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In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
Bit flipping can be used as a postprocessing technique to further improve the performance for successive cancellation list (SCL) decoding of polar codes. However, the number of bit-flipping trials could increase the decoding latency…
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…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
The multidimensional convolutional codes are an extension of the notion of convolutional codes (CCs) to several dimensions of time. This paper explores the class of two-dimensional convolutional codes (2D CCs) and 2D tail-biting…
The computational complexity of optimum decoding for an orthogonal space-time block code G satisfying the orthogonality property that the Hermitian transpose of G multiplied by G is equal to a constant c times the sum of the squared symbols…
We apply Schrijver's semidefinite programming method to obtain improved upper bounds on generalized distances and list decoding radii of binary codes.
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…
We propose a novel decoding algorithm for staircase codes which reduces the effect of undetected component code miscorrections. The algorithm significantly improves performance, while retaining a low-complexity implementation suitable for…
The classification of complex data usually requires the composition of processing steps. Here, a major challenge is the selection of optimal algorithms for preprocessing and classification (including parameterizations). Nowadays, parts of…
Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best…
Solving constrained multi-objective optimization problems (CMOPs) is a challenging task. While many practical algorithms have been developed to tackle CMOPs, real-world scenarios often present cases where the constraint functions are…
In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of…
With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
We show that for (systematic) linear codes the time complexity of unique decoding is O(n^{2}q^{nRH(delta/2/R)}) and the time complexity of minimum distance decoding is O(n^{2}q^{nRH(delta/R)}). The proposed algorithm inspects all error…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…