Soft-decision majority decoding of Reed-Muller codes
We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM (r, m). First, the reliabilities of 2(m) transmitted symbols are recalculated into the reliabilities of 2(m-r) parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to more reliable parity checks. It is proven that for long low-rate codes RM (r, m),our soft-decision algorithm outperforms its conventional hard-decision counterpart by 10 log(10)(pi/2) approximate to 2 dB at any given output error probability. For fixed code rate R and m --> infinity our algorithm increases almost 2(r/2) times the correcting capability of soft-decision bounded distance decoding.
majority decoding reliabilities parity checks gaussian channel