Technology

Correct me if I’m wrong

Well actually, yes, I'm sorry to have to tell you are wrong. Shannon-Fano coding is suboptimal for prefix codes and Huffman coding, while optimal for prefix-based coding, is not necessarily the most efficient compression method for any given data (and often isn't).

Huffman can be optimal given certain strict constraints, but those constraints don't always occur in natural/real- world data.

The best compression method (whether lossless or lossy) depends greatly on the nature of the data to be compressed. Patterns and biases can make certain methods much more efficient (or more practical) in some cases, when they might be useless elsewhere or in general. This is why data is often transformed before compression, using a reversible transformation that "encourages" certain desirable statistical characteristics in the data, so the compression method can better exploit them.

For example, compression software (e.g. gzip) may perform a Burrows-Wheeler transform and other encodings before applying Huffman coding to get a better compression ratio. If Huffman coding was an optimal compression method for all possible data, this would be redundant! Often, E.g. in medical imaging, audio/video data, the data is best analysed in a different domain to better reveal the underlying patterns and redundancies in the data so they cam be easily exploited by compression. E.g. frequency domain instead of time/spatial domain.