Related papers: Spread Codes and Spread Decoding in Network Coding
This paper focuses on a particular transmission scheme called local network coding, which has been reported to provide significant performance gains in practical wireless networks. The performance of this scheme strongly depends on the…
The network communication scenario where one or more receivers request all the information transmitted by different sources is considered. We introduce distributed polynomial-time network codes in the presence of malicious nodes. Our codes…
Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP.…
Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem:…
We propose a simple yet effective wireless network coding and decoding technique for a multiple unicast network. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by…
This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is…
The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a…
We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…
In this paper, we present a coding-theoretic framework for message transmission over packet-switched networks. Network is modeled as a channel which can induce packet errors, deletions, insertions, and out of order delivery of packets. The…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
We introduce the concept of spread of a code, and we specialize it to the case of maximum weight spectrum (MWS) codes. We classify two newly-defined sub-families of MWS codes according to their weight distributions, and completely describe…
Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…
The advent of network coding presents promising opportunities in many areas of communication and networking. It has been recently shown that network coding technique can significantly increase the overall throughput of wireless networks by…
Random linear network code has to sacrifice part of bandwidth to transfer the coding vectors, thus a head of size k log|T| is appended to each packet. We present a distributed random network coding approach based on the Chinese remainder…
Constant dimension codes are e.g. used for error correction and detection in random linear network coding, so that constructions for these codes have achieved wide attention. Here, we improve over 150 lower bounds by describing better…
In many applications of neural network, it is common to introduce huge amounts of input categorical features, as well as output labels. However, since the required network size should have rapid growth with respect to the dimensions of…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…