Stochastic Construction of Error Correcting Codes with Application to Digital Communications

如果没有纠错码，现代社会将变得面目全非；移动电话、DVD等存储设备和高速数据通信将不复存在。然而，大多数关于纠错码的理论结果本质上是渐近的，忽略了计算复杂性问题，也就是说，它们不能代表许多现实生活中的情况。通过在统计学和随机优化方面的最新突破，该项目将开发算法，用于设计受现实有限数据长度和计算复杂性约束的优化纠错码。成功的结果将带来增强的数据通信和存储，极大地惠及行业和消费者。

Modern society would be unrecognisable without error correcting codes; mobile telephones, storage devices such as DVD's and high speed data communications simply would not exist. Yet most theoretical results on error correcting codes are asymptotic in nature and ignore computational complexity issues, that is, they are not representative of many real life situations. By building on recent breakthroughs in statistics and stochastic optimisation, this project will develop algorithms for designing optimised error correcting codes subject to realistic finite data length and computational complexity constraints. Successful outcomes will lead to enhanced data communications and storage, greatly benefiting industry and consumers alike.