# Tag Info

### Is von Neumann's randomness in sin quote no longer applicable?

If you're using some hardware source of entropy/randomness, you're not "attempting to generate randomness by deterministic means" (my emphasis). If you're not using any hardware source of entropy/...
Accepted

### Is von Neumann's randomness in sin quote no longer applicable?

Just because you can't see a pattern doesn't mean that no pattern exists. Just because a compression algorithm can't find a pattern doesn't mean that no pattern exists. Compression algorithms are ...
• 162k

### Efficient compression of simple binary data

Sure, of course there are algorithms. Here is my algorithm: First, check if the file contains ordered binary numbers from $0$ to $2^n-1$, for some $n$. If so, write out a 0 bit followed by $n$ one ...
• 162k
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### Do lossless compression algorithms reduce entropy?

A lot of casual descriptions of entropy are confusing in this way because entropy is not quite as neat and tidy a measure as sometimes presented. In particular, the standard definition of Shannon ...
• 616
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### Can data be compressed to size smaller than Shannon data compression limit?

Actually I don't fully understand this algorithm or the Shannon limit very well, I just know it's the sum of the probability of each character multiplied by log2 of the reciprocal of the probability. ...
• 13.6k
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### Why are these (lossless) compression methods of many similar png images ineffective?

Have a look at how compression algorithms work. At least those in the Lempel-Ziv family (gzip uses LZ77, zip apparently mostly ...
• 72.6k

### Can random suitless $52$ playing card data be compressed to approach, match, or even beat entropy encoding storage? If so, how?

Here is a complete algorithm which reaches the theoretical limit. Prologue: Encoding integer sequences A 13-integer sequence "integer with upper limit $a-1$, integer with upper limit $b-1$, "integer ...
• 1,064
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### Efficient compression of simple binary data

This seems to be a clear use case for delta compression. If $n$ is known a priori this is trivial: store the first number verbatim, and for each next number store only the difference to the previous. ...
• 1,681
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### Efficient compression of simple binary data

PNG encoding does exactly what you want. It works on real life data also, not just extremely organized data. In PNG, each row is encoded with a filter, of which 4 are specified. One of these is "...
• 3,351
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### Why does a MP3 encoder use a fast Fourier transform before applying the psychoacoustic model?

I would suggest a more detailed explanation of mp3 codec. FFT is applied on the time domain signal, so in fact it does not use the result from the MDCT. The input to the psychoacoustic models is in ...
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### Can random suitless $52$ playing card data be compressed to approach, match, or even beat entropy encoding storage? If so, how?

The number of possible arrangements of the cards ignoring suits is $$\frac{52!}{(4!)^{13}}\text,$$ whose logarithm base 2 is 165.976, or 3.1919 bits per card, which is better than the limit you gave. ...
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Represent the string $x$ using the following encoding: $$0, x_k, \dots, 0, x_2, 0, x_1, 1, x_0$$ where $x_0 = x$, $x_{i+1} = \text{len}(x_i)$ is a binary representation of the length of $x_i$ in bits (...