Properties and performance bounds of linear analog block codes

Linear analog block codes have been considered for transmission of discrete-time and continuous-amplitude data. In this paper, the fidelity measure parameter SNR (pSNR) at the receiver is derived for an arbitrary generator matrix P using an additive white Gaussian noise (AWGN) channel. In contrast, it is shown that the performance of linear analog block codes is dependent on the eigenvalues of the matrix PTP and not only on the dimensions of the matrix P. Surprisingly, the quality of the received values is independent of the code rate r, and e.g. a simple identity matrix has the optimal eigenvalues. Furthermore, the theoretical fidelity bound OPTA (Optimum Performance Theoretically Attainable) is used to assess the performance of a transmission system of continuous-amplitude data.