arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1810.08086cs.ITmath.IT
收藏

使用伪码字传输信息

Using Pseudocodewords to Transmit Information

Nathan Axvig

AI总结:

本文提出 insphere modulation,将线性规划解码中的非平凡伪码字转化为可可靠传输的信号,从而获得更高频谱效率且误码率相当或更优的非二进制非线性码本。

摘要:

线性规划解码器有时会输出与二进制码字不对应的分数值序列——这类输出被称为非平凡伪码字。Feldman 等人已经证明,恰恰是非平凡伪码字的存在,阻碍了线性规划解码器达到最大似然性能。本文的目的是从积极的角度看待这些非平凡伪码字,将它们转化为码本中有益的补充。具体而言,我们开发了一种称为 insphere modulation(内切球调制)的新型调制方案,能够可靠地传输码字和伪码字。由此产生的非二进制、非线性码本比其所源自的二进制线性码具有更高的频谱效率,并且在某些情况下具有相同或略好的分组误码率。在推导新调制方案的过程中,我们提出了一种能够计算多面锥体内切球的算法——粗略地说,内切球就是包含在该锥体内的最大球体。这一结果本身可能具有独立的数学意义。

英文摘要:

The linear programming decoder will occasionally output fractional-valued sequences that do not correspond to binary codewords - such outputs are termed nontrivial pseudocodewords. Feldman et al. have demonstrated that it is precisely the presence of nontrivial pseudocodewords that prevents the linear programming decoder from attaining maximum-likelihood performance. The purpose of this paper is to cast a positive light onto these nontrivial pseudocodewords by turning them into beneficial additions to our codebooks. Specifically, we develop a new modulation scheme, termed insphere modulation, that is capable of reliably transmitting both codewords and pseudocodewords. The resulting non-binary, non-linear codebooks have higher spectral efficiencies than the binary linear codes from which they are derived and in some cases have the same or slightly better block error rates. In deriving our new modulation scheme we present an algorithm capable of computing the insphere of a polyhedral cone - which loosely speaking is the largest sphere contained within the cone. This result may be of independent mathematical interest.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑