The mission of visual brain-computer interfaces (BCIs) is to enhance information transfer rate (ITR) to reach high speed towards real-life communication. Despite notable progress, noninvasive visual BCIs have encountered a plateau in ITRs, leaving it uncertain whether higher ITRs are achievable. In this study, we investigate the information rate limits of the primary visual channel to explore whether we can and how we should build visual BCI with higher information rate. Using information theory, we estimate a maximum achievable ITR of approximately 63 bits per second (bps) with a uniformly-distributed White Noise (WN) stimulus. Based on this discovery, we propose a broadband WN BCI approach that expands the utilization of stimulus bandwidth, in contrast to the current state-of-the-art visual BCI methods based on steady-state visual evoked potentials (SSVEPs). Through experimental validation, our broadband BCI outperforms the SSVEP BCI by an impressive margin of 7 bps, setting a new record of 50 bps. This achievement demonstrates the possibility of decoding 40 classes of noninvasive neural responses within a short duration of only 0.1 seconds. The information-theoretical framework introduced in this study provides valuable insights applicable to all sensory-evoked BCIs, making a significant step towards the development of next-generation human-machine interaction systems.