From polar to Reed-Muller codes: A technique to improve the finite-length performance

M. Mondelli, H. Hassani, R. Urbanke, IEEE Transactions on Communications 62 (2014) 3084–3091.


Journal Article | Published | English
Author
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Abstract
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.
Publishing Year
Date Published
2014-09-01
Journal Title
IEEE Transactions on Communications
Volume
62
Issue
9
Page
3084-3091
ISSN
IST-REx-ID

Cite this

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
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. https://doi.org/10.1109/tcomm.2014.2345069
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 62, no. 9 (2014): 3084–91. https://doi.org/10.1109/tcomm.2014.2345069.
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, pp. 3084–3091, 2014.
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.
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.

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