Chapter 7
Irregular Variable-Length Codes for EXIT-Chart Matching1
7.1 Introduction
As demonstrated in Section 6.6, a serially concatenated [275] transmission scheme is capable of achieving iterative decoding [278] convergence to an infinitesimally low probability of error at near-capacity Signal-to-Noise Ratios (SNRs), if the EXtrinsic Information Transfer (EXIT) functions of the inner and outer codecs are well matched. This motivated the design of Irregular Convolutional Code (IrCC) schemes in [149], as described in Section 5.5.
The inverted EXIT function of an outer IrCC channel codec can be specifically shaped in order to match the EXIT function of a serially concatenated inner codec. This is possible because IrCCs amalgamate a number of component Convolutional Codes (CC) [140] having different coding rates, each of which is employed to generate a specific fraction of the IrCCencoded bit stream. As described in Section 5.5, the composite inverted IrCC EXIT function is given as a weighted average of the inverted EXIT functions of the individual component CCs, where each weight is given by the particular fraction of the IrCC-encoded bit stream that is generated by the corresponding component CC. Hence, it is the specific selection of these fractions that facilitates the shaping of the inverted composite IrCC EXIT function. Using the EXIT-chart matching algorithm of [149], the inverted IrCC EXIT chart may be matched to the EXIT function of the inner codec in this way. This facilitates ...
