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，这需要一个能够从地球表面上（和上面）的任何一点提供对全球网络的不受限制的访问的基础设施。该场景的实现需要经由无线网络的高效通信。无线网络的一个主要组成部分是高斯多址信道。 拟议的研究的目的是扩展最近的主要研究人员的结果，导致一种新的程序来构建该通道的代码。 以下两个步骤导致了拟议的程序。 第一步，考虑了一种称为G-加法器信道的简单信道模型，并研究了该信道的多址码。 与某个有限群G相关联的G-加法器通道的输入是G的元素，输出是输入的和（在G上）。从一个更熟悉的基础开始，假设G是有限域F的加法群。结果表明，这种G-加法器通道的多址码可以在类似于差错控制码的代数理论的框架中进行研究和构造。给出了利用最大距离可分码构造具有理想性能的多址码的两种简单方法。G加法器通道不会自然产生。它可以通过“智能”节点在局域网上创建，这些节点根据G. 一个更强的动机的研究或G-加法器通道来自第二步。 第二步：它已被证明，它是可能的高斯多址信道分解成若干个独立的G-加法器的通道，提供了每个这样的通道，然后被用来传输多址码字在G考虑在步骤一。通过T个“调制器”（每个通道输入节点一个）和一个“解调器”实现分解。调制器输出是高斯信道的格型信号空间码字。 *** 与扩频（通常的做法）相比，从上述步骤1和2产生的代码具有以下优点：（l）它们的设计考虑到干扰和噪声是需要不同解决方案的两个不同问题。特别地，活跃用户不会对其他用户的噪声水平做出贡献;（2）解码是简单的和代数的;（3）没有带宽扩展。在这个意义上，在处理将信道分配给忙碌用户的问题的同时。所述码允许传输与经由时分多址（或频分多址）可能传输的信息量相同的信息量。 (4)它们支持每维几个比特的传输，这是设计用于在带限环境中操作的代码的重要属性。(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接收能力的随机接入协议中假设的代码所需的属性。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.