Weighted Euclidean superimposed codes for integer compressed sensing

We introduce a new family of codes, termed weighted Euclidean superimposed codes (WESCs). This family generalizes the class of Euclidean superimposed codes, used in multiuser identification systems. WESCs allow for discriminating bounded, integer-valued linear combinations of real-valued codewords, and can therefore also be seen as a specialization of compressed sensing schemes. We present lower and upper bounds on the largest size of a member of the WESCs family, and show how to use classical coding-theoretic and new compressed sensing analytical tools to devise low-complexity decoding algorithms for these codes.