A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation
Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the dist...
| Authors | Uri Erez |
|---|---|
| Primary category | cs.IT |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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