Related papers: Error correcting codes from sub-exceeding fonction
The binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
Permutation codes were extensively studied in order to correct different types of errors for the applications on power line communication and rank modulation for flash memory. In this paper, we introduce the neural network decoders for…
This paper presents a novel semantic-enhanced decoding scheme for transmitting natural language sentences with multiple short block codes over noisy wireless channels. After ASCII source coding, the natural language sentence message is…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
We consider a point-to-point communication scenario where the receiver maintains a specific linear function of a message vector over a finite field. When the value of the message vector undergoes a sparse update, the transmitter broadcasts…
This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are…
In this paper, we give upper bounds on the sizes of $(d, L)$ list-decodable codes in the Hamming metric space from covering codes with the covering radius smaller than or equal to $d$. When the list size $L$ is $1$, this gives many new…
We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an…
Reducing the threshold voltage of electronic devices increases their sensitivity to electromagnetic radiation dramatically, increasing the probability of changing the memory cells' content. Designers mitigate failures using techniques such…
We consider the energy savings that can be obtained by employing network coding instead of plain routing in wireless multiple unicast problems. We establish lower bounds on the benefit of network coding, defined as the maximum of the ratio…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. Previously, it was shown that finite effective length codes are necessary in…
This work is motivated by the problem of error correction in bit-shift channels with the so-called $ (d,k) $ input constraints (where successive $ 1 $'s are required to be separated by at least $ d $ and at most $ k $ zeros, $ 0 \leq d < k…
Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost…
We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked…
We study the largest possible length $B$ of $(B-1)$-dimensional linear codes over $\mathbb{F}_q$ which can correct up to $t$ errors taken from a restricted set $\mathcal{A}\subseteq \mathbb{F}_q^*$. Such codes can be applied to multilevel…
In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…
The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended…
Achieving fault-tolerance will require a strong relationship between the hardware and the protocols used. Different approaches will therefore naturally have tailored proof-of-principle experiments to benchmark progress. Nevertheless,…