Secure data compression with sphere packing

A system that accomplishes compression using sphere packing with the support of a hyper-elliptic curve providing encryption is presented. In addition, with use of channel code algorithms, high consistency is achieved and the expansion factor is calculated. Results of simulation are also presented where the hyper-elliptic curve encryption is concatenated with sphere packing, followed by a non-binary low density parity check encoder and sphere packing modulation. A gain of 8 dB over uncoded QPSK modulation for BER =10^-4 is achieved on a two tap fading channel. Finally, system complexity is presented for a system based on symbols and a system based on bits.