Related papers: Convolutional Codes for Network-Error Correction
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of…
Synthetic DNA can in principle be used for the archival storage of arbitrary data. Because errors are introduced during DNA synthesis, storage, and sequencing, an error-correcting code (ECC) is necessary for error-free recovery of the data.…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
We consider an \textit{Adaptive Random Convolutional Network Coding} (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and…
In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of…
We present algorithms for initializing a convolutional network coding scheme in networks that may contain cycles. An initialization process is needed if the network is unknown or if local encoding kernels are chosen randomly. During the…
We develop a network coding technique based on flags of subspaces and a corresponding network channel model. To define error correcting codes we introduce a new distance on the flag variety, the Grassmann distance on flags and compare it to…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
The free distance of a convolutional code is a reliable indicator of its performance. However its computation is not an easy task. In this paper, we present some algorithms to compute the free distance with good efficiency that work for…
We design low-complexity error correction coding schemes for channels that introduce different types of errors and erasures: on the one hand, the proposed schemes can successfully deal with symbol errors and erasures, and, on the other…
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…
Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
The article provides a survey on convolutional codes stressing the connections to module theory and systems theory. Constructions of codes with maximal possible distance and distance profile are provided. The article will appear as book…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…