Abstract
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.
Highlights
We show that the well-known technique in [6], though historically developed for uniform bits, provides “correct” EXIT charts with nonuniform bits, which is an interesting conclusion for readers familiar with this technique
The data points show the BEXIT and FEXIT charts obtained by applying the transformations (X)-(XI), Table 1, respectively, on the FEXIT and BEXIT charts given in solid lines
The good match between the data points and the solid lines illustrates the equivalence between FEXIT and BEXIT charts
Summary
It involves a serial concatenation at the transmitter and a joint source-channel serial turbo decoder [1, 2] at the receiver and is sufficiently general to describe several issues that arise with EXIT charts [3] when the bits U: are not uniform. After random interleaving by Π, the inner component is a channel code that produces a sequence of coded bits R: which are sent across the channel.
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