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In this paper we review existing hard-decision decoding algorithms for product codes along with different post-processing techniques used in conjunction with the iterative decoder for product codes. We improve the decoder by Reddy and…
Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions. The resulting codes achieve a higher error-correction performance at the same…
Binary code similarity detection is a core task in reverse engineering. It supports malware analysis and vulnerability discovery by identifying semantically similar code in different contexts. Modern methods have progressed from manually…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
The classical family of $[n,k]_q$ Reed-Solomon codes over a field $\F_q$ consist of the evaluations of polynomials $f \in \F_q[X]$ of degree $< k$ at $n$ distinct field elements. In this work, we consider a closely related family of codes,…
We define a virtual projection of a Reed-Solomon code $RS(q^{l},n,k)$ to an $RS(q,n,k)$ Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the $\alpha$- decoding radius is…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
For finite geometry low-density parity-check codes, heavy row and column weights in their parity check matrix make the decoding with even Min-Sum (MS) variants computationally expensive. To alleviate it, we present a class of hybrid schemes…