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For the additive white Gaussian noise channel with average power constraint, sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the capacity. While the codewords of the original sparse superposition codes are made…
We consider a communication problem in which the receiver must first detect the presence of an information packet and, if detected, decode the message carried within it. We present general nonasymptotic upper and lower bounds on the maximum…
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no…
A new communication scheme for Gaussian parallel relay networks based on superposition coding and partial decoding at the relays is presented. Some specific examples are proposed in which two codebook layers are superimposed. The first…
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by a convex set in $\mathbb{R}^d$. Combinatorial objects known…
We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not…
We introduce 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 our method exploits…
In this paper we investigate the effect of spatial coupling applied to the recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to the bridge between the graphical model describing the iterative interference…
In this paper we address the problem of finding the sensing capacity of sensor networks for a class of linear observation models and a fixed SNR regime. Sensing capacity is defined as the maximum number of signal dimensions reliably…
Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote…
Low-rate and short-packet transmissions are important for ultra-reliable low-latency communications (URLLC). In this paper, we put forth a new family of sparse superposition codes for URLLC, called block orthogonal sparse superposition…
We study the amplitude-constrained additive white Gaussian noise channel. It is well known that the capacity-achieving input distribution for this channel is discrete and supported on finitely many points. The best known bounds show that…
Sparse neural networks are becoming increasingly important as the field seeks to improve the performance of existing models by scaling them up, while simultaneously trying to reduce power consumption and computational footprint.…
We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…
This paper considers delay-limited communication over quasi-static fading channels under a long-term power constraint. A sequence of length-$n$ delay-limited codes for a quasi-static fading channel is said to be capacity-achieving if the…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
In this paper, we study codes with sparse generator matrices. More specifically, low-density generator matrix (LDGM) codes with a certain constraint on the weight of the columns in the generator matrix are considered. In this paper, it is…
Lattices possess elegant mathematical properties which have been previously used in the literature to show that structured codes can be efficient in a variety of communication scenarios, including coding for the additive white Gaussian…
In this paper we consider the generalization of binary spatially coupled low-density parity-check (SC-LDPC) codes to finite fields GF$(q)$, $q\geq 2$, and develop design rules for $q$-ary SC-LDPC code ensembles based on their iterative…
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…