# Improved Adaptive Successive Cancellation List Decoding of Polar Codes
## 3 Improved Segmented CRC-Based Adaptive SCL Algorithm
### Adaptive SCL Decoding Based on Burst Error Bits  
The error bits of the SC decoding algorithm can be divided into two categories. One is burst error caused by channel interference, and the other is error propagation caused by burst error bits. In [22], an SC decoding algorithm which eliminates inter-symbol interference is designed to count the number of burst error bits generated by channel interference. When code length is \(N=1024\) and code rate is \(R=0.5\), Figure 2 illustrates the number of error bits counted for 500,000 data frames for different signal to noise ratio (SNR) by using the experimental method designed in [22; 23].  
Figure 1: Binary tree of SCL (successive cancellation list) decoding.  
Figure 2: The number of error bits for different SNR at \(N=1024\), \(R=0.5\).  
It can be seen that the burst error bits of the SC decoding are mostly within three bits, and the probability of only one burst error bit is the largest. Therefore, if the decoding result does not pass the CRC, there is a great possibility caused by a burst error bit of information. We can select an appropriate information bit \(i_{s}\), which is located in front of all the error bits. When re-decoding, the decoded bits before the \(S\)-th bit are reserved, and the information bits after the \(S\)-th bit are decoded by using the increasing \(L\) decoding algorithm. A schematic diagram of the process is shown in Figure 3.  
In the decoding process, the larger the absolute value of LLR of an information bit is, the more reliable the decision value of the information bit is. Let \(R\) be the set of values LLR of the decoded information bits and frozen bits in SCL, and \(I\) is the set of indexes in \(R\) in the original information sequence. Based on this feature, we can find a suitable value by following these steps:  
Step 1: When the decoding of the segmented CRC fails, we find the \(m\) bits with smaller absolute LLR values in set \(R\) and record the indexes as a set \(I_{e}\).  
Step 2: Let \(S\) be the smallest index in set \(I_{e}\).  
In this paper, the above method is used to dynamically find a position \(S\) in the information sequence, so that all possible burst error bits are located at the right of \(S\) (assuming the decoding order is from left to right), and the SCL decoding is restarted from this bit. It ensures that SCL contains all burst error bits. Compared with the SCAD-SCL and AD-SCL algorithms, the SAD-SCL makes full use of previous decoding results and digs out the available information, which reduces redundant calculation. From the above analysis, the larger the value \(m\) is, the higher the probability of burst error bits contained in the set \(I_{e}\) will be, but the position of \(S\) will be closer to the starting bit of the decoding sequence, which means that this SCL decoding will calculate more nodes. In addition, if the value \(m\) is too small, the burst error bit may be missed in the set \(I_{e}\), which will result in loss of decoding performance. The value \(m\) will be analyzed in detail in Section 4.