Related papers: Data Bits in Karnaugh Map and Increasing Map Capab…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where C_1 and C_2 are classical codes, is used to obtain codes for up to 16 information qubits…
This paper presents a new paradigm for image transmission through analog error correction codes. Conventional schemes rely on digitizing images through quantization (which inevitably causes significant bandwidth expansion) and transmitting…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
Racetrack memory is a non-volatile memory engineered to provide both high density and low latency, that is subject to synchronization or shift errors. This paper describes a fast coding solution, in which delimiter bits assist in…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
Text error correction aims to correct the errors in text sequences such as those typed by humans or generated by speech recognition models. Previous error correction methods usually take the source (incorrect) sentence as encoder input and…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
Quantizing weights and activations of deep neural networks results in significant improvement in inference efficiency at the cost of lower accuracy. A source of the accuracy gap between full precision and quantized models is the…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
We propose a hybrid protocol combining a rectangular error-correcting code - paired with an error-detecting code - and a backward error correction in order to send packages of information over a noisy channel. We depict a linear-time…
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…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Secure quantum networks are a bedrock requirement for developing a future quantum internet. However, quantum channels are susceptible to channel noise that introduce errors in the transmitted data. The traditional approach to providing…
Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both…
We propose a method for applying the quantum error-correction method for errors that occur during quantum gates. Using a perturbation treatment of the noise that allows us to separate it from the ideal evolution of the quantum gate, we…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
Large data sets are increasingly common in cloud and virtualized environments. For example, transfers of multiple gigabytes are commonplace, as are replicated blocks of such sizes. There is a need for fast error-correction or data…