Using List Decoding to Improve the Finite-Length Performance of Sparse Regression Codes
arXiv:2011.00224
Abstract
We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the large-system limit. In this paper, we mainly focus on how to use concatenation of SPARCs and cyclic redundancy check (CRC) codes on the encoding side and use list decoding on the decoding side to improve the finite-length performance of the AMP decoder for SPARCs over complex AWGN channels. Simulation results show that such a concatenated coding scheme works much better than SPARCs with the original AMP decoder and results in a steep waterfall-like behavior in the bit-error rate performance curves. Furthermore, we apply our proposed concatenated coding scheme to spatially coupled SPARCs. Besides that, we also introduce a novel class of design matrices, i.e., matrices that describe the encoding process, based on circulant matrices derived from Frank or from Milewski sequences. This class of design matrices has comparable encoding and decoding computational complexity as well as very close performance with the commonly-used class of design matrices based on discrete Fourier transform (DFT) matrices, but gives us more degrees of freedom when designing SPARCs for various applications.
arXiv comment12 pages, 8 figures, revised
References in corpus (10)
- SPARCs for Unsourced Random Access
- Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
- Approximate message-passing decoder and capacity-achieving sparse superposition codes
- Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes
- Lossy Compression via Sparse Linear Regression: Computationally Efficient Encoding and Decoding
- Replica Analysis and Approximate Message Passing Decoder for Superposition Codes
- Techniques for improving the finite length performance of sparse superposition codes
- Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
- The Error Probability of Sparse Superposition Codes with Approximate Message Passing Decoding
- Least Squares Superposition Codes of Moderate Dictionary Size, Reliable at Rates up to Capacity