An MSE-Based Transfer Chart for Analyzing Iterative Decoding Schemes Using a Gaussian Approximation

An alternative to extrinsic information transfer (EXIT) charts called mean-square error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean-square error (MMSE) for the additive white Gaussian noise (AWGN) channel, a relationship between the rate of any code and the area under a plot of MMSE versus signal-to-noise ratio (SNR) is obtained, when the a priori log-likelihood ratio (LLR) is from a binary input Gaussian channel. Using this result, a justification is provided for designing concatenated codes by matching the EXIT curves of the inner and outer decoder, when the LLRs are assumed to be Gaussian which is also the typical assumption used for code design using EXIT charts. Even though the Gaussian assumption is almost never true, the results presented in this paper represent a step toward the analysis of iterative decoding schemes using a single parameter. Finally, for the special case of AWGN channel it is shown that any capacity-achieving code has an EXIT curve that is a step function