Entropy rate of hidden markov chains and capacity and coding for input-constrained channels

在许多实际的噪声信道中，为了使信道有效地工作，输入序列被约束。例如，在磁和光记录通道中，输入序列以各种方式受到约束，以确保准确的定时并降低某些类型的错误事件的可能性。输入约束也对数据记录信道和带限通信信道中通常存在的记忆进行建模。对于许多最重要的输入约束信道，没有明确的容量公式，容量定义为信息可以无错误传输的最大速率。我们计划集中在两个主要主题的输入受限信道：1）估计和渐近的输入受限信道的容量和2）建设良好的代码，这样的信道。 对于1），我们将研究隐马尔可夫链的熵率的估计和渐近性，并将其应用于输入受限信道的容量;对于2），我们将重点讨论限制错误传播的编码方案和联合收割机结合输入约束和纠错的编码方案。

In many practical noisy channels, input sequences are constrained in order to enable the channel to operate effectively. For instance, in magnetic and optical recording channels input sequences are constrained in a variety of ways to ensure accurate timing and reduce the likelihood of certain kinds of error events. Input constraints also model memory that is typically present in data recording channels and band-limited communication channels.For many of the most important input-constrained channels, there is no explicit formula known for capacity, which is defined as the maximal rate at which information can be transmitted without error. We plan to focus on two main themes for input-constrained channels: 1) estimates and asymptotics for capacity of input-constrained channels and 2) construction of good codes for such channels.   For 1), we will investigate estimates and asymptotics for entropy rate of Hidden Markov chains, and apply this to capacity of input-constrained channels.For 2), we will focus on coding schemes that limit error propagation and coding schemes that combine input constraints with error correction.