$\frac{\boldsymbol{E_b}}{\boldsymbol{N_0}}$.net

Articles in the Blog category

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

   $\newcommand{\re}{\operatorname{Re}}\newcommand{\im}{\operatorname{Im}}\newcommand{\vec}{\operatorname{vec}} \newcommand{\mat}{\operatorname{mat}}$ First some notation:

   • 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 H …

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