Low-Complexity SVD-Based Precoding over Zero-Padded ISI Channels
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×(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(nlog 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.
Related
- Achievability of CSS codes performance limits over Pauli channels under separate ML decoding with bounded graphical complexity
- Private communication via zero-private-capacity quantum channels
- Complexity Rank of AT Algebras of Real Rank Zero
- The exact strong converse exponent for private communication over quantum channels
- Secrecy Outage Analysis over Correlated Composite Generalized-Gamma Fading Channels
BibTeX
@misc{liu2026lowcomplexity,
title = {{Low-Complexity SVD-Based Precoding over Zero-Padded ISI Channels}},
author = {Shuiyin Liu and Amin Sakzad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12784},
eprint = {2610.12784},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12784},
}
RIS
TY - UNPB
TI - Low-Complexity SVD-Based Precoding over Zero-Padded ISI Channels
AU - Shuiyin Liu
AU - Amin Sakzad
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12784
UR - https://arxiv.org/abs/2610.12784
AB - 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×(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(nlog 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.
ER -