1. ## Estimating a Complex Positive semi-definite Matrix using Noisy Observations of its Entries


• Use $\succeq 0$ to mean matrix positive semi-definiteness.
• Use $\vec$ as the …
2. ## Intuition for Mrs. Gerber's Lemma

Mrs. Gerber's Lemma: $X$ is a length-$n$ binary word with arbitrary distribution and $Y$ is a corruption of $X$ through a binary symmetric channel with crossover probability $p$. If $H(X) \geq nv$ then $H …$

3. ## Modifying a Plustek 8100 to Scan Medium Format

The Plustek 8100 is a relatively cheap but good quality film scanner. It produces much nicer scans than most flatbed-type scanners, but it can only capture small format film. In this page I show how to modify a Plustek 8100 to scan medium format (120 film) by stitching together multiple …

4. ## A Class of Multivariate Functions that Behave Like Single-Letter Random Variables

Vector-encoders of a certain pretty restricted class happen to carry precisely the same information content as univariate encoders.

### Claim

Take $X _ 1,\dots, X _ n$ iid over finite alphabet $\mathcal{X}$ and $f:\mathcal{X}^n …$

5. ## Extracting Relevant Information over Many Trials

The information bottleneck scenario goes like this:

We are interested in a quantity $Y$ but only observe $X$ which we must process down to a rate $R \in (0, H(X)).$ To this end, what random variables $(U,Q)$ minimize

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