Precoded Sphere-Packing-Aided Bit-Interleaved Differential Space-Time Coded Modulation Using Iterative Decoding

In this treatise, we investigate a precoded and sphere packing (SP)-aided bit-interleaved differential space-time coded modulation scheme using iterative decoding. The amalgamated design and interworking of the SP, differential encoding, and iteratively detected bit-interleaved schemes are investigated. A rate-1 precoder is integrated into the system, where iterative decoding is carried out between the precoder and an outer channel code. We identify the optimal SP mapping and investigate the convergence behavior of this concatenated scheme with the aid of EXtrinsic Information Transfer (EXIT) charts. Furthermore, we consider various rate-1 precoders having different memory sizes and demonstrate that the memory-1 precoder performs best when an RSC(2,1,5) is employed as the outer code, creating an open EXIT chart convergence tunnel at $E_{b}/N_{0} = 6\ \hbox{dB}$. On the other hand, the memory-3 precoder is more suitable for the proposed system employing irregular convolutional codes, resulting in an infinitesimally low bit error rate at $E_{b}/N_{0} = 5.5\ \hbox{dB}$.