Reliable communication near capacity on nonstandard channels

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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.