Related papers: Decoding generalised hyperoctahedral groups and as…
Computation of the undetected error probability for error correcting codes over the Z-channel is an important issue, explored only in part in previous literature. In this paper we consider the case of Varshamov-Tenengol'ts codes, by…
In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points of the Grassmannian, there exists a canonical path between these points once a complete flag is fixed. These paths are…
We investigate algorithms for encoding of one-point algebraic geometry (AG) codes over certain plane curves called $C_{ab}$ curves, as well as algorithms for inverting the encoding map, which we call "unencoding". Some $C_{ab}$ curves have…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…
In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the…
In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study…
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
The recently-discovered polar codes are seen as a major breakthrough in coding theory; they provably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm.…
The accelerated development of quantum technology has reached a pivotal point. Early in 2014, several results were published demonstrating that several experimental technologies are now accurate enough to satisfy the requirements of…
A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along with several results for infinite classes of cyclic codes with $t=2$ and $t=3$. From these, a theoretically justification of…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
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…
One important classifier ensemble for multiclass classification problems is Error-Correcting Output Codes (ECOCs). It bridges multiclass problems and binary-class classifiers by decomposing multiclass problems to a serial binary-class…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…