Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition

Fuente: arXiv
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Main Authors: Asano, Joe, Hama, Yuto, Iimori, Hiroki, Pradhan, Chandan, Malomsoky, Szabolcs, Ishikawa, Naoki
Format: Preprint
Published: 2026
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_version_ 1866910004277149696
author Asano, Joe
Hama, Yuto
Iimori, Hiroki
Pradhan, Chandan
Malomsoky, Szabolcs
Ishikawa, Naoki
author_facet Asano, Joe
Hama, Yuto
Iimori, Hiroki
Pradhan, Chandan
Malomsoky, Szabolcs
Ishikawa, Naoki
contents In this paper, we propose a method for designing sparse Grassmannian codes for noncoherent multiple-input multiple-output systems. Conventional pairwise error probability formulations under uncorrelated Rayleigh fading channels fail to account for rank deficiency induced by sparse configurations. We revise these formulations to handle such cases in a unified manner. Furthermore, we derive a closed-form metric that effectively maximizes the noncoherent average mutual information (AMI) at a given signal-to-noise ratio. We focus on the fact that the Schubert cell decomposition of the Grassmann manifold provides a mathematically sparse property, and establish design criteria for sparse noncoherent codes based on our analyses. In numerical results, the proposed sparse noncoherent codes outperform conventional methods in terms of both symbol error rate and AMI, and asymptotically approach the performance of the optimal Grassmannian constellations in the high-signal-to-noise ratio regime. Moreover, they reduce the time and space complexity, which does not scale with the number of transmit antennas.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21009
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition
Asano, Joe
Hama, Yuto
Iimori, Hiroki
Pradhan, Chandan
Malomsoky, Szabolcs
Ishikawa, Naoki
Signal Processing
Information Theory
In this paper, we propose a method for designing sparse Grassmannian codes for noncoherent multiple-input multiple-output systems. Conventional pairwise error probability formulations under uncorrelated Rayleigh fading channels fail to account for rank deficiency induced by sparse configurations. We revise these formulations to handle such cases in a unified manner. Furthermore, we derive a closed-form metric that effectively maximizes the noncoherent average mutual information (AMI) at a given signal-to-noise ratio. We focus on the fact that the Schubert cell decomposition of the Grassmann manifold provides a mathematically sparse property, and establish design criteria for sparse noncoherent codes based on our analyses. In numerical results, the proposed sparse noncoherent codes outperform conventional methods in terms of both symbol error rate and AMI, and asymptotically approach the performance of the optimal Grassmannian constellations in the high-signal-to-noise ratio regime. Moreover, they reduce the time and space complexity, which does not scale with the number of transmit antennas.
title Sparse Grassmannian Design for Noncoherent Codes via Schubert Cell Decomposition
topic Signal Processing
Information Theory
url https://arxiv.org/abs/2601.21009