Near-Optimum Soft Decision Decoding of Non-Binary Linear Codes

非二进制线性码的近最优软判决译码

• 批准号: 0515154
• 负责人: Aleksandar Kavcic
• 金额: --
• 依托单位: University of Hawaii
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-15 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0515154&HistoricalAwards=false
• 关键词: Near; Optimum; Soft; Decision; Decoding

Over the past decade, iterative decoding methods have received a great deal of interest due to the astonishing error performances achieved first by turbo codes, and more recently by low-density parity check (LDPC)codes. The importance of these methods can be best realized by the fast integration of turbo codes in several standards and last year, a binary LDPC code was first selected as a standard. Although this last decisionclearly indicates maturity, several issues remain problematic in the implementation of LDPC codes, especially for moderate lengths, which are required in many communications systems. In fact for these lengths, non binary LDPC codes outperform their binary counterparts, but iterative decoding of non binary LDPC codes does not scale well with the size of the finite field used. Furthermore, most standards still contain error control coding schemes based on Reed-Solomon (RS) codes. Although these codes are very powerful and have been used for decades, there still exists a large gap between the best achievable performance and that achieved in commercial products. This research activities address problems related to both classes of non binary codes and can therefore be divided into two major areas: (1) Near-optimum decoding of Reed-Solomon codes; and (2) Reduced complexity decoding of non binary LDPC codes.Reliability based decoding of RS codes using their binary image has been shown to provide promising results at error rates that can be simulated. However several approaches (especially those based on iterativetechniques) RS codes since they are often designed for very low error rates. This research investigates the development of a new reliability based decoding technique which outperforms all previously proposed onesfor RS codes over GF(256). A tight performance analysis of this new approach for any SNR value is also possible. LDPC codes designed over GF(q) and decoded with the belief propagation (BP) algorithm have beenshown to perform better as q increases, but at the expense of an O(q log(q)) increase in complexity. Furthermore the BP algorithm is often too complex for fast VLSI implementations. For q=2, very efficient reduced complexity versions of the BP algorithm have been proposed with negligible performance degradation. However as q increases, the complexity of these approaches increases in O(q^2) and the performance gap with BP also increases with q. The research involves the development of new reducedcomplexity versions of the BP algorithm over GF(q) which keep all advantages obtained for q=2, but with much lower complexity than existing algorithms.

在过去的十年中，迭代译码方法由于首先由Turbo码和最近由低密度奇偶校验码(LDPC)获得的惊人的差错性能而受到极大的关注。这些方法的重要性可以通过Turbo码在几个标准中的快速集成来最好地实现，去年，二进制LDPC码首次被选为标准。虽然最后这一决定清楚地表明了LDPC码的成熟性，但在LDPC码的实施中仍然存在一些问题，特别是对于许多通信系统所要求的中等长度的LDPC码。事实上，对于这些长度，非二进制LDPC码的性能优于它们的二进制对应码，但非二进制LDPC码的迭代译码不能很好地随所使用的有限域的大小而扩展。此外，大多数标准仍然包含基于里德-所罗门(RS)码的差错控制编码方案。虽然这些编码非常强大，并且已经使用了几十年，但在可达到的最佳性能与商业产品中实现的性能之间仍存在很大差距。这项研究解决了与这两类非二进制码相关的问题，因此可以分为两个主要领域：(1)Reed-Solomon码的近最佳译码；(2)非二进制LDPC码的低复杂度译码。基于可靠性的RS码译码利用其二进制图像已经被证明在可以模拟的误码率下提供了有希望的结果。然而，几种方法(尤其是基于迭代技术的方法)RS码，因为它们通常被设计用于非常低的误码率。本研究探讨了一种新的基于可靠性的译码技术的发展，该译码技术的性能优于所有已提出的基于GF(256)上的RS码的译码技术。对于任何SNR值，这种新方法的严格性能分析也是可能的。基于GF(Q)的LDPC码的译码性能随着q的增加而提高，但复杂度却增加了O(q log(Q))。此外，BP算法对于快速VLSI实现而言通常过于复杂。对于Q=2，已经提出了非常有效的降低复杂性的BP算法版本，而性能降级可以忽略不计。然而，随着Q的增加，这些方法的复杂度在O(Q^2)内增大，与BP算法的性能差距也随着Q的增大而增大。研究内容涉及在GF(Q)上开发新的降低复杂度的BP算法，它保持了Q=2时的所有优点，但比现有算法的复杂度低得多。