Related papers: Error correcting code using tree-like multilayer p…
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…
In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
This paper presents a new erasure code called Treeplication designed for distributed recovery of the full information word, while most prior work in coding for distributed storage only supports distributed repair of individual symbols. A…
The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate $t$ asymmetric errors. Our main observation is…
In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions,…
We propose a linear optics scheme with SPDC process to test the fault tolerance property of quantum error correction code. To transmit an unknown qubit robustly through the noisy channel, one may first encode it into a certain quantum error…
In order to communicate a message over a noisy channel, a sender (Alice) uses an error-correcting code to encode her message $x$ into a codeword. The receiver (Bob) decodes it correctly whenever there is at most a small constant fraction of…
Long-distance quantum communication necessitates the use of quantum repeaters, which typically include highly coherent quantum memories. We provide a theoretical analysis of the secret key rates for a quantum repeater system incorporating…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
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…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
Berlekamp and Zigangirov completely determined the capacity error function for binary error correcting codes with noiseless feedback. It is still an unsolved problem if the upper bound for the capacity error function in the non-binary case…
The autoencoder concept has fostered the reinterpretation and the design of modern communication systems. It consists of an encoder, a channel, and a decoder block which modify their internal neural structure in an end-to-end learning…
This letter introduces a multi-rate task-oriented communication (MR-ToC) framework. This framework dynamically adapts to variations in affordable data rate within the communication pipeline. It conceptualizes communication pipelines as…
We propose new methods for Support Vector Machines (SVMs) using tree architecture for multi-class classi- fication. In each node of the tree, we select an appropriate binary classifier using entropy and generalization error estimation, then…