We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to 0.29 dB and 0.31 dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.

中文翻译：

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类产品代码的二进制消息传递解码

我们提出了一种新的二进制消息传递解码算法，用于基于分量代码的有界距离解码（BDD）的类产品代码。该算法被称为具有缩放可靠性的迭代 BDD (iBDD-SR)，它利用了信道可靠性，因此本质上是软的。然而，组件解码器交换的消息是二进制（硬）消息，这显着减少了解码器数据流。交换的二进制消息是通过将信道可靠性与 BDD 解码器输出可靠性相结合而获得的，由应用于 BDD 决策的缩放因子正确传达。我们对广义低密度奇偶校验 (GLDPC) 代码集成和空间耦合 GLDPC 代码集成进行密度演化分析，从中分别得出 iBDD-SR 的乘积和阶梯码的缩放因子，可以获得。对于白色加性高斯噪声通道，与具有相同解码器数据流的传统迭代 BDD (iBDD) 相比，我们展示了乘积和阶梯码的性能增益高达 0.29 dB 和 0.31 dB。此外，我们表明 iBDD-SR 接近理想 iBDD 的性能，可以防止错误纠正。