How do people with arrythmia manage the problem that most bycicle heart rate monitor devices cannot measure accurately their heart rate?
I can't speak to the specifics of arrythmia, but I will challenge the presumption a HR monitor is needed at all. Its entirely possible to train well without gadgets. If you feel the need for a gadget, a power meter would give a majority of cyclists the same advantages, if no more, as a heart rate monitor.
At the elite level, some people now believe that power meter and speed/distance (for runners) supersede the need for heart rate monitors altogether, and many more are less extreme, believing that heart rate is still a useful tool to complement power meters, but not as important as power meters. Combining the two devices does give better results, but requires an awful lot of skill to analyze and understand the results and translate the information into better training outcomes. Much more skill than most individuals have, or want to be bothered with. This area is the domain of professional sports scientists and coaches and elite athletes where seconds over hours makes a difference.