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

9304763里莫尔迪我们正在接近个人通信时代，这需要一种基础设施，能够从地球表面(及以上)的任何一点提供对全球网络的不受限制的访问。此场景的实现需要通过无线网络进行高效通信。无线网络的一个主要组件是高斯多路访问信道。拟议研究的目的是扩展主要研究者的最新结果，从而产生一种为该信道构造代码的新方法。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，并研究了该信道的多址编码。与某个有限群G相关的G加法器通道的输入是G的元素，输出是输入的和(除以G)。首先，假设G是有限域F的加性群，证明了这种G加法器信道的多址接入码可以在类似于差错控制码的代数理论的框架下被研究和构造。给出了利用最大距离可分码构造具有理想性能的多址接入码的两个简单步骤。G加法器通道不是自然而然出现的。它可以通过根据G中的算法添加信息符号的“智能”节点在局域网上创建。研究或G加法器通道的更强动机来自第二步。步骤2：已经证明，可以将高斯多址信道分解成多个独立的G加法器信道，只要每个这样的信道然后被用来在步骤1中考虑的G上传输多址码字。分解是通过T个“调制器”(每个通道输入节点一个)和一个“解调器”获得的。调制器输出是用于高斯信道的格型信号空间码字。*与扩频(通常的做法)相比，上述步骤1和2产生的代码具有以下优势：(L)它们的设计考虑到了干扰和噪声是两个截然不同的问题，需要不同的解决方案。特别是，活跃用户不会对其他用户的噪声水平造成影响；(2)解码简单且代数；(3)没有带宽扩展。在处理将信道分配给忙碌的用户的问题的同时，在某种意义上。这些代码允许传输与通过时分多址(或频分多址)可能相同的信息量。(4)它们支持每维几个比特的传输，这对于被设计为在带宽受限环境中操作的代码来说是一个重要属性。(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)带限高斯信道的信号空间码的设计。(6)它们具有在最近提出的具有多个接收能力的随机接入协议中假定的码所需的属性。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.