Computer Science

We consider the processing of statistical samples X??P θ by a channel p(y|x) , and characterize how the statistical information from the samples for estimating the parameter θ??R d can scale with the mutual information or capacity of the channel. We show that if the statistical model has a sub-Gaussian score function, then the trace of the Fisher information matrix for estimating θ from Y can scale at most linearly with the mutual information between X and Y . We apply this result to obtain minimax lower bounds in distributed statistical estimation problems, and obtain a tight preconstant for Gaussian mean estimation. We then show how our Fisher information bound can also imply mutual information or Jensen-Shannon divergence based distributed strong data processing inequalities.

We define a new measure of causation from a fluctuation-response theorem for Kullback-Leibler divergences, based on the information-theoretic cost of perturbations. This information response has both the invariance properties required for an information-theoretic measure and the physical interpretation of a propagation of perturbations. In linear systems, the information response reduces to the transfer entropy, providing a connection between Fisher and mutual information.

Non-orthogonal multiple-access (NOMA) is a leading technology which gain a lot of interest this past several years. It enables larger user density and therefore is suited for modern systems such as 5G and IoT. In this paper we examined different frame-based codes for a partially active NOMA system. It is a more realistic setting where only part of the users, in an overly populated system, are active simultaneously. We introduce a new analysis approach were the active user ratio, a system's feature, is kept constant and different sized frames are employed. The frame types were partially derived from previous papers on the subject [1][2] and partially novel such as the LPF and the Steiner ETF. We learned the best capacity achieving frame depends on the active user ratio and three distinct ranges where defined. In addition, we introduced a measure called practical capacity which is the maximal rate achieved by simple coding scheme. ETFs always achieve the best practical capacity while LPFs and sparse frames are worse than a random one.

Motivated by applications in machine learning and archival data storage, we introduce function-correcting codes, a new class of codes designed to protect a function evaluation of the data against errors. We show that function-correcting codes are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes which protect the whole data.

We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for N files and K users can be obtained from a non-private scheme that serves only a subset of the demands for the N files and NK users problem. We further use this fact to construct a demand-private scheme for N files and K users from a particular known non-private scheme for N files and NK?�K+1 users. It is then demonstrated that, the memory-rate pair (M,min{N,K}(1?�M/N)) , which is achievable for non-private schemes with uncoded transmissions, is also achievable under demand privacy. We further propose a scheme that improves on these ideas by removing some redundant transmissions. The memory-rate trade-off achieved using our schemes is shown to be within a multiplicative factor of 3 from the optimal when K<N and of 8 when N?�K . Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with N?�K=2 .

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive interpolation method in Bayesian inference for linear regimes to sub-linear ones. A modification of the well-known approximate message passing algorithm to approach the MMSE fundamental limit is also proposed, and its state evolution is rigorously analysed. Our results show that the traditional linear assumption between the signal dimension and number of observations in the replica and adaptive interpolation methods is not necessary for sparse signals. They also show how to modify the existing well-known AMP algorithms for linear regimes to sub-linear ones.

In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences of period pq is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, we derive a lower bound on the 2-adic complexity of the corresponding sequence, which further expands our previous work (Zhao C, Sun Y and Yan T. Study on 2-adic complexity of a class of balanced generalized cyclotomic sequences. Journal of Cryptologic Research,6(4):455-462, 2019). The result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm(RAA) for feedback with carry shift registers(FCSRs), i.e., it is in fact lower bounded by pq?�p?�q?? , which is far larger than one half of the period of the sequences. Particularly, the 2-adic complexity is maximal if suitable parameters are chosen.

Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their excellent performance. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a "convolutional" manner. The number of partitioned components determines the "memory" of SC codes. While adopting higher memories results in improved SC code performance, obtaining optimal SC codes with high memory is known to be hard. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. We propose a probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low complexity optimization algorithms over the cycle properties to construct high memory, high performance quasi-cyclic SC codes. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and codes with uniform partitioning.

In this paper, we explore some properties of Galois hulls of cyclic serial codes over a chain ring and we devise an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average p r -dimension of the Euclidean hull, where F p r is the residue field of R , and we provide some results of its relative growth.

Generalized energy detection (GED) is analytically studied when operates under fast-faded channels and in the presence of generalized noise. For the first time, the McLeish distribution is used to model the underlying noise, which is suitable for both non-Gaussian (impulsive) as well as classical Gaussian noise channels. Important performance metrics are presented in closed forms, such as the false-alarm and detection probabilities as well as the decision threshold. Analytical and simulation results are cross-compared validating the accuracy of the proposed approach in the entire signal-to-noise ratio regime. Finally, useful outcomes are extracted with respect to GED system settings under versatile noise environments and when noise uncertainty is present.