Iterative turbo equalization is capable of achieving impressive performance gains over the conventional non-iterative equalization having the same complexity, when communicating over channels that suffer from intersymbol interference (ISI). The state-of-the-art turbo equalizers employ the logarithmic Bahl-Cocke-Jelinek-Raviv (Log-BCJR) algorithm. However, due to the specific nature of serial data processing, the Log-BCJR algorithm introduces significant processing delays at the receiver. Therefore, in low-latency applications having a high throughput, the turbo equalizer might be deemed less attractive than its conventional counterparts. In order to circumvent this problem, in this paper, we conceived a novel fully parallel turbo equalization algorithm, which is capable of significantly reducing the data processing delay and, hence, improving both the processing latency and the attainable throughput at the receiver. The fully parallel equalizer is then combined with the fully parallel turbo decoder for improving the system performance achieved in terms of the bit error ratio. Furthermore, we propose a novel odd-even interleaver design for employment between the fully parallel equalizer and the fully parallel turbo decoder in order to reduce complexity by 50% in fully parallel turbo equalization arrangements, while retaining a comparable performance. Finally, we compare the computational complexity, latency, throughput, hardware resource requirements, and the bit error ratio of the proposed fully parallel scheme to those of a Log-BCJR-based turbo equalizer benchmarker.