Related papers: Primer and Recent Developments on Fountain Codes
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
Founsure is an open-source software library that implements a multi-dimensional graph-based erasure coding entirely based on fast exclusive OR (XOR) logic. Its implementation utilizes compiler optimizations and multi-threading to generate…
This paper extends linear-complexity concatenated coding schemes to fountain communication over the discrete-time memoryless channel. Achievable fountain error exponents for one-level and multi-level concatenated fountain codes are derived.…
We assess the practicality of random network coding by illuminating the issue of overhead and considering it in conjunction with increasingly long packets sent over the erasure channel. We show that the transmission of increasingly long…
Streaming codes are a class of packet-level erasure codes that are designed with the goal of ensuring recovery in low-latency fashion, of erased packets over a communication network. It is well-known in the streaming code literature, that…
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as…
Modern distributed storage systems often use erasure codes to protect against disk and node failures to increase reliability, while trying to meet the latency requirements of the applications and clients. Storage systems may have caches at…
As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article…
Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple…
Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial codes over finite fields, renowned for achieving list decoding capacity. These codes have found a wide range of applications beyond the traditional scope…
Network transfer and disk read are the most time consuming operations in the repair process for node failures in erasure-code-based distributed storage systems. Recent developments on Reed-Solomon codes, the most widely used erasure codes…
We consider large-scale sensor networks with n nodes, out of which k are in possession, (e.g., have sensed or collected in some other way) k information packets. In the scenarios in which network nodes are vulnerable because of, for…
Identification is a communication paradigm that promises exponential advantages over transmission for applications that do not actually require all messages to be reliably transmitted. Notably, the identification capacity theorems prove…
Reed-Solomon (RS) codes are constructed over a finite field that have been widely employed in storage and communication systems. Many fast encoding/decoding algorithms such as fast Fourier transform (FFT) and modular approach are designed…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
We present a practical algorithm to decode erasures of Reed-Solomon codes over the q elements binary field in O(q \log_2^2 q) time where the constant implied by the O-notation is very small. Asymptotically fast algorithms based on fast…
Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to…
Cloud computing facilitates the access of applications and data from any location by a distributed storage system. Erasure codes offer better data replication technique with reduced storage costs for more reliability. This paper considers…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…