Double-space-cooperation method for increasing channel capacity

Shannon channel capacity theorem poses highest bit-rate of error free transmission over additive white Gaussian noise channel. In addition, he proved that there exists channel code that can theoretically achieve the channel capacity. Indeed fortunately, the latter researchers found some practical channel codes approaching the channel capacity with insignificant losses of spectral efficiency under ignorable bit error rate (BER). The authors note, in general, that bits of the channel codes are not independent of each other in code space. Further, we note that the modulated symbols are not independent among them, as well, in Euclidean Space. By exploiting a usage of the dependencies jointly to signal design, we can transmit two independent signal streams through an additive white Gaussian channel and separate them in Euclidean space at the receiver. The capacity of this approach is found larger than that of Shannon capacity in the same channel assumptions. The numerical results confirm the theoretical procedures.