Implementation and Applications of Practical Codes on Curves

这个计划的目的是设计一个有效的VLSI实现某些代数几何代码，制造一个芯片，并确定这些代码的应用将是有竞争力的。 要考虑的代码是厄米特码和其他代码类似的结构。 这些码的优点在于，对于给定的码元大小，它们比里德-所罗门码长，因此可以更好地利用大数定律，以给出更大的纠错能力。 存在用于这些代码的许多解码算法，包括由co-PI开发的那些。 我们将联合收割机这些算法的最佳元素，成为一个明确的计算算法，非常适合于超大规模集成电路实现。 我们的目标是生产一种使用并行处理，规则和简单结构，简单逻辑和最少迭代次数的芯片。 我们将使用VHDL仿真来验证逻辑设计。 我们还将确定这些代码将是适当的系统和测试的解码器在信道模拟适合这些应用程序的性能。

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.