Invited paper. Partitioned linear block simplex matrix codes for computer memory and real compound channels with memory
J. P. DAILAKIS, D. C. Voukalis · International Journal of Electronics · 1987
A class of partitioned linear block simplex matrix codes is introduced. Linear block codes are studied for improving the reliability of message storage in computer memory with stuck-at defects, noise and errors for real compound channels with memory. An algebraic model of simplex matrix is also presented. Three partitioned classes of linear block codes are introduced to defend the real conditions, combined in one concatenated code for the computer memory and real compound channel with memory. The partitioned linear codes are used in a concatenated mode. Convolutional-TCC, cyclic-CRC, and matrix-MBC codes can be employed as subcodes to construct partitioned linear block simplex matrix codes with specified bounds. Any kind of errors and defects, as we can find in real time conditions, are considered. We also formulate the basic problem of optimal control for the new introduced code system over a finite horizon with which we shall be dealing. The formulation is general but specific enough for a simplex matrix type-B code since state space, control space, and uncertain noise space are in limits and may vary dynamically from one state to the next.