Analysis And Research Of Polar Codes In Decoding

Channel coding could improve the reliable transmission in communication system.Based on the information theory, perfect coding strategy can enhance the channel gain andachieve the limited capacity. In2007, a coding method named polar codes was proposed byArikan Erdal, on channel polarization. Theoretically, polar codes can achieve the channelcapacity while they have a low complexity for algorithm during encoding and decodingperiods.For polar codes, the foundational and the channel polarized theory is expounded in thispaper. Channel polarization leads to separate bit channels, just as the non-noise and full-noisebit channels. The encoding construction is to transmit the information signals throughnon-noise channels and transmit the freeze information through full-noise channels. It couldachieve the faster speed and the higher reliability.The Belief Propagation (BP) and the Successive Cancellation (SC) proposed by Arikan aretwo common decoders. There are two improvements based on SC algorithm, in terms ofSuccessive Cancellation Stack (SCS) and Successive Cancellation List (SCL). In the one hand,we obtain the same performance between SCS and SCL algorithm through analysis andsimulation. Both of them could reach the performance of maximum likelihood algorithm. Inthe other hand, the SCS decoding complexity is lower than SCL. The space complexity ofSCS decoder is O (DN), which is D times of the SC decoder. Moreover, SCS algorithm islimited by the maximal depth of stack and similar to SC algorithm under the high signal-to-noise ratio condition. The complexity of SCL decoder is O (LN log N). We could find and analyze differences during BP, SC and SCL algorithms through aimage transmission system on polar codes. By the analysis of transmitting a256*256grayscale graphic, we find out the conclusion. As the signal-to-noise ratio is increasing, thesystem performance is getting better under the BAWGN channel. When the signal-to-noiseratio reaches up to3db, the system could obtain high quality recovery. There is a distinctadvantage of SCL algorithm under the condition of high error rate in BEC and BSC throughthe analysis of BER，FER and PSNR.