Achieving Ergodic Capacity in Gaussian Fast Fading Multiple Access Channels using Compute-Forward Multiple Access

Conceptos Básicos

The compute-forward multiple access (CFMA) scheme can achieve the ergodic sum capacity of a two-user Gaussian fast fading multiple access channel (MAC) under appropriate channel conditions.

Resumen

This paper investigates the CFMA scheme for a two-user Gaussian fast fading MAC with channel state information only available at the receiver (CSIR). The key contributions are:

1. CFMA is extended to fading channels with new technical contributions, including the analysis of ambiguity decoding of lattice codes in the CFMA scheme. This subsumes known results for CFMA in fixed channels and successive interference cancellation (SIC) decoding with lattice codes for the Gaussian MAC.

2. Sufficient and necessary conditions are identified under which the entire ergodic capacity is achievable using CFMA. A key is that the scaling parameter in the code construction should be chosen judiciously based on the channel statistics.

3. The impact of channel statistics is investigated. It is found that in general, large mean and small variance of the channel gains benefit the capacity achievability. Numerical examples illustrate the theoretical findings.

Estadísticas

The ergodic sum capacity of the two-user Gaussian fast fading MAC is given by:
C(P, h) = 1/2 E_h [log (1 + Ph^2_1 + Ph^2_2)]

Citas

"Compute-forward multiple access (CFMA) is a generalized CF scheme proposed in [3], which allows the users to have different rates whereas each user shares the same rate in the original CF."
"It is not a straightforward task to extend the CFMA scheme to the fading case. CFMA and the original compute-and-forward scheme use lattice decoding (quantization with respect to lattice) which relies on the algebraic structure of lattice codes. The first observation in the fading case is that since each symbol in a codeword experiences a possibly different channel gain, the algebraic structure of lattice codes will be corrupted from the decoder's perspective, so it is not immediately clear how to extend the lattice decoder to the fading case."

Ideas clave extraídas de

Compute-Forward Multiple Access for Gaussian Fast Fading Channels

by Lanwei Zhang... a las arxiv.org 05-01-2024

https://arxiv.org/pdf/2404.19468.pdf

Consultas más profundas

How can the CFMA scheme be extended to multi-user Gaussian fast fading MACs

In extending the CFMA scheme to multi-user Gaussian fast fading MACs, the key lies in adapting the decoding process to handle multiple users efficiently. One approach is to employ a multi-user detection technique that can decode linear combinations of codewords from all users simultaneously. This involves designing sophisticated algorithms that can handle the increased complexity of decoding multiple signals in a fading environment. By leveraging the principles of CFMA and extending them to accommodate multiple users, it is possible to achieve the benefits of compute-forward transmission in a multi-user scenario.

What are the potential challenges in applying CFMA to practical wireless systems with imperfect channel state information

Applying CFMA to practical wireless systems with imperfect channel state information (CSI) poses several challenges. One major challenge is the need to adapt the decoding process to account for the uncertainty in channel conditions. Imperfect CSI can lead to errors in decoding linear combinations of codewords, affecting the overall performance of the system. Additionally, the computational complexity of CFMA schemes may increase when dealing with imperfect CSI, as more sophisticated algorithms are required to mitigate the impact of channel estimation errors. Ensuring robustness against channel variations and optimizing the system for imperfect CSI are crucial aspects that need to be addressed in practical implementations of CFMA.

Can the CFMA approach be combined with other advanced coding and modulation techniques to further improve the performance in fading channels

The CFMA approach can be combined with other advanced coding and modulation techniques to further enhance performance in fading channels. By integrating CFMA with techniques such as space-time coding, diversity schemes, and adaptive modulation, it is possible to improve the reliability and efficiency of data transmission in fading environments. For example, incorporating spatial diversity through multiple antennas can help combat fading effects and improve signal quality. Adaptive modulation techniques can also be used to adjust the transmission parameters based on channel conditions, maximizing the data rate while maintaining reliability. By synergizing CFMA with these advanced techniques, it is possible to achieve higher throughput, better spectral efficiency, and increased reliability in fading channels.