Related papers: Convolutional Codes: Techniques of Construction
Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper…
Two product array codes are used to construct the (24, 12, 8) binary Golay code through the direct sum operation. This construction provides a systematic way to find proper (8, 4, 4) linear block component codes for generating the Golay…
The definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and…
A new family of codes based on polar codes, soft concatenation and list+CRC decoding is proposed. Numerical experiments show the performance competitive with industry standards and Tal, Vardy approach.
Neuro-Evolution is a field of study that has recently gained significantly increased traction in the deep learning community. It combines deep neural networks and evolutionary algorithms to improve and/or automate the construction of neural…
A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length delta. Furthermore, their extended…
In this paper, we present a new method to construct solvable groups with derived length four and four character degrees. We then use this method to present a number of new families of groups with derived length four and four character…
This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given…
We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one…
We introduce Text Encoded Extrusions (TEE), a text-based representation that expresses mesh construction as sequences of face extrusions rather than polygon lists, and a method for generating 3D meshes from TEE using a large language model…
We present a novel way to encode compositional information in high-dimensional (HD) vectors. Inspired by chromosomal crossover, random HD vectors are recursively interwoven, with a fraction of one vector's components masked out and replaced…
Reed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with…
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to…
This paper addresses the construction of observable convolutional codes that exhibit good performance with the available decoding algorithms for erasure channels. Our construction is based on the use of input/state/output (I/S/O)…
Recent advances in high-throughput genomics technologies have resulted in the sequencing of large numbers of (near) complete genomes. These genome sequences are being mined for important functional elements, such as genes. They are also…
This comprehensive survey examines the field of alphabetic codes, tracing their development from the 1960s to the present day. We explore classical alphabetic codes and their variants, analyzing their properties and the underlying…
We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for…