Related papers: Finite field matrix channels for network coding
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 in Coding for errors and erasures in…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
We consider discrete memoryless channels with input alphabet size $n$ and output alphabet size $m$, where $m=$ceil$(\gamma n)$ for some constant $\gamma>0$. The channel transition matrix consists of entries that, before being normalised,…
Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding…
We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the…
In this paper, fading Gaussian multiuser channels are considered. If the channel is perfectly known to the transmitter, capacity has been established for many cases in which the channels may satisfy certain information theoretic orders such…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
We study finite-length bounds for source coding with side information for Markov sources and channel coding for channels with conditional Markovian additive noise. For this purpose, we propose two criteria for finite-length bounds. One is…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known…
The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of…
We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
In this paper, we consider the information-theoretic characterization of the set of achievable rates and distortions in a broad class of multiterminal communication scenarios with general continuous-valued sources and channels. A framework…
The problem of learning a channel decoder is considered for two channel models. The first model is an additive noise channel whose noise distribution is unknown and nonparametric. The learner is provided with a fixed codebook and a dataset…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. Using this new concept, we derive properties of maximum rank distance (MRD) codes that parallel…
How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet,…
Motivated by an important insight from neural science, we propose a new framework for understanding the success of the recently proposed "maxout" networks. The framework is based on encoding information on sparse pathways and recognizing…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…