Related papers: Generalized parallel concatenated block codes base…
In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of…
In this paper, we introduce a deep learning-based decoder designed for concatenated coding schemes over a deletion/substitution channel. Specifically, we focus on serially concatenated codes, where the outer code is either a convolutional…
We present an MPI + OpenACC implementation of the kernel-independent barycentric Lagrange treecode (BLTC) for fast summation of particle interactions on GPUs. The distributed memory parallelization uses recursive coordinate bisection for…
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding…
The decoding performance of polar codes strongly depends on the decoding algorithm used, while also the decoder throughput and its latency mainly depend on the decoding algorithm. In this work, we implement the powerful successive…
We present a decode-and-forward transmission scheme based on spatially-coupled low-density parity-check (SC-LDPC) codes for a network consisting of two (possibly correlated) sources, one relay, and one destination. The links between the…
Recently, Bhaintwal and Wasan studied the Generalized Reed-Muller codes over the prime power integer residue ring. In this paper, we give a generalization of these codes to Generalized Reed-Muller codes over Galois rings.
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC…
A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum code. It is known…
With the growing complexity and capability of contemporary robotic systems, the necessity of sophisticated computing solutions to efficiently handle tasks such as real-time processing, sensor integration, decision-making, and control…
A linear code $C$ with the property that $C \cap C^{\perp} = \{0 \}$ is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes…
In this paper, we introduce the concept of spatially coupled turbo codes (SC-TCs), as the turbo codes counterpart of spatially coupled low-density parity-check codes. We describe spatial coupling for both Berrou et al. and Benedetto et al.…
A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual…
We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain, as a particular case, the Generalized Skew Goppa codes. By providing a new parity check matrix for the…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
It's known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. We call the coupled information bits the correlated bits. In this paper, concatenation schemes are studied for polar codes (as inner…
This paper investigates the design of spatially coupled low-density parity-check (SC-LDPC) codes constructed from connected-chain ensembles for bit-interleaved coded modulation (BICM) schemes. For short coupling lengths, connecting multiple…