Universal fixed-to-variable source coding in the finite blocklength regime

A universal source coding problem is considered in the finite blocklength regime for stationary memoryless sources. A new coding scheme is presented that encodes based on the type class size and the empirical support set of the sequence. It is shown that there is no loss in dispersion relative to the case when the source distribution is known. A new bound is obtained on the third order asymptotic coding rate. Numerical results are presented for finite blocklengths comparing the proposed coding scheme with a variety of coding schemes including Lempel-Ziv.