Modulated Sparse Regression Codes

Kuan Hsieh, Ramji Venkataramanan

Abstract: We study a generalization of sparse regression codes (SPARCs) for communication over the complex AWGN channel. In a SPARC, the codebook is defined in terms of a design matrix, and each codeword is a generated by multiplying the design matrix with a sparse message vector. In the standard SPARC construction, information is encoded in the locations of the nonzero entries of the message vector. In this paper we generalize the construction and consider modulated SPARCs, where information is encoded in both the locations and the values of the non-zero entries of the message vector. We focus on the case where the non-zero entries take values from a Phase Shift Keying (PSK) constellation. We propose a computationally efficient Approximate Message Passing (AMP) decoder, and obtain analytical bounds on the state evolution parameters which predict the error performance of the AMP decoder. Using these bounds, we show that PSK-modulated SPARCs are asymptotically capacity achieving for the complex AWGN channel. We also provide numerical simulation results to demonstrate the error performance at finite code lengths. These results show that introducing modulation to the SPARC design can significantly reduce decoding complexity without sacrificing error performance.