Related papers: Capacity-achieving codes: a review on double trans…
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by…
Luby Transform (LT) codes are a class of fountain codes that have proved to perform very efficiently over the erasure channel. These codes are rateless in the sense that an infinite stream of encoded symbols can be generated on the fly.…
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
We establish the classical capacity of optical quantum channels as a sharp transition between two regimes---one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
We derive the density evolution equations for non-binary low-density parity-check (LDPC) ensembles when transmission takes place over the binary erasure channel. We introduce ensembles defined with respect to the general linear group over…
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…
In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. This provides a mathematical explanation for the emergence of…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that…
We study $t$-designs of parameters $(n,k,\lambda)$ over finite fields as group divisible designs and set systems admitting a transitive action of a linear group encoded in an hypergraph $G$ whose vertex set of size $n$ is partitioned into…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
This paper studies evaluation of the capacity region for interference networks with point-to-point (p2p) capacity-achieving codes. Such capacity region has recently been characterized as union of several sub-regions each of which has…
We describe some pseudorandom properties of binary linear codes achieving capacity on the binary erasure channel under bit-MAP decoding (as shown in Kudekar et al this includes doubly transitive codes and, in particular, Reed-Muller codes).…
Designing capacity-achieving coding schemes for the band-limited additive colored Gaussian noise (ACGN) channel has been and is still a challenge. In this paper, the capacity of the band-limited ACGN channel is studied from a fundamental…
We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
We consider the N-user broadcast erasure channel with public feedback and side information. Before the beginning of transmission, each receiver knows a function of the messages of some of the other receivers. This situation arises naturally…