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

Articles in the Blog category

1. 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 $H …$

2. 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 …

3. 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 $f:\mathcal{X}^n …$

4. 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 …

5. Hypersphere Cap Volumes in Matlab

   The volume of a height-$h$ cap of a ball of radius $r$ in dimension $n$ can be derived:

   \begin{equation} \operatorname{vol}(\operatorname{cap}) = \frac{1}{2} \cdot \frac{\pi^{n/2}}{\Gamma\left(1+n/2\right)} \cdot r^n \cdot I_{(2rh-h^2)/r …

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