Low-complexity signal processing boosts communication over intersymbol interference channels
Low-Complexity SVD-Based Precoding over Zero-Padded ISI Channels
Information Theory
Summary
Signals sent over some communication channels can get mixed up with their neighbors, causing errors. The authors propose a clever math-based method to untangle these mixed signals efficiently using a special kind of matrix structure. This method uses fast algorithms to send and receive signals with fewer errors and lower complexity than traditional approaches. Their tests show better performance in simulated scenarios compared to older methods, improving the reliability of data transmission.
What this means in practice
- •For wireless communication engineers: Design transmitters and receivers that handle intersymbol interference efficiently with low complexity and improved error rates using FFT-based SVD precoding and equalization.
- •For fiber optic system designers: Increase data reliability over fiber channels experiencing memory effects by applying low-complexity SVD-based precoding for adaptive power and modulation control.
Authors
Shuiyin Liu, Amin Sakzad
Abstract
We propose a low-complexity SVD-based transceiver for zero-padded memory-$1$ ISI channels. Appending a single zero-padding symbol to an $n$-symbol block yields an $n\times(n-1)$ channel matrix with an \emph{exact symmetric tridiagonal Toeplitz Gram matrix}. This structure provides closed-form singular values and vectors, enabling exact SVD precoding and equalization via FFTs without explicitly forming dense SVD matrices. The resulting implementation has $O(n\log n)$ complexity and incurs only a $1/n$ rate penalty. The resulting parallel scalar subchannels enable joint adaptive PAM and power allocation for SER minimization, followed by exact soft-information computation for LDPC decoding. At comparable code rates near $0.945$, simulations show that our proposed scheme outperforms a conventional TX-FFE/RX-DFE system with hard-decision Reed-Solomon (RS) decoding by approximately $5$ dB at FER $10^{-5}$. At high SNR, it achieves nearly the same FER performance as a SOVA-based receiver with LDPC decoding, while replacing trellis-based detection with fast SVD precoding and exact scalar soft-output computation.