--- _id: '6739' abstract: - lang: eng text: 'We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smaller error probability than polar codes under MAP decoding. This motivates us to introduce a family of codes that “interpolates” between RM and polar codes, call this family C inter = {C α : α ∈ [0, 1j}, where C α|α=1 is the original polar code, and C α|α=0 is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of α. MAP decoding has in general exponential complexity, but empirically the performance of polar codes at finite block lengths is boosted by moving along the family Cinter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder. We demonstrate the performance gain via numerical simulations for transmission over the erasure channel as well as the Gaussian channel.' author: - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Hamed full_name: Hassani, Hamed last_name: Hassani - first_name: Rudiger full_name: Urbanke, Rudiger last_name: Urbanke citation: ama: 'Mondelli M, Hassani H, Urbanke R. From polar to Reed-Muller codes: A technique to improve the finite-length performance. IEEE Transactions on Communications. 2014;62(9):3084-3091. doi:10.1109/tcomm.2014.2345069' apa: 'Mondelli, M., Hassani, H., & Urbanke, R. (2014). From polar to Reed-Muller codes: A technique to improve the finite-length performance. IEEE Transactions on Communications. IEEE. https://doi.org/10.1109/tcomm.2014.2345069' chicago: 'Mondelli, Marco, Hamed Hassani, and Rudiger Urbanke. “From Polar to Reed-Muller Codes: A Technique to Improve the Finite-Length Performance.” IEEE Transactions on Communications. IEEE, 2014. https://doi.org/10.1109/tcomm.2014.2345069.' ieee: 'M. Mondelli, H. Hassani, and R. Urbanke, “From polar to Reed-Muller codes: A technique to improve the finite-length performance,” IEEE Transactions on Communications, vol. 62, no. 9. IEEE, pp. 3084–3091, 2014.' ista: 'Mondelli M, Hassani H, Urbanke R. 2014. From polar to Reed-Muller codes: A technique to improve the finite-length performance. IEEE Transactions on Communications. 62(9), 3084–3091.' mla: 'Mondelli, Marco, et al. “From Polar to Reed-Muller Codes: A Technique to Improve the Finite-Length Performance.” IEEE Transactions on Communications, vol. 62, no. 9, IEEE, 2014, pp. 3084–91, doi:10.1109/tcomm.2014.2345069.' short: M. Mondelli, H. Hassani, R. Urbanke, IEEE Transactions on Communications 62 (2014) 3084–3091. date_created: 2019-07-31T07:20:21Z date_published: 2014-09-01T00:00:00Z date_updated: 2021-01-12T08:08:46Z day: '01' doi: 10.1109/tcomm.2014.2345069 extern: '1' external_id: arxiv: - '1401.3127' intvolume: ' 62' issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1401.3127 month: '09' oa: 1 oa_version: Preprint page: 3084-3091 publication: IEEE Transactions on Communications publication_identifier: issn: - 0090-6778 publication_status: published publisher: IEEE quality_controlled: '1' status: public title: 'From polar to Reed-Muller codes: A technique to improve the finite-length performance' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 62 year: '2014' ...