An Interlace Coding System (ICS) involving data compression code, data encryption code and error correcting code is proposed and its error performance on additive white Gaussian noise (AWGN) channel with quadrature phase shift keying (QPSK) is analyzed. The proposed system handles data compression, data encryption and error correcting processes together, i.e. adds error correcting redundancy to the block lists of the dictionary in which compression system constructs to reduce source redundancy. Each block list is encoded by Ziv-Lempel code and Data Encryption Standard (DES). As the catastrophic condition determined by the data compression procedure is not negligible, error correcting redundancy should be added so as to avoid catastrophic condition. We found that the catastrophic condition depends only on the size of the dictionary for our proposed system. Thus, by employing a large dictionary, good error performance can be applied by the proposed system and the catastrophic condition can be avoided.

The optimal coding strategy for signal detection in the correlated gaussian noise is established for the distributed sensors system with essentially zero transmission rate constraint. Specifically, we are able to obtain the same performance as in the situation of no restriction on rate from each sensor terminal to the fusion center. This simple result contrasts with the previous ad hoc studies containing many unnatural assumptions such as the independence of noises contaminating received signal at each sensor. For the design of optimal coder, we can use the classical Levinson-Wiggins-Robinson fast algorithm for block Toeplitz matrix to evaluate the necessary weight vector for the maximum-likelihood detection.