相关论文: Identification Codes via Prime Numbers
This paper investigates the first- and second-order maximum achievable rates of codes with/without cost constraints for mixed {channels} whose channel law is characterized by a general mixture of (at most) uncountably many stationary and…
In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…
In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic…
Research aimed at scaling up neuroscience inspired learning algorithms for neural networks is accelerating. Recently, a key research area has been the study of energy-based learning algorithms such as predictive coding, due to their…
We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
Most prime gaps results have been proven using tools from analytic or algebraic number theory in the last few centuries. In this paper, we would like to present some probabilistic way of proving many essential results. A major component of…
The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations-the generation processes cannot be fully traced,…
Guessing random additive noise decoding (GRAND) algorithm has emerged as an excellent decoding strategy that can meet both the high reliability and low latency constraints. This paper proposes a successive addition-subtraction algorithm to…
This article presents a novel method for establishing an information theoretically secure encryption key over wireless channels. It exploits the fact that data transmission over wireless links is accompanied by packet error, while noise…
We analyze deterministic message identification via channels with non-discrete additive white noise and with a noiseless feedback link under both average power and peak power constraints. The identification task is part of Post Shannon…
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as…
Huffman Codes are optimal Instantaneous Fixed-to-Variable (FV) codes in which every source symbol can only be encoded by one codeword. Relaxing these constraints permits constructing better FV codes. More specifically, recent work has shown…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
In the splitting model, information theoretic authentication codes allow non-deterministic encoding, that is, several messages can be used to communicate a particular plaintext. Certain applications require that the aspect of secrecy should…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. Motivated by…
Hashing methods have been widely used for applications of large-scale image retrieval and classification. Non-deep hashing methods using handcrafted features have been significantly outperformed by deep hashing methods due to their better…
Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
Likelihood-based generative models are the backbones of lossless compression due to the guaranteed existence of codes with lengths close to negative log likelihood. However, there is no guaranteed existence of computationally efficient…
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction.…