Forward error correction apparatus and method in a high-speed data transmission system

A forward error correction method for decoding coded bits transmitted over a radio channel after being generated by encoding as many binary bits as the number of rows with low density parity check matrixes having the rows and columns, the method comprising the steps of:

• (a) converting coded bits received over the radio channel into a log likelihood ratio (LLR) value, and setting the converted value as an initial input value of variable nodes;
• (b) delivering messages applied to the variable nodes to check nodes connected to the variable nodes;
• (c) checking a message having a minimum absolute value among the messages delivered from the variable nodes, and determining a sign of the message having the minimum absolute value by calculating the product of signs of other messages except a message of a variable node that is to transmit the checked message;
• (d) receiving, by the variable nodes, messages updated in the check nodes connected to the variable nodes, adding up signs of the received messages and a sign of an initial message, applying a weighting factor of 1 to the sum of messages received from all other check nodes connected to the variable nodes except the check node that is to transmit the checked message when all signs are identical, and when all signs are not identical, applying a weighting factor having a predetermined value smaller than 1 to the sum of messages received from all other check nodes connected to the variable nodes except the check node that is to transmit the checked message and adding the initial input value to the weighted sum;
• (e) updating, by the variable nodes, an LLR by adding up messages received from the check nodes connected to the variable nodes and an initial input LLR;
• and
• (f) hard-deciding the updated LLR values and performing parity check on the hard decision values by using the low density parity code matrixes.