Related papers: Concentric Permutation Source Codes
This paper describes a new set of block source codes well suited for data compression. These codes are defined by sets of productions rules of the form a.l->b, where a in A represents a value from the source alphabet A and l, b are -small-…
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…
This work introduces a symplectic framework for quantum error correcting codes in which local structure is analyzed through an anticode perspective. In this setting, a code is treated as a symplectic space, and anticodes arise as maximal…
Scalar quantization and probabilistic shaping are applied to the distributed source coding of Gaussian sources, with mean-square error distortion. A coding scheme with a modulo interval, dithering, and truncated Gaussian shaping is shown to…
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We present an optimal method for encoding cluster assignments of arbitrary data sets. Our method, Random Cycle Coding (RCC), encodes data sequentially and sends assignment information as cycles of the permutation defined by the order of…
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation…
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…
This paper introduces the notion of multiset codes as relevant to the problem of reliable information transmission over permutation channels. The motivation for studying permutation channels comes from the effect of out of order delivery of…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a precoding step before the polar transform. In this scheme, the polar transform (as a mapper) and the…
A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code…
The recently proposed set-up of source coding with a side information "vending machine" allows the decoder to select actions in order to control the quality of the side information. The actions can depend on the message received from the…
Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with…
We present a technique for automatically transforming kernel-based computations in disparate, nested loops into a fused, vectorized form that can reduce intermediate storage needs and lead to improved performance on contemporary hardware.…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
Joint source-channel coding is a compelling paradigm when low-latency and low-complexity communication is required. This work proposes a theoretical framework that integrates classification and anomaly detection within the conventional…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…