Studies On Decoding And Application Of Low-Density Parity-Check Codes

When they are decoded by sum-product algorithm iteratively, Low-Density Parity-Check codes have good performance to near Shannon limit. LDPC codes can be defined in GF (2) and GF (q) (q>2). We make extensive research on the principles, decoding algorithms and application of Binary LDPC codes and Q-ary LDPC. Main efforts include:1 Based on decoding performance, complexity and latency of finite-geometry low-density parity-check (FG-LDPC) codes, an efficient decoding algorithm was proposed. The new algorithm is a hybrid bit-flipping (BF)/majority-logic (MLG) decoding scheme. In BF decoding, an efficient method was explored to measure the reliability of the checks. At the completion of a small number of iterations, the output from BF decoding is decoded by MLG decoding. In the hybrid algorithm, there are no float operations. Simulation results show the efficiency of the hybrid algorithm.2 To improve the performance of the Belief Propagation (BP) decoding for short and middle length Low-Density Parity-Check (LDPC) codes, we propose a modified BP decoding based on the correction of channel information. This decoding is multi-stage iterative decoder. The key elements of the proposed algorithm are the symbol selection and the correction process of channel information. The selection of symbol is based on the changes of the sign for the variable node message. At each stage the channel message on a select variable node are replaced by both positive and negative saturated messages respectively. After iterative decoding, the final corrected message on the select variable node is decided based on the sum of the absolute values of LLR on all the variable nodes. Simulation results show that the proposed algorithm can achieve better error performance.3 Q-LDPC(q-ary Low-density parity-check) codes has better performance than that of Binary-LDPC (B-LDPC) at the short and medium block length, but the decoder of Q-LDPC has more complexity. For Q-LDPC a new stop criterion is proposed. By analyzing the changing of the maximum posteriori probability of the variable node, the criterion decides whether the iteration of the decoder should be stopped. The simulation results show that the stop criterion could reduce the computation complexity of the Q-LDPC decoder with negligible performance loss.4 For the short and middle length Q-LDPC codes, there are some cycles in the parity-check matrix. So the BER (Bit Error rate) and BLER (Block Error Rate) performances are affected by cycles largely. In each iteration, the elements in GF(q) which has the maximum posteriori probability on some variable nodes oscillate owing to cycles. In this paper, to reduce effects of oscillating on decoding, for oscillating variable nodes, the previous posteriori probabilities is added to the current posteriori probabilities. From the computer simulation, the modified decoding algorithm can achieve better BER and BLER for short and middle length Q-LDPC codes.5 Space-time block codes (STBC) is the attractive techniques for high bit-rate and high capacity transmission. For more coding gains, a concatenation schemes of Q-LDPC and STBC is discussed and a method to provide soft metric for each symbol and the related decoding are discussed. Simulations show that this system achieves better error rate performance than binary LDPC-STBC both on AWGN channel and flat Rayleigh fading channel.