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We consider the decoding of LDPC codes over GF(q) with the low-complexitymajority algorithm from [1]. A modification of this algorithm with multiplethresholds is suggested. A lower estimate on the decoding radius realized bythe new algorithm is derived. The estimate is shown to be better than theestimate for a single threshold majority decoder. At the same time thetransition to multiple thresholds does not affect the order of complexity.

On the Multiple Threshold Decoding of LDPC codes over GF(q)