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Iterative decoding of graph-based codes and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces sparse regression LDPC codes (SR-LDPC codes) and their decoding. Sparse regression codes (SPARCs) are a class of error correcting codes that build on ideas from compressed sensing and can be decoded using AMP. In certain settings, SPARCs are known to achieve capacity; yet, their performance suffers at finite block lengths. Likewise, low-density parity-check (LDPC) codes can be decoded efficiently using belief propagation and can also be capacity achieving. This article introduces a novel concatenated coding structure that combines an LDPC outer code with a SPARC-inspired inner code. Efficient decoding for such a code can be achieved using AMP with a denoiser that performs belief propagation on the factor graph of the outer LDPC code. The proposed framework exhibits performance improvements over SPARCs and standard LDPC codes for finite block lengths and results in a steep waterfall in error performance, a phenomenon not observed in uncoded SPARCs.
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Polar Codes with Local-Global Decoding
Error correction coding schemes with local-global decoding are motivated by practical data storage applications where a balance must be achieved between low latency read access and high data reliability. As an example, consider a 4KB codeword, consisting of four 1KB subblocks, that supports a local-global decoding architecture. Local decoding can provide reliable, low-latency access to individual 1KB subblocks under good channel conditions, while global decoding can provide a “safety-net” for recovery of the entire 4KB block when local decoding fails under bad channel conditions. Recently, Ram and Cassuto have proposed such local-global decoding architectures for LDPC codes and spatially coupled LDPC codes. In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. The coupling scheme incorporates a systematic outer polar code and a partitioned mapping of the outer codeword to semipolarized bit-channels of the inner polar codes. Error rate simulation results are presented for 2 and 4 subblocks.
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- Award ID(s):
- 2212437
- PAR ID:
- 10415205
- Date Published:
- Journal Name:
- Proceedings of 14th Annual Non-Volatile Memories Workshop
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC), whose respective field size and section sizes are equal. For such codes, an efficient decoding algorithm is proposed based on approximate message passing (AMP) that dynamically shares soft information between inner and outer decoders. This dynamic exchange of information is facilitated by a denoiser that runs belief propagation (BP) on the factor graph of the outer LDPC code within each AMP iteration. It is shown that this BP denoiser falls within the framework of non-separable denoising functions and subsequently, that state evolution holds for the proposed AMP-BP algorithm. Leveraging the rich structure of SR-LDPC codes, this article proposes an efficient low-dimensional approximate state evolution recursion that can be used for efficient hyperparameter tuning, thus paving the way for future work on optimal code design. Finally, numerical simulations demonstrate that SR-LDPC codes outperform contemporary codes over the AWGN channel for parameters of practical interest. SR-LDPC codes are shown to be viable means for obtaining shaping gains over the AWGN channel.more » « less
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
