A variety of low-density parity-check (LDPC) ensembles have now been observed
to approach capacity with message-passing decoding. However, all of them use
soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of
their component codes. In this paper, we show that one can approach capacity at
high rates using iterative hard-decision decoding (HDD) of generalized product
codes. Specifically, a class of spatially-coupled GLDPC codes with BCH
component codes is considered, and it is observed that, in the high-rate
regime, they can approach capacity under the proposed iterative HDD. These
codes can be seen as generalized product codes and are closely related to
braided block codes. An iterative HDD algorithm is proposed that enables one to
analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on
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