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The analysis of Belief Propagation and other algorithms for the {\em reconstruction problem} plays a key role in the analysis of community detection in inference on graphs, phylogenetic reconstruction in bioinformatics, and the cavity…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
When do diffusion models reproduce their training data, and when are they able to generate samples beyond it? A practically relevant theoretical understanding of this interplay between memorization and generalization may significantly…
We consider the dynamics of belief propagation decoding of spatially coupled Low-Density Parity-Check codes. It has been conjectured that after a short transient phase, the profile of "error probabilities" along the spatial direction of a…
We investigate the reasons behind the superior performance of belief propagation decoding of non-binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over…
We analyze the quantum binary adder channel, i.e. the quantum generalization of the classical, and well-studied, binary adder channel: in this model qubits rather than classical bits are transmitted. This of course is as special case of the…
Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this…
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…
Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the…
For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform.…
This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the LM rate (Hui, 1983; Csisz\'ar-K\"orner, 1981),…
The excellent performance of convolutional low-density parity-check codes is the result of the spatial coupling of individual underlying codes across a window of growing size, but much smaller than the length of the individual codes.…
It is known that sparse superposition codes asymptotically achieve the channel capacity over the additive white Gaussian noise channel with both maximum likelihood decoding and efficient decoding (Joseph and Barron in 2012, 2014). Takeishi…
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for…
The effect of "good", point-to-point capacity achieving, code sequences on an additional signal, of bounded variance, transmitted over the additive Gaussian noise channel is examined. For such code sequences, it is shown that their effect,…
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by…
Achievable data rates in wireless systems rely heavily on the available channel state information (CSI) throughout the network. However, feedback links, which provide this information, are scarce, unreliable, and subject to security…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…
We derive a new upper bound on the string oblivious transfer capacity of discrete memoryless channels. The main tool we use is the tension region of a pair of random variables introduced in Prabhakaran and Prabhakaran (2014) where it was…
Motivated by applications of rateless coding, decision feedback, and ARQ, we study the problem of universal decoding for unknown channels, in the presence of an erasure option. Specifically, we harness the competitive minimax methodology…