Core Concepts
The author explores the relationship between mutual information and linear minimum mean-square error in Viterbi decoding using the Kalman filter structure.
Abstract
The content discusses deriving mutual information and LMMSE for Viterbi decoding of convolutional codes using innovations. It relates to the Kalman filter structure, showing a connection between mutual information and estimation errors.
The paper presents a detailed analysis of covariance matrices, innovations, and their implications for decoding processes. The discussion extends to Gaussian signals, non-Gaussian scenarios, and the relationship between mutual information and LMMSE.
Key points include the application of Kalman filter principles to convolutional coding, calculation of covariance matrices for innovations, and insights into mutual information's relation to estimation errors.
The study highlights how innovations can be used effectively in Viterbi decoding processes for better understanding and optimization.
Stats
The trace of this matrix represents the linear minimum mean-square error (LMMSE).
The average mutual information per branch for Viterbi decoding is given using covariance matrices.
In the case of QLI codes, from the covariance matrix of the soft-decision input to the main decoder, we can get a matrix.
The observations are given by zk = sk + wk, where {sk} is a zero-mean finite-variance signal process and {wk} is a zero-mean white noise process.
zk = √ρ xk + wk corresponds to the observation equation in the Kalman filter.
I[xk; zk] is represented using Rj or using Mj and Pj.
If xj are not Gaussian, then I[xk; zk] becomes an inequality.
Let z = {zk} be a received sequence where each component zj is represented as zj = cxj + wj.
Quotes
"The hard-decision input to the main decoder in an SST Viterbi decoder can be regarded as innovation corresponding to input."
"Convolutional coding corresponds to signal process with observations given by zk = √ρ xk + wk."
"The study shows that approximating average mutual information is sandwiched between SNR times filtering LMMSEs."