15 problems

In a memory approximate message passing (MAMP) receiver, let $\hat{\phi}_t(\cdot)$ denote the code constraint associated with the forward-error-correction (FEC) decoder at iteratio…

Consider the given BDD signal model and compare AMP and AMP-SI using Toeplitz sensing matrices with the corresponding state-evolution prediction, as well as using independent and i…

Let $p_{\mathsf{Dyn}}$ be the balanced binary dynamic prior with $0\leq\rho\leq 1/2$, and let $T^{\mathsf{Dyn}}$ be its state evolution mapping, with coordinates…

Let $p_{\mathsf{ML}}$ be the balanced binary multilayer prior with $0\leq\rho\leq 1/2$, and let $T^{\mathsf{ML}}$ be its state evolution mapping, with coordinates…

For Algorithm, let the vectors $\boldsymbol{u}^{\ell}=\beta\boldsymbol{H}{\boldsymbol{x}}^{\ell-1}-\boldsymbol{\theta}^{\ell-1} \circ\boldsymbol{z}^{\ell-1}$ and…

Let $P_0$ be a signal distribution and $P_\mathrm{out}(y\mid z)$ an output likelihood satisfying the symmetry conditions that $P_0(x_1)=P_0(x_2)$ whenever $|x_1|=|x_2|$ and…

The replica method gives a potential $\phi(\mathbf{q},\hat{\mathbf{q}},\mathbf{m},\hat{\mathbf{m}},\mathbf{q}_{12},\hat{\mathbf{q}}_{12})$, whose extrema determine self-consistency…

Informative-solution conjecture.

State-evolution characterization conjecture. The fixed points of the SE characterize the asymptotic behavior of the spectral estimator.

Approximate message passing with side information (AMP-SI) is an AMP algorithm whose conditional denoiser can depend on the coordinate index through the side information; its state…

Ma–Takeda fixed-point conjecture. The FPs of the SE equations are the same as those of the asymptotic energy function.

Let $\bm{A}$ be unitarily invariant, and let $\bm{W}_t$ be given by the specified linear estimator. Define … with $v_0^2=\operatorname{E}\{X^2\}$, where $\Phi_t$ and $\Psi_t$ are t…

The decoder is considered for power-allocated signals encoded with structured operators, including structured Hadamard-based operators, and its asymptotic dynamical behavior is ana…

AMP-UD large-system conjecture. AMP-UD can achieve the MMSE for stationary ergodic inputs in the limit of large linear systems where the matrix has i.i.d. random entries.

Consider the state evolution derived for the approximate message passing algorithm for matrix factorization in the large-system limit. State evolution conjecture. The derived state…