Sparse superposition codes: A practical approach

Sparse Superposition Codes are a class of capacity achieving codes for which decoding can be interpreted as a compressive sensing problem. The approximate message passing algorithm, proven to be effective in compressive sensing, has been proposed in different incarnations as a valid decoding approach. However, most literature focuses on infinite code length and asymptotic performance, while the strong reliance on matrix-and vector-wise operations suggests that a hardware-oriented approach might be more efficient. This work analyzes the performance of two decoding algorithms with finite code lengths and fixed point precision: 5-bit codeword symbol quantization is shown to cause performance degradation ≤ 0.15 dB. In-algorithm quantization values are proposed, together with code construction and algorithm approximations that cause negligible performance degradation. After selecting a set of codes as a case study, a decoding complexity estimation is performed, demonstrating that a fully parallel architecture is unfeasible. Suggestions and improvements towards partially-parallel solutions are given.