Random Bit Flipping and EXIT Charts for Nonuniform Binary Sources and Joint Source-Channel Turbo Systems

Joint source-channel turbo techniques have recently been explored a lot in literature as one promising possibility to lower the end-to-end distortion, with fixed length codes, variable length codes, and (quasi) arithmetic codes. Still, many issues remain to be clarified before production use. This short contribution clarifies very concisely several issues that arise with EXIT charts and nonuniform binary sources (a nonuniform binary source can be the result of a nonbinary source followed by a binary source code). We propose two histogram-based methods to estimate the charts and discuss their equivalence. The first one is a mathematical generalization of the original EXIT charts to nonuniform bits. The second one uses a random bit flipping to make the bits virtually uniform and has two interesting advantages: (1) it handles straightforwardly outer codes with an entropy varying with the bit position, and (2) it provides a chart for the inner code that is independent of the outer code.