Related papers: Reed-Muller Identification
The model of identification via channels, introduced by Ahlswede and Dueck, has attracted increasing attention in recent years. One such promising direction is message identification via channels, introduced by Ahlswede and Dueck. Unlike in…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
In this work, we study the performance of Reed--Solomon codes against adversarial insertion-deletion (insdel) errors. We prove that over fields of size $n^{O(k)}$ there are $[n,k]$ Reed-Solomon codes that can decode from $n-2k+1$ insdel…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
Consider the identification (ID) via channels problem, where a receiver wants to decide whether the transmitted identifier is its identifier, rather than decoding the identifier. This model allows to transmit identifiers whose size scales…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
Deterministic identification offers an efficient solution for scenarios where decoding entire messages is unnecessary. It is commonly used in alarm systems and control systems. A key advantage of this approach is that the capacity for…
This paper considers the performance of Reed-Muller (RM) codes transmitted over binary memoryless symmetric (BMS) channels under bitwise maximum-a-posteriori (bit-MAP) decoding. Its main result is that, for a fixed BMS channel, the family…
We discuss concepts of message identification in the sense of Ahlswede and Dueck via general quantum channels, extending investigations for classical channels, initial work for classical-quantum (cq) channels and "quantum fingerprinting".…
We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating…
Recent work have shown that Reed-Muller (RM) codes achieve the erasure channel capacity. However, this performance is obtained with maximum-likelihood decoding which can be costly for practical applications. In this paper, we propose an…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels with respect to bit error rate. This paper extends that work by showing that RM codes defined on non-binary fields,…
In this paper, we study the problem of constructing projective systematic authentication schemes based on binary linear codes. In systematic authentication, a tag for authentication is generated and then appended to the information, also…
Multi-User Detection is fundamental not only to cellular wireless communication but also to Radio-Frequency Identification (RFID) technology that supports supply chain management. The challenge of Multi-user Detection (MUD) is that of…
Traffic signal control has the potential to reduce congestion in dynamic networks. Recent studies show that traffic signal control with reinforcement learning (RL) methods can significantly reduce the average waiting time. However, a…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
The subspace design property for additive codes is a higher-dimensional generalization of the minimum distance property. As shown recently by Brakensiek, Chen, Dhar and Zhang, it implies that the code has similar performance as random…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…