| Summary: | 碩士 === 國立雲林科技大學 === 電機工程系 === 107 === In November 2016 3GPP agreed to adopt Polar codes for the Enhanced Mobile Broadband (eMBB) control channels for the 5G New Radio (NR) interface. At the same meeting 3GPP agreed to use LDPC for the corresponding data channel. Since codes used in data channel are generally of large block sizes, and codes in control channel are of small sizes, we may say that LDPC code has finally become the coding scheme for large block sizes, and polar code has become the coding scheme for small block sizes.
This thesis mainly discusses the successive cancellation (SC) and belief propagation (BP) decoding rules for polar code. The performance of these decoders will be analyzed and compared with the BP for low-density parity-check (LDPC) decoder.
Theoretically, it has been verified that LDPC code achieves the Shannon limit. Polar codes, when using SC decoding strategy, can make the transmission rate approach the channel capacity. Therefore the Shannon limit can also be achieved. In addition, there exist other decoding strategies, such as BP algorithm, that can furthermore lower down the error rate when block size of polar code gets larger. BP decoder has become a popular choice in polar code systems. Especially when the code block size is large, BP exhibits lower error rate than SC decoders.
Since iterative operations are applied in BP decoding algorithm, we first tried to find out the optimal maximum number of iterations through experiments. Then decoding performance was simulated for various code lengths and rates. Coding gain and amount of calculation were evaluated for each of the mentioned decoding algorithms. Simulation results show that the error performance of LDPC code is better than that of polar code for every choice of block size and code rate. For polar code with smaller code block length, SC decoder performs better than BP. And as the block size increases, BP will improve faster and outperform SC. For example, when code rate is R=0.8 and bit error rate is 10-3, SC is 0.31 dB better than BP if code block size is N = 26. But BP will turn out to be 0.32 dB better than SC when the code block size in increased to 211.
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