Build trust with BF? He doesn't trust me.

My bf told me he doesn't trust me. He accuses me of lying and cheating often and I am most definitely not. It's not even close to being on my mind. We've been together for a little over a year so it really hurts that the person I've chosen to open myself up to and be with thinks these things about me.

I send him pics when I'm out sometimes partly because we like sending pics and partly because I know it helps him to feel comfortable that I am where I say. But I don't like that he needs that. Especially because sometimes it's difficult/not possible to send pics like at work sometimes. Sometimes he will randomly ask to Skype. Sometimes it can turn into a big issue if I miss his calls and the reason doesn't make sense to him (my phone does some stupid stuff sometimes while I'm out where he says it rang on his end and I didn't get the call. Or sometimes I put my phone on silent and forget to put the sound back on and miss the calls).

It is stressful because this relationship means a lot to me. I am and have been in it 100% and I feel like I do my part to show him and express that. I am at a loss at how to help us... Please if you have any ideas or tips on how to build trust in this situation or if anyone has been I'm a similar situation I would appreciate feedback. I know some people will say it can't change and that's just how he is but I want to think we can work on it. He says he doesn't want to think of me like that.