{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/cyclically-equivariant-neural-decoders-for","title":"Cyclically Equivariant Neural Decoders for Cyclic Codes","arxiv_id":"2105.05540","date":"2021-05-12","proceeding":null,"authors":["Xiangyu Chen","Min Ye"],"abstract":"Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders","url_abs":"https://arxiv.org/abs/2105.05540v1","url_pdf":"https://arxiv.org/pdf/2105.05540v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"cyclically-equivariant-neural-decoders-for","repo_url":"https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2105.05540","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2105.05540"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders","reach":null}],"summary":{"ran_honours":1,"unverified":1},"by_repo_kind":{"official":{"samples":2,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"6fe49c4c33fe022c","entry":"add_list_size","repo":"cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders","repo_kind":"official","path":"app/test_list_decoding.py","file_url":"https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders/blob/HEAD/app/test_list_decoding.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6fe49c4c33fe022c"}},{"code_sha256_prefix":"433e315f19b1d5dc","entry":"cycnet","repo":"cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders","repo_kind":"official","path":"model/cycnet.py","file_url":"https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders/blob/HEAD/model/cycnet.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"433e315f19b1d5dc"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}