TABLE OF CONTENTS A soft-decision decoder is characterized by the fact that it retains received symbol reliability information supplied by the demodulator. This reliability information is used by the decoder to improve its decisions when deciding which code word was transmitted. Very often the use of soft-decision decoding leads to a gain of at least 2.0 dB with respect to hard-decision decoding. A hard-decision decoder simplifies its operation and subsequent implementation requirements by discarding the received symbol reliability information.
The efficient decoding of LDPC codes relies on the sum product algorithm (SPA) (Moreira and Farrell, 2006). The SPA is a symbol-by-symbol soft-in soft-out iterative decoding algorithm. Iterations are employed on the received symbols to improve the reliability of the decoded symbols, based on the code parity-check matrix H. A stop condition is defined for the iterations. When the stop condition is reached the available symbol reliability values are used to make hard decisions and to output a decoded binary n-tuple. Let v = ( v 1, v 2, ..., v i, ..., v n) denote a code word and let y denote a received n-tuple the coordinates of which are soft values. The SPA is implemented by computing the marginal probabilities P( vi y), for 1 ? i ? n. A detailed description of SPA decoding of LDPC codes is available in MacKay and Neal (1999).
