Multiple-Access Codes & Random-Access Protocols with Multiple Reception

9304763里莫尔迪我们正在接近个人通信的时代，这需要一种能够从地球表面的任何一点（或以上）不受限制地访问全球网络的基础设施。此场景的实现需要通过无线网络进行有效的通信。无线网络的一个主要组成部分是高斯多址信道。提出的研究目的是扩展首席研究员最近的结果，导致一个新的程序来构建该信道的代码。以下两个步骤导致了拟议的程序。步骤1考虑了一种更简单的信道模型g加法器信道，并对该信道的多址码进行了研究。G加法器通道与某个有限群G相关联，它的输入是G的元素，输出是输入（在G上）的和。从更熟悉的基础开始，假设G是有限域f的加性群。结果表明，可以在类似于误差控制码的代数理论的框架中研究和构造此类G加法器信道的多址码。给出了用最大距离可分离码构造具有理想性质的多址码的两个简单方法。g加法器信道不会自然产生。它可以通过“智能”节点在局域网上创建，这些节点根据g中的算法添加信息符号。研究g加法器通道的更强动机来自第二步。步骤2：已经表明，有可能将高斯多址信道分解为许多独立的G加法器信道，前提是每个这样的信道随后用于在步骤1中考虑的G上传输多址码字。分解通过T个“调制器”（每个通道输入节点一个）和一个“解调器”获得。调制器输出为高斯信道的格型信号空间码字。***与扩频（通常做法）相比，上述步骤1和2产生的代码具有以下优点：(1)它们的设计牢记干扰和噪声是两个不同的问题，需要不同的解决方案。特别是，活跃用户不会影响其他用户的噪音水平；(2)解码简单、代数化；(3)没有带宽扩展。从某种意义上说，在解决为繁忙用户分配频道的问题时。这些代码允许通过时分多址（或频分多址）传输相同数量的信息。(4)它们支持每维数位的传输，这是设计用于在带宽有限的环境中运行的代码的重要属性。(5)它们是强大的编码和整形技术的自然产物，这些技术彻底改变了（单用户）带宽有限的高斯信道的信号空间编码设计。(6)它们具有最近提出的具有多接收能力的随机访问协议中所假定的代码所需的属性。这些协议可以实现任意接近1的吞吐量。

9304763 Rimoldi We are approaching the era of personal communication which requires an infrastructure capable of providing untethered access to a global network from any point on (and above) the surface of the earth. Implementation of this scenario requires efficient communication via a wireless network. One major component of a wireless network is the Gaussian multiple-access channel. The objective of the proposed research is to extend recent results of the principal investigator leading to a novel procedure to construct codes for this channel. The following two steps have led to the proposed procedure. Step 1 A simpler channel model called G-adder channel was considered and multiple-access codes for this channel were studied. The G-adder channel associated to some finite group G has inputs that are elements of G and output that is the sum (over G) of the inputs. To start on a more familiar ground it was assumed that G is the additive group of a finite field F. It was shown that multiple-access codes for such G-adder channels can be studied and constructed in a framework that is akin to the algebraic theory of error control codes. Two simple procedures to construct multiple-access codes with desirable properties via maximum distance separable codes were given. A G-adder channel does not arise naturally. It can be created on a local area network by means of "smart" nodes that add information symbols according to the arithmetic in G. A stronger motivation for the study or G-adder channels came from step two. Step 2: It has been shown that it is possible to decompose the Gaussian multiple-access channel into a number of independent G-adder channels provided that each such channel is then used to transmit multiple-access codewords over G considered in step one. The decomposition is obtained via T "modulators" (one for each channel input node) and a "demodulator." The modulator outputs are lattice-type signal-space codewords for the Gaussian channel. *** Compared to spread spectrum (the common practice) the codes resulting from steps 1 and 2 above have the following advantages: (l) They are designed keeping in mind that interference and noise are two distinct problems that need different solutions. In particular, active users do not contribute to the noise level of other users; (2) Decoding is simple and algebraic; (3) There is no bandwidth expansion. in the sense that while taking care of the problem of assigning the channel to busy users. the codes allow transmission of the same amount of information that would be possible via time-division multiple-access (or frequency-division multiple-access). (4) They support transmission of several bits per dimension which is an important attribute for codes designed to operate in a bandlimited environment. (5) They are natural offspring of the powerful coding and shaping techniques that have revolutionized the design of signal-space codes for the (single-user) bandlimited Gaussian channel. (6) They have the properties that are needed for the codes assumed in recently proposed random-access protocols with multiple reception capability. These protocols can achieve throughputs arbitrarily close to 1.