A transceiver architectures can contain an encoder and a decoder for communicating high speed transmissions. The encoder can modulate signal data for being mapped in a constellation that is generated based on concatenations of an E8 lattice having binary and non-binary codes. The data can be transmitted at a high speed according to the constellation with an embedded E8 lattice configuration in order to generate a coding gain. A decoder operates to decode the received input signal data with a decreased latency or a minimal latency with a high spectral efficiency.

Cable systems and assemblies integrate a reduced number of twin axial cables to transmit and received in a full-duplex transmission signals at transmission speeds greater than or equal to one hundred Giga bytes per second. The reduced number of twin axial cables comprise four or less twin axial cables, in which each pair forms a single twin axial full-duplex cable for passive or active communication of the signals at multiple different transmission rates concurrently. A processor can be integrated with the twin axial cables and operate to encode the signals for fast transmission speeds at the different transmission rates.

Cable systems and assemblies integrate a reduced number of twin axial copper pairs to transmit and received in a full-duplex transmission signals at transmission speeds greater than or equal to one hundred Giga bytes per second. The reduced number of twin axial copper pairs comprise four or less twin axial copper pairs, in which each pair forms a single twin axial full-duplex cable for passive or active communication of the signals. A processor can be integrated with the twin axial copper pairs operate to encode the signals for fast transmission speeds.

A transceiver architecture can contain an encoder and a decoder for communicating high speed transmissions. The encoder can modulate signal data based on a product code of an E8 lattice based on binary and non binary codes that creates an extended Hamming code of a multi-level structure of E8 with four bit estimates. During decoding the multi-level E8 decoding is performed on the Hamming code and then row decoding and column decoding are performed. Then lattice decoding is performed on the output of the row and column decoding. This decoding process can be iteratively performed a predetermined number of times until the encoded bits are decoded.