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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…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem…
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…
Given $r\geq 3$ and $2^{r-1}+1\leq n< 2^{r}-1$, an $[n,n-r,3]$ shortened Hamming code that can detect a maximal number of double errors is constructed. The optimality of the construction is proven.
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same…
While code large language models have demonstrated remarkable progress in code generation, the generated code often exhibits poor runtime efficiency, limiting its practical application in performance-sensitive scenarios. To address this…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
Turbo codes and CRC codes are usually decoded separately according to the serially concatenated inner codes and outer codes respectively. In this letter, we propose a hybrid decoding algorithm of turbo-CRC codes, where the outer codes, CRC…
An efficient scheme to increase the performance of polar codes at short and moderate block lengths is a concatenation of CRC code and a polar code. In order to obtain better result of the concatenation, a CRC code with best error control…
We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
The orienteering problem is a route optimization problem which consists in finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather than the speed in terms…
Streaming codes (SCs) are packet-level codes that recover erased packets within a strict decoding-delay deadline. Streaming codes for various packet erasure channel models such as sliding-window (SW) channel models that admit random or…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…
Locally repairable codes (LRCs) have received significant recent attention as a method of designing data storage systems robust to server failure. Optimal LRCs offer the ideal trade-off between minimum distance and locality, a measure of…