Reserch On Two Improved Decoding Algorithms Of Polar Codes

As a new method of channel coding based on channel polarization phenomenon, polar codes were proposed by E.Arikan in 2009. Because of their ability to achieve Shannon capacity with low encoding and decoding complexities, polar codes have become one of the highly anticipated research focus in the channel coding field after they were proposed. At present, polar codes have been widely used in source coding, wiretap channel coding, joint source-channel coding, etc, and they have a good application prospect.In the practical application of polar codes, the decoding algorithm is particularly important. Generally, polar codes adopt Successive-Cancelation(SC) or Belief propagation(BP) decoding algorithm. However, due to the serial processing nature, SC algorithm has a high decoding latency and low throughput. As a fully parallel decoding algorithm, BP algorithm not only has advantages with respect to the above shortcomings but also provides better bite error rate(BER) performance for long polar codes. However, in the decoding process BP algorithm needs multiple iterations, as a result, a large number of calculations and high complexity are needed. In practical application, it still needs further improvement.Therefore, this thesis first proposes an improved BP decoding algorithm with an early termination strategy. By observing the hard decision values of T consecutive iterations of an information bit, where T is a value chosen by simulation, we determine whether the information bit has reached convergence. Once all the information bits satisfy the convergence condition, we terminate the iteration process. Simulation results show that, for different code lengths of polar codes, this improved algorithm not only obtain almost the same decoding performance as the original BP algorithm, but also efficiently reduce the number of iterations in the process of decoding, thus reduce the decoding complexity.In addition, due to the complexity in hardware implementation of the BP decoding algorithm, it is usually approximated by min sum algorithm(MSA). However it will result in a performance degradation phenomenon because of the approximate. So we propose two improved MSA for polar codes, namely normalized min sum algorithm(NMSA) with a normalization factor and offset min sum algorithm(OMSA) with a offset factor, respectively, where the values of the two factors can be obtained by Monte Carlo simulation.For the NMSA, simulation results show that its performance is very close to that of the original BP decoding algorithms in low SNR range, but there is a certain gap between the two decoding algorithms in moderate-to-high SNR range. While the improved algorithm has a better performance than the original MSA in the whole SNR range, which suggests a certain effectiveness. Furthermore, it can be seen from the simulation results that the improved algorithm is more suitable for moderate and low SNR range. Besides, compared with the original MSA, the OMSA also has a great improvement of decoding performance, and it even can achieve the same performance as BP algorithm within low and moderate-to-high SNR region, unfortunately it shows performance loss again at 4d B. It is obvious that, compared with the NMSA,the OMSA can show a better performance in moderate-to-high SNR range, but it has a much higher computational complexity and a slower decoding process.