When the sampling rate at the output of a channel carrying coded information varies, the performance of the decoder can be significantly degraded. For example, for simple linear codes, even as the SNR goes to infinity, one cannot successfully decode the input sequence because two or more distinct input sequences can potentially give rise to the same output sequence.
To address this issue, we adopt the following model. An input sequence is first encoded by a linear block code. The output is then passed through a set of linear transformations, which model the uncertainty of the sampling rate. The transformations include, for the simplest case, a family of identity matrices with one column repeated, or more generally, a symbolic dynamics (d,k) pattern.
Our goal is to identify which conditions impose on the linear block code, and in which properties of the family of the transformations no two input sequences result in the non-zero overlapping set of outputs. We also want to determine the most efficient precoding technique which will eliminate the identification problem while keeping the rate of the code as high as possible.