Unequal symbol probabilities always reduce a source’s entropy below its bit capacity

Evidence

Although quantizers very often have a number of levels, which are powers of 2, such as 16, 256 or 65,536, because this makes best use of a binary word, there is no reason that other numbers of levels cannot be used, especially if entropy coding is going to be employed. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2656 (#expands, via linked claim)

Categorization

• XREF: connects to: A data source’s entropy gives the minimum bits needed to encode it — David Howard, Jamie Angus, coustics and Psychoacoustics, 2625; Quantizer levels need not be powers of two when entropy coding is used — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2656; A source sending one symbol repeatedly conveys zero information despite infinite potential self-information. (+3 more)

Broader Connections

• Information content of a signal is measured by its probability of occurrence #corroborates (0.80)
• Quantizer levels need not be powers of two when entropy coding is used #expands (0.78) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2656
• Audio compression maximizes information by encoding only unpredictable signal parts #expands (0.75)
• A source sending one symbol repeatedly conveys zero information despite infinite potential self-information. #qualifies (0.72)