EXIT Functions for Parallel Concatenated Insertion Convolutional Codes

Insertion convolutional codes and the underlying principles attract more and more attention, e. g., in iterative decoding, joint channel coding and cryptography or even in channel estimation. Known bits (dummy bits) are inserted into the information bit sequence before convolutional (turbo) encoding. These bits support the decoding of the information bits resulting in an improved decoding quality. Although this concept is widely employed, there does not exist any theoretical evaluation of these codes. We provide a basis for such an evaluation by means of their EXIT charts. We will analytically derive their EXIT charts as a function of the EXIT charts associated with the underlying convolutional code for a transmission over a BEC as well as a binary input/continuous output AWGN channel. These results can be adopted to all applications where perfect information is exploited by a SISO decoder and provide an excellent basis for the analytical prediction of the expected gains.