Spatially Coupled Sparse Regression Codes with Sliding Window AMP Decoding

We analyze the performance of spatially coupled sparse regression codes (SC-SPARCs) over the AWGN channel with a sliding window approximate message passing (AMP) decoder. In an SC-SPARC, the codewords are sparse linear combinations of columns of a Gaussian matrix that has a block-wise band-diagonal structure. In this paper we introduce and motivate the sliding-window AMP decoder for SC-SPARCs, and present the first steps towards a fully rigorous proof that the SC-SPARCs with sliding window AMP decoding are asymptotically capacity-achieving. We also provide numerical simulation results demonstrating the error performance of the sliding window AMP decoder at finite code lengths.

[1]  Andrea Montanari,et al.  The dynamics of message passing on dense graphs, with applications to compressed sensing , 2010, 2010 IEEE International Symposium on Information Theory.

[2]  Ramji Venkataramanan,et al.  Techniques for Improving the Finite Length Performance of Sparse Superposition Codes , 2017, IEEE Transactions on Communications.

[3]  Paul H. Siegel,et al.  Windowed Decoding of Spatially Coupled Codes , 2011, IEEE Transactions on Information Theory.

[4]  Andrew R. Barron,et al.  Fast Sparse Superposition Codes Have Near Exponential Error Probability for $R<{\cal C}$ , 2014, IEEE Transactions on Information Theory.

[5]  Nicolas Macris,et al.  Universal Sparse Superposition Codes With Spatial Coupling and GAMP Decoding , 2017, IEEE Transactions on Information Theory.

[6]  Nicolas Macris,et al.  Proof of threshold saturation for spatially coupled sparse superposition codes , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[7]  Ramji Venkataramanan,et al.  Spatially Coupled Sparse Regression Codes: Design and State Evolution Analysis , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[8]  Andrew R. Barron,et al.  Least squares superposition codes of moderate dictionary size, reliable at rates up to capacity , 2010, 2010 IEEE International Symposium on Information Theory.

[9]  Ramji Venkataramanan,et al.  Capacity-Achieving Sparse Superposition Codes via Approximate Message Passing Decoding , 2015, IEEE Transactions on Information Theory.

[10]  Ramji Venkataramanan,et al.  The Error Probability of Sparse Superposition Codes With Approximate Message Passing Decoding , 2017, IEEE Transactions on Information Theory.

[11]  Florent Krzakala,et al.  Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes , 2013, 1312.1740.

[12]  Florent Krzakala,et al.  Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes , 2015, IEEE Transactions on Information Theory.