From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance

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-alpha:alpha is an element of[0;1]}, where C alpha vertical bar(alpha=1) is the original polar code, and C alpha vertical bar(alpha=0) is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of alpha. 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 C-inter 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.

Published in:
2014 Ieee International Symposium On Information Theory (Isit), 131-135
Presented at:
IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, JUN 29-JUL 04, 2014
New York, Ieee

 Record created 2015-04-13, last modified 2018-09-13

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