In this paper, a bidirectional Fano algorithm (BFA) is proposed, in which a forward decoder (FD) and a backward decoder (BD) search in the opposite direction in the code tree simultaneously. It is shown that the proposed BFA can achieve more than twice the decoding throughput compared to the conventional unidirectional Fano algorithm (UFA) and there is higher throughput improvement at low signal-to-noise ratio (SNR). This new BFA decoding technique is applied in the parallel convolutional decoding architecture in very high throughput systems, such as the WirelessHD system. Due to the variability in the decoding delays of the parallel codewords, a scheduler is introduced in the parallel Fano decoding architecture which can dynamically allocate the idle decoders to assist with decoding the other parallel codewords in a bidirectional manner. It is shown that the proposed parallel Fano decoding with scheduling can dramatically increase the decoding throughput compared to the parallel Fano decoding without scheduling, and its computational complexity is much lower than that of parallel Viterbi decoding, especially at high SNR. The performance of the parallel Fano decoding with different scheduling schemes is also compared and analyzed in detail in the paper.