论文标题
在本地可测试的代码的开发中使用集合理论
Use of Set Shaping theory in the development of locally testable codes
论文作者
论文摘要
在开发可当地测试的代码时，通过在代码字中创建冗余，将信息添加到编码消息中。在本文中，我们提出了一种替代方法，其中在该消息中介绍了冗余，必须在编码之前而不是在代码字中传输。这种方法利用了集合理论，其目标是研究的研究函数f（x）= y，该函数将一组字符串转换为一组相等大小，由较大长度的字符串组成。这样，这种类型的函数将自变量x转换为因变量y，其发射概率由先前发射的变量来调节。因此，如果解码器解码与等于零的条件概率关联的符号，我们会检测到消息中的错误。如果使用的函数f是最小化平均信息内容的功能，则我们开发了可以有效测试的代码。实际上，从压缩方面观察到，较大的字符串长度是通过选择较少的熵选择字符串的事实来补偿的。
In developing locally testable codes, information is added to the coded message by creating redundancy in the codewords. In this article, we propose an alternative method in which redundancy is introduced on the message that must be transmitted before its encoding and not in the codewords. This approach exploits the Set Shaping Theory whose goal is the study the bijection functions f(X)=Y that transform a set of strings into a set of equal size made up of strings of greater length. In this way, this type of function transforms the independent variable x into the dependent variable y whose emission probability is conditioned by the previously emitted variables. Thus, if the decoder decodes a symbol associated with a conditional probability equal to zero, we detect an error in the message. If the function f used is the one that minimizes the average information content, we develop a code that can be tested efficiently. In fact, it is observed, in terms of compression, that the greater length of the strings is compensated by the fact of having chosen the strings with less entropy.
