Technology is described herein for a generalized low-density parity-check (GLDPC) decoder. A GLDPC decoder comprises an LDPC decoder and a syndrome decoder. The LDPC decoder is configured to generate a codeword for encoded data. The syndrome decoder is configured to decode a syndrome of punctured check nodes based on a linear block code having more than one information bit. The GLDPC decoder is configured to control the LDPC decoder to compute an initial value of the syndrome of the punctured check nodes based on an initial estimate of the codeword from the LDPC decoder. The GLDPC decoder is configured to alternate between controlling the syndrome decoder to correct the syndrome and controlling the LDPC decoder to update the codeword based on the corrected syndrome. The GLDPC decoder is configured to provide a decoded version of the encoded data based on a final estimate of the codeword.