Probabilistic Decoding of Nonbinary Majority Decodable Codes

Probabilistic decoding of nonbinary majority decodable codes is considered. An optimal decoding rule is formulated and a method of computing the check weight multipliers is described. Upper and lower bounds are derived on the probability of decoding error in arbitrary semicontinuous and discrete output-symmetric channels. As an example, we consider the characteristics of majority-logic decoders in combination with orthogonal signals in a channel with white Gaussian noise.