Woodpecker

I live in northern New Hampshire and have quite a large and varied woodpecker population in my wooded backyard. Recently, I spotted what I thought was a hairy woodpecker at my bird block. However, instead of just a small red patch at the nape of the neck, this bird has an entire red cap. Otherwise, it looks like a hairy woodpecker. It was about 10-11 inches long, white back, white outer tail feathers, black wings with spots/strips on wings-- not a ladder back design. Had a sharp, loud pip-pip squawk. Who is this guy?? He is not shy!!