Related papers: Public key cryptography and error correcting codes…
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…
We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
This study introduces a decentralized approach to secure wireless communication using a cryptographic secret key generation algorithm among distributed nodes. The system model employs Gaussian prime numbers, ensuring the collaborative…
New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input…
We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network…
The generalization of Shannon's theory to include messages with given autocorrelations is presented. The analytical calculation of the channel capacity is based on the transfer matrix method of the effective 1D Hamiltonian. This bridge…
Continuous-Variable Quantum Key Distribution (CVQKD) at large distances has such high noise levels that the error-correcting code must have very low rate. In this regime it becomes feasible to implement random-codebook error correction,…
We study a new class of codes for Gaussian multi-terminal source and channel coding. These codes are designed using the statistical framework of high-dimensional linear regression and are called Sparse Superposition or Sparse Regression…
The use of multiple antenna arrays in transmission and reception has become an integral part of modern wireless communications. To quantify the performance of such systems, the evaluation of bounds on the error probability of realistic…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
The use of parity-check gates in information theory has proved to be very efficient. In particular, error correcting codes based on parity checks over low-density graphs show excellent performances. Another basic issue of information…
The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
Sparse regression codes (SPARCs) are a promising coding scheme that can approach the Shannon limit over Additive White Gaussian Noise (AWGN) channels. Previous works have proven the capacity-achieving property of SPARCs with Gaussian design…