Related papers: Generic Decoding of Restricted Errors
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
All the current modern encryption algorithms utilize fixed symbols for plaintext and cyphertext. What I mean by fixed is that there is a set and limited number of symbols to represent the characters, numbers, and punctuations. In addition,…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
Generalized concatenated codes were introduced in the 1970s by Zinoviev. There are many types of codes in the literature that are known by other names that can be viewed as generalized concatenated codes. Examples include matrix-product…
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…
Existing large-scale optimization schemes are challenged by both scalability and cyber-security. With the favorable scalability, adaptability, and flexibility, decentralized and distributed optimization paradigms are widely adopted in…
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…
The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle…
We consider the problem of designing decentralized schemes for coded caching. In this problem there are $K$ users each caching $M$ files out of a library of $N$ total files. The question is to minimize $R$, the number of broadcast…
We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to…
Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be…
We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg…
In this paper, after reviewing the main points of image encryption and threshold function, we introduce the methods of chaotic image encryption based on pseudorandom bit padding that the bits be generated by the novel generalized threshold…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, in this paper, we consider…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
Recent systems on structured prediction focus on increasing the level of structural dependencies within the model. However, our study suggests that complex structures entail high overfitting risks. To control the structure-based…
A generalization of the Reiger bound is presented for the list decoding of burst errors. It is then shown that Reed-Solomon codes attain this bound.