Related papers: Efficient Systematic Deletions/Insertions of $0$'s…
In coding theory, an error-correcting code can be encoded either systematically or non-systematically. In a systematic encode, the input data is embedded in the encoded output. Conversely, in a non-systematic code, the output does not…
The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we further study this intriguing mathematical problem,…
In this paper, we study the following problem: given $n$ subsets $S_1, \dots, S_n$ of an integer universe $U = \{0,\dots, u-1\}$, having total cardinality $N = \sum_{i=1}^n |S_i|$, find a prefix-free encoding $enc : U \rightarrow \{0,1\}^+$…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
Several new applications and a number of new mathematical techniques have increased the research on error-correcting codes in the Lee metric in the last decade. In this work we consider several coding problems and constructions of…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
In this letter, we present a hybrid iterative decoder for non-binary low density parity check (LDPC) codes over binary erasure channel (BEC), based on which the recursion of the erasure probability is derived to design non-binary LDPC codes…
Error-control-coding (ECC) techniques are widely used in modern digital communication systems to minimize the effect of noisy channels on the quality of received signals. Motivated by the fact that both communication and imaging can be…
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…
Block codes, which correct asymmetric errors with limited-magnitude, are studied. These codes have been applied recently for error correction in flash memories. The codes will be represented by lattices and the constructions will be based…
This paper presents flexible storage codes, a class of error-correcting codes that can recover information from a flexible number of storage nodes. As a result, one can make a better use of the available storage nodes in the presence of…
Permutation codes in the Ulam metric, which can correct multiple deletions, have been investigated extensively recently. In this work, we are interested in the maximum size of permutation codes in the Ulam metric and aim to design…
We improve the upper bound of Levenshtein for the cardinality of a code of length 4 capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we will construct an…
This paper investigates the error probability of several decoding methods for a source code with decoder side information, where the decoding methods are: 1) symbol-wise maximum a posteriori decoding, 2) successive-cancellation decoding,…
The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…
Reliability is an important requirement for both communication and storage systems. Due to continuous scale down of technology multiple adjacent bits error probability increases. The data may be corrupted due soft errors. Error correction…
Systematic polar codes are shown to outperform non-systematic polar codes in terms of the bit-error-rate (BER) performance. However theoretically the mechanism behind the better performance of systematic polar codes is not yet clear. In…
We consider the problem of correcting insertion and deletion errors in the $d$-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors…