A New Burst and Random Error Correcting Code: Non-Binary Projection Coding

本项目由美国国家科学基金会（NSF）小企业创新研究（SBIR）项目资助，该项目旨在为小企业，特别是小型高科技公司提供参与NSF研究的机会。SBIR项目的第一阶段是筛选有前途的提案，并确定公司是否可以进行高质量的研究。第二阶段为主要研究项目。第三阶段是将nsf资助的研究转化为商业应用和技术创新，由后续的私人风险资本或其他非联邦融资支持。本项目为一期项目，主要研究一种基于多数逻辑编码扩展的纠错编码技术。代码具有代数结构，允许在基本代码中以自然方式使用循环编码的混合代码设计。所得到的混合码在保留简单迭代方案的同时，增加了随机纠错能力，每次迭代的错误数量都显著减少。本研究将二进制投影码理论扩展到非二进制元素（符号），并研究这些非二进制投影码的性能。二进制和非二进制投影码的擦除解码也将被研究。一个成功的努力可能导致一个相对便宜的编解码器，能够在高码率和非常高的比特率下有效地运行。许多商业和政府应用存在，包括宽带ISDN，分组数据交换和卫星和流星突发传输系统。

This project is funded under the National Science Foundation's (NSF) Small Business Innovation Research (SBIR) program, which is designed to provide an opportunity for small business, particularly the small high technology firm, to participate in NSF research. Phase I of the SBIR program serves as a filter to select promising proposals and determine if the firm can do high quality research. Phase II is the principal research project. Phase III is the conversion of the NSF-funded research into commercial applications and technological innovation supported by follow-on private venture capital or other non-federal financing. This is a Phase I project to conduct research in a new error correction coding technique based on an extension of majority logic coding. The code has an algebraic structure that permits a hybrid code design that employs cyclic coding in a natural fashion withn the basic code. The resulting hybrid code has increased random error correction capability while retaining the simple iterative scheme, wherin the number of errors is reduced significantly with each iteration. The research will extend binary projection code theory to non-binary elements (symbols) and investigate the performance of these non-binary projection codes. Erasure decoding of both binary and nonbinary projection codes will also be investigated. A successful effort could lead to a relatively inexpensive codec capable of efficient operation at high code rates and very high bit rates. Numerous commercial and government applications exist, including broadband ISDN, packet data switching and satellite and meteor burst transmission systems.