相关论文: Two-dimensional Burst Error Correcting Code using …

We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…

We present a novel error correcting code and decoding algorithm which have construction similar to expander codes. The code is based on a bipartite graph derived from the subsumption relations of finite projective geometry, and Reed-Solomon…

Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…

We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…

In communication and storage systems, error correction codes (ECCs) are pivotal in ensuring data reliability. As deep learning's applicability has broadened across diverse domains, there is a growing research focus on neural network-based…

The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors…

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…

This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are…

In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…

We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS honeycomb code, is geometrically similar to…

Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…

This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…

We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms…

The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as…

Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…

Three-dimensional (3D) printing's accessibility enables rapid manufacturing but also poses security risks, such as the unauthorized production of untraceable firearms and prohibited items. To ensure traceability and accountability,…

The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is…

We study low-delay error correction codes for streaming recovery over a class of packet-erasure channels that introduce both burst-erasures and isolated erasures. We propose a simple, yet effective class of codes whose parameters can be…

The finite field multiplier is mainly used in many of today's state of the art digital systems and its hardware implementation for bit parallel operation may require millions of logic gates. Natural causes or soft errors in digital design…

Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…