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Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes

Published in ISIT 2021, 2021

Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM codes. One of its main drawbacks, however, is the large amount of computations needed. In this paper, we devise a new algorithm to lower the computational budget while keeping a performance close to that of the RPA decoder. The proposed approach consists of multiple sparse RPAs that are generated by performing only a selection of projections in each sparsified decoder. In the end, a cyclic redundancy check (CRC) is used to decide between output codewords. Simulation results show that our proposed approach reduces the RPA decoder’s computations up to 80% with negligible performance loss.

Recommended citation: D. Fathollahi, N. Farsad, S. A. Hashemi and M. Mondelli, "Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes," 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 1082-1087, doi: 10.1109/ISIT45174.2021.9517887

Polar Coded Computing: The Role of the Scaling Exponent

Published in ISIT 2022, 2022

We consider the problem of coded distributed computing using polar codes. The average execution time of a coded computing system is related to the error probability for transmission over the binary erasure channel in recent work by Soleymani, Jamali and Mahdavifar, where the performance of binary linear codes is investigated. In this paper, we focus on polar codes and unveil a connection between the average execution time and the scaling exponent μ of the family of codes. In the finite-length characterization of polar codes, the scaling exponent is a key object capturing the speed of convergence to capacity. In particular, we show that (i) the gap between the normalized average execution time of polar codes and that of optimal MDS codes is O(n–1/μ), and (ii) this upper bound can be improved to roughly O(n–1/2) by considering polar codes with large kernels. We conjecture that these bounds could be improved to O(n–2/μ) and O(n–1), respectively, and provide a heuristic argument as well as numerical evidence supporting this view.

Recommended citation: D. Fathollahi and M. Mondelli, "Polar Coded Computing: The Role of the Scaling Exponent," 2022 IEEE International Symposium on Information Theory (ISIT), 2022, pp. 2154-2159, doi: 10.1109/ISIT50566.2022.9834712