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Efficient Iterative Techniques for Soft Decision Decoding of Reed-Solomon Codes

机译：Reed-Solomon码软判决解码的有效迭代技术

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Two new iterative soft decision decoding methods for Reed-Solomon (RS) codes are proposed. These methods are based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In the first proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the distribution of reliability values will change and deterministic errors can be avoided. This method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods. The second method is based on information correction in BP decoding. It means that we determine least reliable bits and by changing their channel information, the convergence of the decoder is improved. Compared to the first method, this method needs less BP iterations (less complexity) but its performance is not as good.
机译：提出了两种针对里德-所罗门码的迭代软判决解码方法。这些方法基于位级置信传播（BP）解码。为了使BP解码对于RS码有效，我们使用了扩展的二进制奇偶校验矩阵，与原始的代码二进制奇偶校验矩阵相比，该矩阵具有更低的密度和更少的4周期数。在第一个提出的方法中，我们利用了RS码的循环结构。基于此属性，我们可以将置信度传播算法应用于具有相同二进制奇偶校验矩阵的接收符号的任何循环移位版本。对于接收符号的每个移位版本，可靠性值的分布将改变，并且可以避免确定性错误。与硬判决解码相比，此方法可显着提高RS码的性能。该性能也优于某些流行的软判决解码方法。第二种方法基于BP解码中的信息校正。这意味着我们确定最不可靠的位，并通过更改其通道信息来改善解码器的收敛性。与第一种方法相比，该方法需要较少的BP迭代（较少的复杂性），但是其性能却不如后者。

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