Related papers: Fountain Codes with Varying Probability Distributi…
In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has…
The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. The proposed source model in this…
Linear layered probabilistic shaping (LLPS) is proposed, an architecture for linear codes to efficiently encode to shaped code words. In the previously proposed probabilistic amplitude shaping (PAS) architecture, a distribution matcher (DM)…
In this letter, we provide the construction of repairable fountain codes (RFCs) for distributed storage systems that are information-theoretically secure against an eavesdropper that has access to the data stored in a subset of the storage…
Machine learning has had a major impact on data compression over the last decade and inspired many new, exciting theoretical and applied questions. This paper describes one such direction -- relative entropy coding -- which focuses on…
We address the use of linear randon fountain codes caching schemes in a heterogeneous satellite network. We consider a system composed of multiple hubs and a geostationary Earth orbit satellite. Coded content is memorized in hubs' caches in…
We introduce probabilistic language tries (PLTs), a unified representation that makes explicit the prefix structure implicitly defined by any generative model over sequences. By assigning to each outgoing edge the conditional probability of…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
Rooted trees with probabilities are convenient to represent a class of random processes with memory. They allow to describe and analyze variable length codes for data compression and distribution matching. In this work, the Leaf-Average…
The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…
This paper proposes Fulcrum network codes, a network coding framework that achieves three seemingly conflicting objectives: (i) to reduce the coding coefficient overhead to almost n bits per packet in a generation of n packets; (ii) to…
Phylogenetic inference, the task of reconstructing how related sequences evolved from common ancestors, is a central objective in evolutionary genomics. The current state-of-the-art methods exploit probabilistic models of sequence evolution…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded…
The order of letters is not always relevant in a communication task. This paper discusses the implications of order irrelevance on source coding, presenting results in several major branches of source coding theory: lossless coding,…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…