Margin Propagation based XOR-SAT Solvers for Decoding of LDPC Codes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929237001240576 |
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| author | Nandi, Ankita Chakrabartty, Shantanu Thakur, Chetan Singh |
| author_facet | Nandi, Ankita Chakrabartty, Shantanu Thakur, Chetan Singh |
| contents | Decoding of Low-Density Parity Check (LDPC) codes can be viewed as a special case of XOR-SAT problems, for which low-computational complexity bit-flipping algorithms have been proposed in the literature. However, a performance gap exists between the bit-flipping LDPC decoding algorithms and the benchmark LDPC decoding algorithms, such as the Sum-Product Algorithm (SPA). In this paper, we propose an XOR-SAT solver using log-sum-exponential functions and demonstrate its advantages for LDPC decoding. This is then approximated using the Margin Propagation formulation to attain a low-complexity LDPC decoder. The proposed algorithm uses soft information to decide the bit-flips that maximize the number of parity check constraints satisfied over an optimization function. The proposed solver can achieve results that are within $0.1$dB of the Sum-Product Algorithm for the same number of code iterations. It is also at least 10x lesser than other Gradient-Descent Bit Flipping decoding algorithms, which are also bit-flipping algorithms based on optimization functions. The approximation using the Margin Propagation formulation does not require any multipliers, resulting in significantly lower computational complexity than other soft-decision Bit-Flipping LDPC decoders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Margin Propagation based XOR-SAT Solvers for Decoding of LDPC Codes Nandi, Ankita Chakrabartty, Shantanu Thakur, Chetan Singh Information Theory Signal Processing Decoding of Low-Density Parity Check (LDPC) codes can be viewed as a special case of XOR-SAT problems, for which low-computational complexity bit-flipping algorithms have been proposed in the literature. However, a performance gap exists between the bit-flipping LDPC decoding algorithms and the benchmark LDPC decoding algorithms, such as the Sum-Product Algorithm (SPA). In this paper, we propose an XOR-SAT solver using log-sum-exponential functions and demonstrate its advantages for LDPC decoding. This is then approximated using the Margin Propagation formulation to attain a low-complexity LDPC decoder. The proposed algorithm uses soft information to decide the bit-flips that maximize the number of parity check constraints satisfied over an optimization function. The proposed solver can achieve results that are within $0.1$dB of the Sum-Product Algorithm for the same number of code iterations. It is also at least 10x lesser than other Gradient-Descent Bit Flipping decoding algorithms, which are also bit-flipping algorithms based on optimization functions. The approximation using the Margin Propagation formulation does not require any multipliers, resulting in significantly lower computational complexity than other soft-decision Bit-Flipping LDPC decoders. |
| title | Margin Propagation based XOR-SAT Solvers for Decoding of LDPC Codes |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2402.04959 |