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We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Neural machine translation (NMT) has achieved new state-of-the-art performance in translating ambiguous words. However, it is still unclear which component dominates the process of disambiguation. In this paper, we explore the ability of…
Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…
In this paper we introduce Neural Network Coding(NNC), a data-driven approach to joint source and network coding. In NNC, the encoders at each source and intermediate node, as well as the decoder at each destination node, are neural…
Automatic spelling and grammatical correction systems are one of the most widely used tools within natural language applications. In this thesis, we assume the task of error correction as a type of monolingual machine translation where the…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our…
In this paper we address the problem of selecting factor-graph permutations of polar codes under belief propagation (BP) decoding to significantly improve the error-correction performance of the code. In particular, we formalize the…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…
Channel coding is vital for reliable sixth-generation (6G) data transmission, employing diverse error correction codes for various application scenarios. Traditional decoders require dedicated hardware for each code, leading to high…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
A class of network codes have been proposed in the literature where the symbols transmitted on network edges are binary vectors and the coding operation performed in network nodes consists of the application of (possibly several)…
Recently, universal neural machine translation (NMT) with shared encoder-decoder gained good performance on zero-shot translation. Unlike universal NMT, jointly trained language-specific encoders-decoders aim to achieve universal…
We analyze the performance of encoder-decoder neural models and compare them with well-known established methods. The latter represent different classes of traditional approaches that are applied to the monotone sequence-to-sequence tasks…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…