We introduce a new family of error correction codes based on sparse superposition called Quasi- Orthogonal} Sparse Superposition Codes (QO-SSC). The core of QO-SSC is a special structure of the SSC projection matrix which is obtained by concatenation of orthogonal submatrices. Concrete examples of QO-SCC constructions based on Zadoff- Chu sequences and Kerdock bent sequences are provided. A low-complexity iterative successive interference cancellation algorithm is proposed for QO-SSC decoding. Performance evaluations show that QO-SSC is an efficient solution for short- packet transmission at low signal-to-noise ratios, as it achieves lower block error rate than conventional coded modulation schemes, e.g., QPSK- modulated polar codes. As a further advantage, QO-SSC features a low PAPR when transmitted using OFDM waveforms.