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 P^TP 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.