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Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be…
Sparse random linear network coding (SRLNC) used as a class of erasure codes to ensure the reliability of multicast communications has been widely investigated. However, an exact expression for the decoding success probability of SRLNC is…
We analyze the convergence rates of two popular variants of coordinate descent (CD): random CD (RCD), in which the coordinates are sampled uniformly at random, and random-permutation CD (RPCD), in which random permutations are used to…
The bit-error threshold of the standard ensemble of Low Density Parity Check (LDPC) codes is known to be close to capacity, if there is a non-zero fraction of degree-two bit nodes. However, the degree-two bit nodes preclude the possibility…
The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…
Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…
We derive upper and lower bounds for the error exponents of lossless streaming compression of two correlated sources under the blockwise and symbolwise settings. We consider the linear scaling regime in which the delay is a scalar multiple…
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
We analyze the prediction error of principal component regression (PCR) and prove high probability bounds for the corresponding squared risk conditional on the design. Our first main result shows that PCR performs comparably to the oracle…
There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error meeting the bound have support of size $k$ only. In this note, linear codes of full…
We consider ensembles of channel codes that are partitioned into bins, and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs. Two main…
We establish an equivalence between two important random ensembles of linear codes: random linear codes (RLCs) and random Reed-Solomon (RS) codes. Specifically, we show that these models exhibit identical behavior with respect to key…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
This work contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two…
Exponential error bounds for the finite-alphabet interference channel (IFC) with two transmitter-receiver pairs, are investigated under the random coding regime. Our focus is on optimum decoding, as opposed to heuristic decoding rules that…
This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…