An Ultimate-Shannon-Limit-Approaching Gbps Throughput Encoder/Decoder System

A turbo-Hadamard code (THC) is a type of low-rate channel code with capacity approaching the ultimate Shannon limit, i.e., −1.59 dB. In this brief, we investigate the hardware design of a turbo-Hadamard encoder/decoder system. The entire system has been implemented on an FPGA board. A bit error rate (BER) of 10⁻⁵ can be achieved at <inline-formula> <tex-math notation="LaTeX">$E_{b}/N_{0} = 0.04$ </tex-math></inline-formula> dB with a throughput of 3.2 Gbps or at <inline-formula> <tex-math notation="LaTeX">$E_{b}/N_{0} = -0.45$ </tex-math></inline-formula> dB with a throughput of 1.92 Gbps.