Implementation and Applications of Practical Codes on Curves

该计划的目标是为某些代数几何代码设计高效的VLSI实现，制造芯片，并确定这些代码将具有竞争力的应用。要考虑的码是厄米特码和其他结构相似的码。这些码的优点在于，对于给定的符号大小，它们比里德-所罗门码更长，因此可以更好地利用大数定律来提供更大的纠错能力。存在用于这些码的许多译码算法，包括由共同PI开发的那些。我们将把这些算法的最佳元素结合到一个显式的计算算法中，该算法非常适合于VLSI实现。其目标是生产一种使用并行处理、规则和简单的结构、简单的逻辑和最少的迭代次数的芯片。我们将使用VHDL语言仿真来验证逻辑设计。我们还将识别适合这些编码的系统，并在适合这些应用的信道模拟中测试解码器的性能。

The objective of this program is to design an efficient VLSI implementation for certain algebraic geometry codes, to fabricate a chip, and to identify applications where these codes would be competitive. The codes to be considered are Hermitian codes and other codes similar in structure. The advantage of these codes is that, for a given symbol size, they are longer than Reed- Solomon codes and can therefore take better advantage of the law of large numbers to give much greater error correction capability. A number of decoding algorithms for these codes exist, including those developed by the co-PIs. We will combine the best elements of these algorithms into an explicit computational algorithm that is well suited to VLSI implementation. The goal is to produce a chip that uses parallel processing, regular and simple structures, simple logic, and a minimal number of iterations. We will verify the logic design using a VHDL simulation. We will also identify systems where these codes would be appropriate and test the performance of the decoder in channel simulations appropriate to those applications.