  For the additive white Gaussian noise channel with average power constraint,
sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the
capacity. While the codewords of the original sparse superposition codes are
made with a dictionary matrix drawn from a Gaussian distribution, we consider
the case that it is drawn from a Bernoulli distribution. We show an improved
upper bound on its block error probability with least squares decoding, which
is fairly simplified and tighter bound than our previous result in 2014.
