The Improvement Of The Decoding Performance Of The Concatenation Of BCH Codes And Systematic Polar Codes

In the area of the increasingly sophisticated channel coding theory, Erdal Arikan proposed polar codes based on channel polarization in 2009.The performance of Polar codes based on the channel polarization has been proven to achieve the channel capacity of the Shannon limit when the block length N tends to infinity. Meanwhile, due to the highly structured and low complexity of the encoding and decoding process, polar codes have created a new era for channel coding. However, the performance of polar codes with a short block length is rather poor compared to other codes such as LDPC codes, Turbo codes.Firstly, the theory of polar codes are introduced, analyzed finite block length range, especially the reason that error performance is not good enough in the short block length polar codes under polar decoding. Then SC decoding algorithm is a single-pass algorithm for polar codes and is more susceptible to error propagation. We introduced the SCL decoding algorithm reduces the probability of losing the correct symbol in the decoding process compared with the SC decoding algorithm. Meanwhile, systematic polar codes, compared with non-systematic polar codes, can improve the system robustness in terms of the error propagation resistance. In this thesis, we propose to apply the SCL decoding algorithm to systematic polar codes. The error pattern at the output of the non-systematic polar codes decoder is not uniform. The use of the systematic polar codes as the inner code overcomes this non-uniform error distribution by producing a uniform error pattern in this thesis. Finally, since the shortcomings of low error rate of decay in short block length polar codes. We can use other pattern cascading manner according to the inherent characteristics of the inner and outer code decoding. As a result, it can achieve complementary advantages and disadvantages so as to improve decoding performance.For the problem that the decoding the error performance in finite block length field polar codes is not good enough, we adopt a concatenated scheme with a systematic polar code as an inner code and a BCH code as an outer code to improve the decoding performance over the AWGN channel. Moreover, it is necessary to carefully devise an interleaving scheme to map those bits with high error probability to certain bits of the BCH code. This is the process to randomize the burst errors. The interleaving scheme needs to make the number of errors after the de-interleaving process within the error correction capability of the BCH codes. Simulation and analysis show that the proposed concatenated scheme by thesis improves the error performance in finite block length field polar codes decoding, moreover the scheme complexity is increased less, thereby increasing the feasibility of practical application of polar codes.