The Ultra-Reliable Low Latency Communication (URLLC) applications have been proposed in recent years, targeting a round-trip end-to-end latency less than 1 ms with high reliability. Therefore, an order of magnitude improvements are needed in all layers of the wireless communication stack. This is a particular challenge for the physical layer, where typically a processing time of the order of microseconds is required for the computationally intensive demodulation and error correction processing, among other operations. Conventionally, the reception of signals, the demodulation processing and the error correction processing are performed consecutively at the receiver. However, this approach is associated with processing times on the order of hundreds of microseconds, preventing URLLC. Therefore, this paper proposes a novel processing architecture, which is capable of performing reception, Orthogonal Frequency Division Multiplexing (OFDM) demodulation and turbo decoding concurrently, rather than consecutively, hence significantly reducing the processing time. In order to achieve concurrent operation, the OFDM demodulation is performed using a novel cumulative Fast Fourier Transform (FFT), which produces successively more reliable estimates of all transmitted symbols in each successive clock cycle. At the same time, a Fully-Parallel Turbo Decoder (FPTD) is used to recover successively more reliable estimates of all bits in each successive clock cycle.