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Racetrack memory is a new technology which utilizes magnetic domains along a nanoscopic wire in order to obtain extremely high storage density. In racetrack memory, each magnetic domain can store a single bit of information, which can be…
It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the grid cells of the mammalian cortex, analog error correction…
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…
Emerging applications in manufacturing, wireless communication, and molecular data storage require robust coding schemes that remain effective under physical distortions where codewords may be arbitrarily fragmented and partially missing.…
The usefulness of part-of-speech tags for parsing has been heavily questioned due to the success of word-contextualized parsers. Yet, most studies are limited to coarse-grained tags and high quality written content; while we know little…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error…
Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…
In coding theory, handling errors that occur when symbols are inserted or deleted from a transmitted message is a long-standing challenge. Optimising redundancy for insertion and deletion channels remains a key open problem with significant…
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions…
We introduce function-correcting partition codes (FCPCs), which are a natural generalization of function-correcting codes (FCCs). An FCPC is defined directly on a partition of the message space, rather than on a specific target function. We…
(Partial) Unit Memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is…
Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…
For general exact repair regenerating codes, the optimal trade-offs between storage size and repair bandwith remain undetermined. Various outer bounds and partial results have been proposed. Using a simple chain rule argument we identify…
In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes…
The use of partial geometries to construct parity-check matrices for LDPC codes has resulted in the design of successful codes with a probability of error close to the Shannon capacity at bit error rates down to $10^{-15}$. Such…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures…