无速率限制的并行随机输入输出码的构造
Construction of Unrestricted Rate Parallel Random Input Output Code
摘要：
提出了一种两页无码率限制PRIO码的编码方案，即每一页可以有不同的码率。在第二页中，每个消息的代码由代码长度为n的两个互补码字组成。总共有2n-1个不相交的码，以保证2n-1个消息的唯一可解码性。在第一页中，每个消息的代码由所有权重u向量组成，其非零元素被限制在（2u-1）个相同位置，其中非负整数u小于或等于代码长度的一半。在第一页中寻找不相交的代码等价于构造等重码，并且不相交代码的数目是等重码中码字的已知数目。我们的编码方案是构造性的，码长是任意的，所设计的码的和速率比以前的工作都要高。
英文摘要：
A coding scheme for two-page unrestricted-rate PRIO code that each page may have different code rates is proposed. In the second page, the code for each messages consists of two complementary codewords with code length n. There are a total of 2n-1 codes which are disjoint to guarantees uniquely decodable for 2n-1 messages. In the first page, the code for each message consists of all weight-u vectors with their non-zero elements restricted to (2u-1) same positions, where non-negative integer u is less than or equal to half of code length. Finding codes to be disjoint in first page is equivalent to construction of constant-weight codes, and the numbers of disjoint codes are the best-known numbers of codewords in constant-weight codes. Our coding scheme is constructive, and the code length is arbitrary.The sum rates of our proposed codes are higher than those of previous work.
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