Related papers: Error correcting codes from sub-exceeding fonction
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
In the setting of error correcting codes, Alice wants to send a message $x \in \{0,1\}^n$ to Bob via an encoding $\text{enc}(x)$ that is resilient to error. In this work, we investigate the scenario where Bob is a low space decoder. More…
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…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5983 such inequivalent perfect codes and 2165 extended perfect codes. Efficient…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets…
Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP.…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
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…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
A new network construction method is presented for building of scalable, high throughput, low latency networks. The method is based on the exact equivalence discovered between the problem of maximizing network throughput (measured as…