Related papers: Enhanced Algebraic Error Control for Random Linear…
Matching algorithms can be used for identifying errors in quantum systems, being the most famous the Blossom algorithm. Recent works have shown that small distance quantum error correction codes can be efficiently decoded by employing…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…
The problem of securing a network coding communication system against an eavesdropper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
In this paper, we discuss two-stage encoding algorithms capable of correcting a fraction of asymmetric errors. Suppose that the encoder transmits $n$ binary symbols $(x_1,\ldots,x_n)$ one-by-one over the Z-channel, in which a 1 is received…
Network coding is a highly efficient data dissemination mechanism for wireless networks. Since network coded information can only be recovered after delivering a sufficient number of coded packets, the resulting decoding delay can become…
The inherent uncertainty of communication channels implies that any coding scheme has a non-zero probability of failing to correct errors, making retransmission mechanisms essential. To ensure message reliability and integrity, a dual-layer…
We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling,…
Characterization of the delay profile of systems employing random linear network coding is important for the reliable provision of broadcast services. Previous studies focused on network coding over large finite fields or developed Markov…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Error correcting codes play a central role in digital communication, ensuring that transmitted information can be accurately reconstructed despite channel impairments. Recently, autoencoder (AE) based approaches have gained attention for…
In extremely large-scale multiple input multiple output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming…