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Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for All Rates Below Capacity

Publication ,  Journal Article
Reeves, G; Pfister, HD
Published in: IEEE Transactions on Information Theory
January 1, 2023

This paper considers the performance of Reed–Muller (RM) codes transmitted over binary memoryless symmetric (BMS) channels under bitwise maximum-a-posteriori (bit-MAP) decoding. Its main result is that, for a fixed BMS channel, the family of binary RM codes can achieve a vanishing bit-error probability at rates approaching the channel capacity. This partially resolves a long-standing open problem that connects information theory and error-correcting codes. In contrast with the earlier result for the binary erasure channel, the new proof does not rely on hypercontractivity. Instead, it combines a nesting property of RM codes with new information inequalities relating the generalized extrinsic information transfer function and the extrinsic minimum mean-squared error.

Duke Scholars

Published In

IEEE Transactions on Information Theory

DOI

EISSN

1557-9654

ISSN

0018-9448

Publication Date

January 1, 2023

Related Subject Headings

  • Networking & Telecommunications
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Reeves, G., & Pfister, H. D. (2023). Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for All Rates Below Capacity. IEEE Transactions on Information Theory. https://doi.org/10.1109/TIT.2023.3286452
Reeves, G., and H. D. Pfister. “Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for All Rates Below Capacity.” IEEE Transactions on Information Theory, January 1, 2023. https://doi.org/10.1109/TIT.2023.3286452.
Reeves G, Pfister HD. Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for All Rates Below Capacity. IEEE Transactions on Information Theory. 2023 Jan 1;
Reeves, G., and H. D. Pfister. “Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for All Rates Below Capacity.” IEEE Transactions on Information Theory, Jan. 2023. Scopus, doi:10.1109/TIT.2023.3286452.
Reeves G, Pfister HD. Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for All Rates Below Capacity. IEEE Transactions on Information Theory. 2023 Jan 1;

Published In

IEEE Transactions on Information Theory

DOI

EISSN

1557-9654

ISSN

0018-9448

Publication Date

January 1, 2023

Related Subject Headings

  • Networking & Telecommunications
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing