Related papers: One Code Fits All: Strong stuck-at codes for versa…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may…
In this paper, we propose an encoding scheme for partitioned linear block codes (PLBC) which mask the stuck-at defects in memories. In addition, we derive an upper bound and the estimate of the probability that masking fails. Numerical…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
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 work, we study a new model of defect memory cells, called partially stuck-at memory cells, which is motivated by the behavior of multi-level cells in non-volatile memories such as flash memories and phase change memories. If a cell…
We provide a general formulation for the code-based test compression problem with fixed-length input blocks and propose a solution approach based on Evolutionary Algorithms. In contrast to existing code-based methods, we allow unspecified…
This paper explores the design of convolutional codes for varying constraint lengths, focusing on their role in error correction in digital communication systems. Convolutional codes are essential in achieving reliable data transmission…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
In data storage and data transmission, certain patterns are more likely to be subject to error when written (transmitted) onto the media. In magnetic recording systems with binary data and bipolar non-return-to-zero signaling, patterns that…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
This paper considers coding for so-called partially stuck (defect) memory cells. Such memory cells can only store partial information as some of their levels cannot be used fully due to, e.g., wearout. First, we present new constructions…
Large-scale distributed storage systems typically use erasure codes to provide durability of data in the face of failures. A set of $k$ blocks to be stored is encoded using an $[n, k]$ code to generate $n$ blocks that are then stored on…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…