For the additive white Gaussian noise channel with average power constraint, it is shown that sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the capacity. We study the upper bounds on its block error probability with least squares decoding when a dictionary with which we make codewords is drawn from an unbiased Bernoulli distribution. We improve the upper bounds shown by Takeishi et.al. in 2014 with fairly simplified form.
['Yoshinari Takeishi', "Jun'ichi Takeuchi"]
An improved upper bound on block error probability of least squares superposition codes with unbiased Bernoulli dictionary