  We study the problem of compression for the purpose of similarity
identification, where similarity is measured by the mean square Euclidean
distance between vectors. While the asymptotical fundamental limits of the
problem - the minimal compression rate and the error exponent - were found in a
previous work, in this paper we focus on the nonasymptotic domain and on
practical, implementable schemes. We first present a finite blocklength
achievability bound based on shape-gain quantization: The gain (amplitude) of
the vector is compressed via scalar quantization and the shape (the projection
on the unit sphere) is quantized using a spherical code. The results are
numerically evaluated and they converge to the asymptotic values as predicted
by the error exponent. We then give a nonasymptotic lower bound on the
performance of any compression scheme, and compare to the upper (achievability)
bound. For a practical implementation of such a scheme, we use wrapped
spherical codes, studied by Hamkins and Zeger, and use the Leech lattice as an
example for an underlying lattice. As a side result, we obtain a bound on the
covering angle of any wrapped spherical code, as a function of the covering
radius of the underlying lattice.
