Four Intuitive Messages for LDPC Codes

Four new messages for decoding of low-density parity-check (LDPC) codes are proposed. An a posteriori probability ratio (APPR) message, an a posteriori probability (APP) message, and an a posteriori probability difference (APPD) message for variable and check nodes are derived for sum-product decoding of LDPC codes. Also, we propose a hybrid APPD-APPR message, which denotes a hybrid message with an APPD variable node message and APPR check node message. All the proposed messages require only addition, subtraction, multiplication, and division operations for decoding of LDPC codes. We show that the hybrid APPD-APPR message-passing has the lowest complexity among the proposed messages.