In this paper we review existing hard-decision decoding algorithms for product codes along with different post-processing techniques used in conjunction with the iterative decoder for product codes. We improve the decoder by Reddy and Robinson and use it to create a new post-processing technique. The performance of this new post-processing technique is evaluated through simulations, and these suggest that our new post-processing technique outperforms previously known post-processing techniques which are not tailored for specific codes. The cost of using the new post-processing technique is that the algorithm becomes more complex. However, the post-processing is applied very rarely unless the channel is very noisy, and hence the increase in computational complexity is negligible for most choices of parameters. Finally, we propose a new algorithm that combines existing techniques in a way that avoids the error floor with short relatively high rate codes. The algorithm should also avoid the error floor with long high rate codes, but further work is needed to confirm this.

在本文中，我们回顾了现有的产品代码硬决策解码算法，以及与产品代码的迭代解码器结合使用的不同后处理技术。我们通过Reddy和Robinson改进了解码器，并使用它来创建新的后处理技术。通过仿真评估了这种新的后处理技术的性能，这些结果表明，我们的新后处理技术的性能优于之前已知的，并非为特定代码量身定制的后处理技术。使用新的后处理技术的代价是算法变得更加复杂。但是，除非通道非常嘈杂，否则很少进行后处理，因此对于大多数参数选择而言，计算复杂性的增加可以忽略不计。最后，我们提出了一种新算法，该算法结合了现有技术，从而以较短的较高速率码避免了错误底限。该算法还应避免使用高码率长的错误基底，但是需要进一步的工作来确认这一点。