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IEEE International Symposium on Information Theory (ISIT)

A Score Function for Sequential Decoding of Polar Codes

Peter Trifonov

Published Jun 1, 2018• 56 citations
Publisher

Abstract

A novel score function is proposed for sequential decoding of polar codes. Significant reduction of the average decoding complexity is achieved by biasing the path metrics in the min-sum version of the stack successive cancellation decoding algorithm with its expected value. The proposed approach can be also used for near-ML decoding of short extended BCH codes.

DOI
10.1109/isit.2018.8437559

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Advances in computer science research•Jan 1, 2015•1 citation
A novel score function is proposed for sequential decoding of polar codes. Significant reduction of the average decoding complexity is achieved by biasing the path metrics in the min-sum version of the stack successive cancellation decoding algorithm with its expected value. The proposed approach can be also used for near-ML decoding of short extended BCH codes.
Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting operations without visible degradation in the code’s error-correction performance. In an SCL decoding with an optimum metric function we show that, on average, the correct branch’s bit-metric value must be equal to the bit-channel capacity, and on the other hand, the average bit-metric value of a wrong branch can be at most zero. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. For relatively reliable bit-channels, the bit metric for a wrong branch becomes very large negative number, which enables us to detect and prune such paths. We prove that, for a threshold lower than the bit-channel cutoff rate, the probability of pruning the correct path decreases exponentially by the given threshold. Based on these findings, we presented a pruning technique, and the experimental results demonstrate a substantial decrease in the amount of sorting procedures required for SCL decoding. In the stack algorithm, a similar technique is used to significantly reduce the average number of paths in the stack.
Polar codes represent an emerging correcting codes with power to approach the capacity of a discrete memoryless channel.However, the decoding performance of polar codes with traditional successive cancellation (SC) algorithm cannot match that of the low-density parity-check or Turbo codes.In this paper, a modified successive cancellation stack (MSCS) polar decoder is proposed.Unlike the original SC stack polar (SCS) decoders, we propose a modified path that can significantly reduce latency of SCS decoders.Simulation results in the binary-input additive white Gaussian noise channel show that modified algorithm has the slightly performance as the SCS algorithm.Moreover, the time and space complexity of the MSCS decoder is much lower than that of the SCS and can be very close to that of the SC in the high SNR regime.