Related papers: Concentric Permutation Source Codes
We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$.…
In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an…
Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…
Large information sizes in samples and features can be encoded to speed up the learning of statistical models based on linear algebra and remove unwanted signals. Encoding information can reduce both sample and feature dimension to a…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…
Compression for machines is an emerging field, where inputs are encoded while optimizing the performance of downstream automated analysis. In scalable coding for humans and machines, the compressed representation used for machines is…
This paper investigates the design of low-complexity error correction codes for the verification step in continuous variable quantum key distribution (CVQKD) systems. We design new coding schemes based on quasi-cyclic repeat-accumulate…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
We determine the rate region of the vector Gaussian one-helper source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a simple scheme that separates the lossy vector quantization from the…
Current per-shot encoding schemes aim to improve the compression efficiency by shot-level optimization. It splits a source video sequence into shots and imposes optimal sets of encoding parameters to each shot. Per-shot encoding achieved…
In language processing, transformers benefit greatly from text being condensed. This is achieved through a larger vocabulary that captures word fragments instead of plain characters. This is often done with Byte Pair Encoding. In the…
Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword…
In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes Hybrid LDPC codes. Although efficient optimization techniques…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
Overfitted neural video codecs offer a decoding complexity orders of magnitude smaller than their autoencoder counterparts. Yet, this low complexity comes at the cost of limited compression efficiency, in part due to their difficulty…
Channel coding is vital for reliable sixth-generation (6G) data transmission, employing diverse error correction codes for various application scenarios. Traditional decoders require dedicated hardware for each code, leading to high…
The promising improvement in compression efficiency of Versatile Video Coding (VVC) compared to High Efficiency Video Coding (HEVC) comes at the cost of a non-negligible encoder side complexity. The largely increased complexity overhead is…