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Register a new userPerformance Analysis of Raptor Codes under Maximum-Likelihood (ML) Decoding
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Added by
Peng Wang
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor codes, particularly under maximum-likelihood (ML) decoding, which provides an optimal benchmark on the system performance for the other decoding schemes to compare against. For the first time, this paper provides an upper bound and a lower bound, on the packet error performance of Raptor codes under ML decoding, which is measured by the probability that all source packets can be successfully decoded by a receiver with a given number of successfully received coded packets. Simulations are conducted to validate the accuracy of the analysis. More specifically, Raptor codes with different degree distribution and pre-coders, are evaluated using the derived bounds with high accuracy.
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A complexity-adaptive tree search algorithm is proposed for $boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive cancellation (SC) decoding for practical error rates when applied to polar codes and short Reed-Muller (RM) codes, e.g., block lengths up to $N=128$. By modifying the algorithm to limit the worst-case complexity, one obtains a near-ML decoder for longer RM codes and their subcodes. Unlike other bit-flip decoders, no outer code is needed to terminate decoding. The algorithm can thus be applied to modified $boldsymbol{G}_N$-coset code constructions with dynamic frozen bits. One advantage over sequential decoders is that there is no need to optimize a separate parameter.
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CA-Polar codes have been selected for all control channel communications in 5G NR, but accurate, computationally feasible decoders are still subject to development. Here we report the performance of a recently proposed class of optimally precise Maximum Likelihood (ML) decoders, GRAND, that can be used with any block-code. As published theoretical results indicate that GRAND is computationally efficient for short-length, high-rate codes and 5G CA-Polar codes are in that class, here we consider GRANDs utility for decoding them. Simulation results indicate that decoding of 5G CA-Polar codes by GRAND, and a simple soft detection variant, is a practical possibility.
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