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Soft-decision majority decoding of Reed-Muller codes

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2 Author(s)
Dumer, I. ; Coll. of Eng., California Univ., Riverside, CA, USA ; Krichevskiy, R.

We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM(r,m). First, the reliabilities of 2m transmitted symbols are recalculated into the reliabilities of 2m-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 log10(π/2)≈2 dB at any given output error probability. For fixed code rate R and m→∞, our algorithm increases almost 2r/2 times the correcting capability of soft-decision bounded distance decoding

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 1 )