Sparse Regression codes: Recent results and future directions

Sparse Superposition or Sparse Regression codes were recently introduced by Barron and Joseph for communication over the AWGN channel. The code is defined in terms of a design matrix; codewords are linear combinations of subsets of columns of the matrix. These codes achieve the AWGN channel capacity with computationally feasible decoding. We have shown that they also achieve the optimal rate-distortion function for Gaussian sources. Further, the sparse regression codebook has a partitioned structure that facilitates random binning and superposition. In this paper, we review existing results concerning Sparse Regression codes and discuss directions for future research.