data transmission...

We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal number of points for curves of their respective genera. Linear network coding transmits information in ...

Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang [?] introduced a metric on the set af vector-spaces and showed that a minimal distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and re...

Security aspects of the Index Coding with Side Information (ICSI) problem are investigated. Building on the results of Bar-Yossef et al. (2006), the properties of linear coding schemes for the ICSI problem are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is shown that the coding s...

We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is inspired by the methods of the author utilizing the osculating spaces of Veronese varieties. Linear network coding transmits information in terms of a basis of a ...