Performance Estimation And Analysis For BIBD-LDPC Codes

Low-density parity check (LDPC) codes are a class of linear block codes, with SPA algorithm, they provide near Shannon-Limit capacity performance on the binary input additive white Gaussian noise (AWGN) channel. Balanced Incomplete Block Design (BIBD) codes, as a special case of the LDPC codes, have excellent performance. Because it is extremely difficult to analyze the codes, people know little about their structure and characteristic, we just can get the error performance of the code by simulation. But the longer the code length, the greater the cost of time and resources required for the simulation. On the other hand, the existing analysis methods are also unsuitable for the practical code, because it is difficult to fully satisfied prerequisite. Take the above problems of BIBD-LDPC codes into account, this paper propose a semi-analytical method to estimate long BIBD-LDPC codes.Here is the process of the semi-analytical method:first choose one code as the estimation code, we simulate the SNR of the rest code, with the simulation results, we get the relationship between the SNR and the code length by the curve fitting. We can calculate the SNR of the code with specified length from the fitting curve or fitting formula, then analyze estimation results of different fitting types. The semi-analytical method has a prominent feature, it can estimate the performance of the long code though short code, without simulation.Firstly, we study the first-class BIBD-LDPC codes, using shorten BIBD-LDPC codes on the same Galois field for performance estimation and analysis. For example, the parity check matrix of the (2715,2535) BIBD-LDPC codes on GF (181) is composed of15blocks. Choose different number of blocks, we can obtain a number of shorten BIBD-LDPC codes with different code lengths. Research have found that the result of the quadratic polynomial fitting and linear polynomial fitting is better than other polynomial fitting at a BER of10-5, estimation errors are less than5%.Secondly, we extended the research result to BIBD-LDPC codes on different Galois field. Because it is difficult to simulate the long code, so we mainly estimate and analyze the performance of the long code using the performance of short codes. Research can be divided into two part, first use all short codes to estimate long code, estimation results of BIBD codes on different Galois field are similar with the result of shorten BIBD-LDPC codes on the same Galois field. Then use part of the short code to estimate, the results have shown that with an appropriate estimation method, the result of part estimation are close to the result of complete estimation. Even if the bit error rate is changed, for example, when bit error rate is10-6, this method is also effective, the percentage error is no more than2%.Finally, the paper analyzes other factors that impact the performance of BIBD-LDPC codes, such as six-cycle density in parity check matrix, the gap between the signal to noise ratio and Shannon limit. Simulation results have shown that for BIBD-LDPC codes, the bit error rate increased with the code length, it is because the six-cycle density is also increasing, indicating that the six-cycle density is effective for BIBD-LDPC performance estimation.