We establish the precise asymptotics of the quantization and entropy coding errors for fractional Brownian motion with respect to the supremum norm and $L^p [0,1]$-norm distortions. We show that all moments in the quantization problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremum-norm distortion, our proof uses an explicit construction of efficient codebooks based on a particular entropy constrained coding scheme.
"High Resolution Quantization and Entropy Coding for Fractional Brownian Motion." Electron. J. Probab. 11 700 - 722, 2006. https://doi.org/10.1214/EJP.v11-344