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

该项目由美国国家科学基金会(NSF)的小企业创新研究(SBIR)计划资助，该计划旨在为小企业，特别是小型高科技公司提供参与NSF研究的机会。SBIR计划的第一阶段作为一个过滤器，选择有希望的提案，并确定公司是否能够进行高质量的研究。第二阶段是主要的研究项目。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资金支持。这是第一阶段的项目，旨在研究基于多数逻辑编码的扩展的新的纠错编码技术。该代码具有允许混合代码设计的代数结构，该混合代码设计以与基本代码自然的方式采用循环编码。得到的混合码增强了随机纠错能力，同时保留了简单的迭代方案，其中每次迭代的错误数量都显著减少。该研究将二元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。还将研究二进制和非二进制投影码的擦除译码。成功的努力可以导致能够在高码率和非常高的比特率下有效操作的相对便宜的编解码器。存在许多商业和政府应用，包括宽带综合业务数字网、分组数据交换以及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.