TY - GEN
T1 - Recursive projection-aggregation decoding of Reed-Muller codes
AU - Ye, Min
AU - Abbe, Emmanuel
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms based on list-decoding algorithms and code concatenation.We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.
AB - We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms based on list-decoding algorithms and code concatenation.We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.
UR - http://www.scopus.com/inward/record.url?scp=85073158195&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85073158195&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2019.8849269
DO - 10.1109/ISIT.2019.8849269
M3 - Conference contribution
AN - SCOPUS:85073158195
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2064
EP - 2068
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -