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We report on the first error-free terahertz (THz) wireless communication at 0.310 THz for data rates up to 8.2 Gbps using a 18-GHz-bandwidth GaAs/AlGaAs field-effect transistor as a detector. This result demonstrates that low-cost commercially-available plasma-wave transistors whose cut-off frequency is far below THz frequencies can be employed in THz communication. Wireless communication over 50 cm is presented at 1.4 Gbps using a uni-travelling-carrier photodiode as a source. Transistor integration is detailed, as it is essential to avoid any deleterious signals that would prevent successful communication. We observed an improvement of the bit error rate with increasing input THz power, followed by a degradation at high input power. Such a degradation appears at lower powers if the photodiode bias is smaller. Higher-data-rate communication is demonstrated using a frequency-multiplied source thanksto higher output power. Bit-error-rate measurements at data rates up to 10 Gbps are performed for different input THz powers. As expected, bit error rates degrade as data rate increases. However, degraded communication is observed at some specific data rates. This effect is probably due to deleterious cavity effects and/or impedance mismatches. Using such a system, realtime uncompressed high-definition video signal is successfully and robustly transmitted.