Random Binning and Turbo Source Coding for Lossless Compression of Memoryless Sources

We propose a tree structured variable length random binning scheme that enables an error correcting code to act as a source code. The existing source coding schemes based on turbo codes, low density parity check codes, and repeat accumulate codes can be regarded as practical implementations of this random binning scheme. We investigate the performance of lossless turbo source coding relative to the proposed tree structured random binning scheme. Our numerical results show that the compression rate achieved by lossless turbo source coding is far from the tree structured random binning bound. In that, we suggest improvements to enable short block length turbo source codes to achieve compression rates close to the tree structured random binning bound.