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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05740 |
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Table of Contents:
- We see that convolutional coding/Viterbi decoding has the structure of the Kalman filter (or the linear minimum variance filter). First, we calculate the covariance matrix of the innovation (i.e., the soft-decision input to the main decoder in a Scarce-State-Transition (SST) Viterbi decoder). Then a covariance matrix corresponding to that of the one-step prediction error in the Kalman filter is obtained. Furthermore, from that matrix, a covariance matrix corresponding to that of the filtering error in the Kalman filter is derived using the formula in the Kalman filter. As a result, the average mutual information per branch for Viterbi decoding of convolutional codes is given using these covariance matrices. Also, the trace of the latter matrix represents the linear minimum mean-square error (LMMSE). We show that an approximate value of the average mutual information is sandwiched between half the SNR times the average filtering and one-step prediction LMMSEs. In the case of QLI codes, from the covariance matrix of the soft-decision input to the main decoder, we can get a matrix. We show that the trace of this matrix has some connection with the linear smoothing error.