Reliable communication near capacity on nonstandard channels

美国国家科学基金会提案0118670“在非标准信道上接近容量的可靠通信”的摘要。1948年，美国数学家克劳德·香农(1916-2001)发表了他的经典论文《通信的数学理论》，开启了数字时代。在香农论文中的许多开创性观点中，也许最重要的是通道容量的概念。简而言之，通信信道的容量(通常称为香农极限)是在该信道上能够可靠地传输信息的最大可能速率。香农展示了如何计算极限，但没有解释如何实际实现这一极限。然而，自1948年以来，几代通信研究人员朝着建立在香农极限附近运行的实用系统的最终目标稳步前进。1993年5月，克劳德·贝鲁(Claude Berrou)领导的一组法国研究人员引入了“Turbo码”，这是一个历史性的里程碑。Berrou证明了Turbo码在一类重要但受限的信道--高斯信道上达到了接近香农限的性能，这是卫星和深空通信的良好模型。这项研究涉及使用基本的Turbo码思想来扩展可以获得接近香农限的通信的信道范围。要考虑的信道模型包括用于光通信、海量数据存储的信道，以及在蜂窝电话和其他多用户系统中遇到的信道。2.1993年Berrou等人发现了Turbo码，紧随其后的是Gallager的低密度奇偶校验码的发现和改进，以及随后重复累加码的发明，这使纠错码领域发生了革命性的变化，并注入了活力。然而，这种非凡的研究大多局限于相对较小的一组标准信道模型，主要是二进制擦除信道(BEC)、二进制对称信道(BSC)和加性高斯白噪声(AWGN)信道。对于这些信道，香农的问题，即以接近信道容量的速率可靠和实际地通信的问题现在已经得到解决。但香农定理告诉我们，在接近容量的速率下进行可靠通信在任何信道上都是可能的，而不仅仅是BEC、BSC和AWGN。从这个角度来看，香农的问题几乎没有得到解决。然而，人们相信，经过适当的修改，上述“类涡流”码(连同相关的迭代译码算法)可用于解决几乎任何信道上的Shannon问题，因此，本研究的目的是研究二进制类“涡流”码在各种非标准信道模型上的有效性，包括非二进制和非对称信道。

Abstract for NSF Proposal 0118670 "Reliable Communication Near Capacity on Nonstandard Channels." In 1948 the American mathematician Claude Shannon (1916-2001) ushered in the digital age with the publication of his classic paper "A Mathematical Theory of Communication." Of the many seminal ideas in Shannon's paper, perhaps the most important is the notion of channel capacity. In brief, the capacity (often called the Shannon limit) of a communications channel, is the maximum possible rate at which information can be transmitted reliably over the channel. Shannon showed how to calculate the limit but did not explain how it could be achieved practically. Since 1948, however, generations of communications researchers have made steady progress towards the ultimate goal of building practical systems that operate near the Shannon limit. An historic milestone was reached in May of 1993 with the introduction of "turbo codes" by a group of French researchers led by Claude Berrou. Berrou showed that turbo codes attain practically near Shannon-limit performance on an important but restricted class of channels, the Gaussian channels, which are good models for satellite and deep-space communication. This research is concerned with using the underlying turbo code ideas to extend the range of channels for which near Shannon-limit communication can be attained. The channel models to be considered include channels for optical communication, mass storage of data, and the channels encountered in cellular phone and other multi-user systems. 2. The 1993 discovery of turbo codes by Berrou et al., which was closely followed by therediscovery of, and improvement on, Gallager's low-density parity-check codes, and the subsequent invention of repeat-accumulate codes, has revolutionized and energized the field of error-correcting codes. However, most of this extraordinary research has been restricted to a relatively small set of standard channel models, predominantly the binary erasure channel (BEC), the binary symmetric channel (BSC), and the additive white Gaussian noise (AWGN) channel. For these channels, Shannon's Problem, viz., the problem of communicating reliably and practically at rates close to channel capacity, has now been solved. But Shannon's theorem tells us that reliable communication at rates near capacity is possible on any channel, not just the BEC, the BSC, and the AWGN. From this viewpoint, Shannon's problem has barely been scratched. It is believed, however, that the "turbolike'' codes mentioned above (together with the associated iterative decoding algorithms) can be used, after suitable modifications, to solve Shannon's Problem on virtually any channel. Thus the object of this research is to study the effectiveness of binary "turbolike'' codes on a variety of nonstandard channel models, including nonbinary and nonsymmetric channels.