相关论文: Identification Codes via Prime Numbers

Ahlswede and Dueck showed possibility to identify with high probability one out of $M$ messages by transmitting $1/C\log\log M$ bits only, where $C$ is the channel capacity. It is known that this identification can be based on…

Hashing is promising for large-scale information retrieval tasks thanks to the efficiency of distance evaluation between binary codes. Generative hashing is often used to generate hashing codes in an unsupervised way. However, existing…

In this paper we analyse the construction of identification codes. Identification codes are based on the question "Is the message I have just received the one I am interested in?", as opposed to Shannon's transmission, where the receiver is…

This paper presents a new distributed approach for generating all prime numbers in a given interval of integers. From Eratosthenes, who elaborated the first prime sieve (more than 2000 years ago), to the current generation of parallel…

The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of…

Continuing our earlier work (quant-ph/0401060), we give two alternative proofs of the result that a noiseless qubit channel has identification capacity 2: the first is direct by a "maximal code with random extension" argument, the second is…

Generating primes is a fundamental problem in modern cryptography. Deterministic primality tests work well for special integers such as Mersenne or Proth primes, but these forms are quite restrictive. In this paper, we give a direct method…

This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested…

This paper examines the maximum code rate achievable by a data-driven communication system over some unknown discrete memoryless channel in the finite blocklength regime. A class of channel codes, called learning-based channel codes, is…

Ahlswede and Dueck identification has the potential of exponentially reducing traffic or exponentially increasing rates in applications where a full decoding of the message is not necessary and, instead, a simple verification of the message…

In first-year programming courses it is often difficult to show students how an algorithm can be discovered. In this paper we present a program format that supports the development from specification to code in small and obvious steps; that…

Prime numbers play a very vital role in modern cryptography and especially the difficulties involved in factoring numbers composed of product of two large prime numbers have been put to use in many modern cryptographic designs. Thus, the…

Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be…

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…

We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super…

Determining the prime factors of a given number N is a problem, which requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by P. Shor for quantum computers. However, the realization of…

We implement a quantum protocol for prime number identification based on entanglement dynamics, using IBM quantum processors. The method links the primality of an integer to specific Fourier components extracted from the time evolution of…

This paper addresses the problem of learning binary hash codes for large scale image search by proposing a novel hashing method based on deep neural network. The advantage of our deep model over previous deep model used in hashing is that…

We consider wiretap channels with uncertainty on the eavesdropper channel under (i) noisy blockwise type II, (ii) compound, or (iii) arbitrarily varying models. We present explicit wiretap codes that can handle these models in a unified…

Biometric applications, such as person re-identification (ReID), are often deployed on energy constrained devices. While recent ReID methods prioritize high retrieval performance, they often come with large computational costs and high…