Related papers: Tutorial on algebraic deletion correction codes
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
One peculiarity with deletion-correcting codes is that perfect $t$-deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius $t$ with respect to the…
To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…
This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…
We generalize Helberg's number-theoretic construction of multiple insertion-deletion correcting binary codes to non-binary alphabets and describe a linear decoding algorithm for correcting multiple deletions.
In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (BDC$_p$) every bit is deleted…
We study faulty successive cancellation decoding of polar codes for the binary erasure channel. To this end, we introduce a simple erasure-based fault model and we show that, under this model, polarization does not happen, meaning that…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction.…
The one-bit deletion and duplication channel is investigated. An input to this channel consists of a block of bits which experiences either a deletion, or a duplication, or remains unchanged. For this channel a capacity expression is…
These lecture notes on channel coding were developed for a one-semester course for graduate students of electrical engineering. Chapter 1 reviews the basic problem of channel coding. Chapters 2-5 are on linear block codes, cyclic codes,…
We improve Levenshtein's upper bound for the cardinality of a code of length four that is capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we construct…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
We consider explicit constructions of multi-level lattice codes that universally approach the capacity of the compound block-fading channel. Specifically, building on algebraic partitions of lattices, we show how to construct codes with…