Bits-back coding software guide

| In this document, I rst review the theory behind bits-back coding (aka. free energy coding) (Frey and Hinton 1996) and then describe the interface to C-language software that can be used for bits-back coding. This method is a new approach to the problem of optimal compression when a source code produces multiple codewords for a given symbol. It may seem that the most sensible codeword to use in this case is the shortest one. However, in the proposed bits-back approach, random codeword selection yields an eeective codeword length that can be less than the shortest codeword length. If the random choices are Boltzmann distributed, the eeective length is optimal for the given source code. The software which I describe in this guide is easy to use and the source code is only a few pages long. I illustrate the bits-back coding software on a simple quantized Gaussian mixture problem.