Puncturing Schemes For Rate-Compatible LDPC Codes

In time-varying fading channel, several pairs of encoder/decoder are always used to adapt different channel conditions. Rate compatible code is one of the most effective ways to realize alternate rates with only one encoder/decoder. Since Li and Narayanan applied the rate compatible idea into LDPC code, the construction of rate compatible LDPC codes has became one focus in the field. In this thesis, we proposed three puncturing schemes for rate compatible LDPC codes based on some new cost functions.Firstly, it is proved that the punctured nodes that can be recovered early in the decoding process is more reliable than those who be recovered lately. So the proposed puncturing scheme tries to maximize the number of nodes which can be recovered in the first iteration. In the beginning of the selecting process, once one node is punctured, the variable nodes that connect the punctured node via the same check node will not be the candidates for puncturing. The rule ensures each check node connects only one punctured node. In order to concentrate the punctured, check nodes that connected with maximum number of punctured nodes will be firstly chosen, and then the new punctured node will be chosen from the variable nodes which have the maximum number of these check nodes. The simulation results show that the codes constructed by the proposed puncturing scheme have good performance, especially at high rates.Since survived check nodes (SCNs) can recover the punctured nodes, the more SCNs one punctured node connects with, the more reliable it is. Based on the importance of one-step recoverable (1-SR) nodes and SCNs, another puncturing scheme which tries to maximize the number of1-SR nodes and SCNs is introduced. Maximize the number of1-SR nodes at first, and then count the number of SCNs that each candidate variable node connects with and puncture the one who has the least number of SCNs. The. simulation results show that the punctured codes have very good performance in a wide range of code rates.According to the analysis of the decoding process, the check nodes and variable nodes can be classified in terms of their contribution in decoding. At first, the check nodes are grouped based on the number of punctured node that they connected with. Since the check node that connects with only one punctured node can recover that node, it has the highest priority. The check nodes which connect with no punctured nodes have the lowest priority, because they done nothing for the punctured nodes in the first iteration of the decoding process. Then the variable nodes will be classified according to the number of SCNs which they connect with. Simulations results show the punctured codes have very good error performance and fast convergence rate.