Approaching the Ergodic Capacity of the MIMO Channel with Lattice Codes

2015 IEEE International Symposium on Information Theory (ISIT)

2015

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The performance of lattice codes in the additive white Gaussian noise (AWGN) channel has attracted much attention lately, however, their performance under ergodic fading channels has been relatively unexplored. We show that lattice coding and decoding achieve the capacity of the ergodic pointto-point and multiple-access channels (MAC). Additionally, a lowcomplexity scheme is proposed for the ergodic MAC. At moderate and high signal-to-noise ratio (SNR), the sum rate achieved by the low-complexity scheme is within a constant gap to the ergodic MAC sum capacity, whereas at low SNR the gap to capacity diminishes quadratically with linear SNR decrease.

Section: Discussionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 90%

See 1 more Smart Citation

Achieving the ergodic capacity with lattice codes

2015 IEEE International Symposium on Information Theory (ISIT)

2015

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“…The extension of Theorem 2 to complex-valued channels is straightforward, using techniques similar to [32,Theorem 2]. The channel would then be ordered with respect to the magnitude of channel coefficients.…”

Section: B Ergodic Fadingmentioning

confidence: 99%

On the Separability of Ergodic Fading MIMO Channels: A Lattice Coding Approach

2018

IEEE Trans. Commun.

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This paper addresses point-to-point communication over block-fading channels with independent fading blocks. When both channel state information at the transmitter (CSIT) and receiver (CSIR) are available, most achievable schemes use separable coding, i.e., coding independently and in parallel over different fading states. Unfortunately, separable coding has drawbacks including large memory requirements at both communication ends. In this paper a lattice coding and decoding scheme is proposed that achieves the ergodic capacity without separable coding, with lattice codebooks and decoding decision regions that are universal across channel realizations. We first demonstrate this result for fading distributions with discrete, finite support whose sequences are robustly typical. Results are then extended to continuous fading distributions, as well as multiple-input multiple-output (MIMO) systems. In addition, a variant of the proposed scheme is presented for the MIMO ergodic fading channel with CSIR only, where we prove the existence of a universal codebook that achieves rates within a constant gap to capacity for finite-support fading distributions. The gap is small compared with other schemes in the literature. Extension to continuous-valued fading is also provided.

“…This concludes the proof for real-valued channels. For complex-valued channels, we follow in the footsteps of [25,Theorem 2], and hence only a sketch of the proof is provided. With a slight abuse of notation, we denote the complex-valued elements by a superscript ∼ .…”

Section: System Modelmentioning

confidence: 99%

Ergodic Fading MIMO Dirty Paper and Broadcast Channels: Capacity Bounds and Lattice Strategies

IEEE Trans. Wireless Commun.

2017

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A multiple-input multiple-output (MIMO) version of the dirty paper channel is studied, where the channel input and the dirt experience the same fading process and the fading channel state is known at the receiver (CSIR). This represents settings where signal and interference sources are co-located, such as in the broadcast channel. First, a variant of Costa's dirty paper coding (DPC) is presented, whose achievable rates are within a constant gap to capacity for all signal and dirt powers. Additionally, a lattice coding and decoding scheme is proposed, whose decision regions are independent of the channel realizations. Under Rayleigh fading, the gap to capacity of the lattice coding scheme vanishes with the number of receive antennas, even at finite Signal-to-Noise Ratio (SNR). Thus, although the capacity of the fading dirty paper channel remains unknown, this work shows it is not far from its dirt-free counterpart. The insights from the dirty paper channel directly lead to transmission strategies for the two-user MIMO broadcast channel (BC), where the transmitter emits a superposition of desired and undesired (dirt) signals with respect to each receiver. The performance of the lattice coding scheme is analyzed under different fading dynamics for the two users, showing that high-dimensional lattices achieve rates close to capacity.