Lossless source coding using tree structured random binning

We propose a tree structured variable length random binning scheme for lossless compression of binary memoryless sources. Previously proposed source coding schemes based on nested error correcting codes can be regarded as practical implementations of this random binning scheme. For sufficiently large data blocks, we prove that the proposed scheme asymptotically achieves the entropy limit. We also derive the distribution of the compression rate achieved by the tree structured random binning scheme. Comparing this distribution with the distribution obtained using a library of random binning schemes, we show that a nested code can achieve rates close to a library of codes but with much lower encoding/decoding complexity.