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Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best…
In this letter, we propose a reliability-based windowed decoding scheme for spatially-coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial…
In this paper non-trivial non-linear binary systematic AMDS codes are classified in terms of their weight distributions, employing only elementary techniques. In particular, we show that their length and minimum distance completely…
The generalized Hamming weights (GHWs) of a linear code C extend the concept of minimum distance, which is the minimum cardinality of the support of all one-dimensional subspaces of C, to the minimum cardinality of the support of all…
The insertion-deletion codes were motivated to correct the synchronization errors. In this paper we prove several coordinate-ordering-free upper bounds on the insdel distances of linear codes, which are based on the generalized Hamming…
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent…
In this paper, we propose and study $r$-minimal codes, a natural extension of minimal codes which have been extensively studied with respect to Hamming metric, rank metric and sum-rank metric. We first propose $r$-minimal codes in a general…
The advancement of deep learning has led to the development of neural decoders for low latency communications. However, neural decoders can be very complex which can lead to increased computation and latency. We consider iterative pruning…
In this paper, we derive the exact weight distributions that emerge during each stage of successive cancellation decoding of polar codes. Though we do not compute the distance spectrum of polar codes, the results allow us to get an estimate…
We achieve new results on skew polynomial rings and their quotients, including the first explicit example of a skew polynomial ring where the ratio of the degree of a skew polynomial to the degree of its bound is not extremal. These methods…
In this letter we propose a new hybrid code called "RM-Polar" codes. This new codes are constructed by combining the construction of Reed-Muller (RM) code and Polar code. It has much larger minimum Hamming distance than Polar codes,…
Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for both unique string…
Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is…
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…
We consider the question of determining the higher weights or the generalized Hamming weights of affine Grassmann codes and their duals. Several initial as well as terminal higher weights of affine Grassmann codes of an arbitrary level are…
It has been shown that maximum distance profile (MDP) convolutional codes have optimal recovery rate for windows of a certain length, when transmitting over an erasure channel. In addition, the subclass of complete MDP convolutional codes…
Decomposition is a proven way to shrink deep networks without changing input-output dimensionality or interface semantics. We bring this idea to hyperdimensional computing (HDC), where footprint cuts usually shrink the feature axis and…
We introduce the sum-rank metric analogue of Reed--Muller codes, which we called linearized Reed--Muller codes, using multivariate Ore polynomials. We study the parameters of these codes, compute their dimension and give a lower bound for…