  The number of random bits required to approximate a target distribution in
terms of un-normalized informational divergence is considered. It is shown that
for a variable-to-variable length encoder, this number is lower bounded by the
entropy of the target distribution. A fixed-to-variable length encoder is
constructed using M-type quantization and Tunstall coding. It is shown that the
encoder achieves in the limit an un-normalized informational divergence of zero
with the number of random bits per generated symbol equal to the entropy of the
target distribution. Numerical results show that the proposed encoder
significantly outperforms the optimal block-to-block encoder in the finite
length regime.
