Analysis of Performance of Linear Analog Codes

TL;DR

This paper analyzes the mean squared error performance of linear analog codes, deriving bounds and demonstrating that unitary codes can achieve optimal bounds, but nonlinear codes may offer better performance.

Contribution

It introduces bounds for MSE performance of linear analog codes and shows that unitary codes can achieve these bounds, highlighting the potential of nonlinear codes.

Findings

Unitary codes can achieve both ML and LMMSE bounds.

Linear analog codes are less effective compared to nonlinear codes.

Nonlinear codes may provide superior performance for analog coding.

Abstract

In this paper we carefully study the MSE performance of the linear analog codes. We have derived a lower bound of the MSE performance under Likelihood(ML) and Linear Minimal Mean Square Error(LMMSE) decoding criteria respectively. It is proved in this essay that a kind of linear analog codes called \emph {unitary codes} can simultaneously achieve both of these two bounds. At the same time, we compare the obtained linear analog codes' MSE bounds with the performance of some existing nonlinear codes. The results showed that linear analog codes are actually not very satisfying and convinced us that more concerns should be cast onto the nonlinear class in order to find powerful analog codes.