Method and apparatus for decomposing received symbol signal modulated with bit reflected gray code in bit information

An apparatus for decomposing a received symbol signal into bit information for iterative decoding, the apparatus comprising:

• a positive integer converter configured to calculate a positive integer of the received symbol signal;
• a sign determinator configured to determine a sign of the received symbol signal;
• and
• an arithmetic unit configured to convert the received symbol signal into information per bit in parallel using a value of the received symbol signal based on the positive integer and the determined sign, a value that is indicative of a bit arrangement in the received symbol signal, a difference from an absolute value of the received symbol signal, and a coordinate shifting value of at least one bit group constituting the received symbol signal.

A receiving system configured to perform bitwise decomposition, the receiving system comprising:

• a soft bit metric generator configured to convert a demodulated M-ary (array) channel symbol signal into information per bit for iterative decoding using m bits, wherein m=log2 M, the soft bit metric generator comprising:
• a positive integer converter configured to calculate a positive integer;
• a positive integer converter configured to calculate a positive integer of the received symbol signal;
• a sign determinator configured to determine a sign of the received symbol signal;
• and
• an arithmetic unit configured to convert the received symbol signal into information per bit using a value of the received symbol signal based on the positive integer and the determined sign, a value that is indicative of a bit arrangement in the received symbol signal, and a coordinate shifting value of at least one bit group constituting the received symbol signal.