No abstract

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.

It is known that lattice coding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This paper addresses the performance of lattice codes in the ergodic fading channel. Using nested lattice codes and ambiguity decoding, we show that the rates achieved by lattice coding and decoding are within a constant gap of the capacity of the ergodic channel at moderate and high signal-to-noise-ratio (SNR), and within a gap that decreases quadratically with the SNR for the low SNR regime.Index Terms-Channel capacity, nested lattice codes, ergodic channel, minimum mean-square error (MMSE) estimation.

For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single-input single-output (SISO) and multiple-input multiple-output (MIMO) point-to-point channel as well as the multiple-access channel (MAC), with channel state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a time-varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our encoder has a similar structure to that of Erez and Zamir. For the SISO channel, the gap to capacity is bounded by a constant under a wide range of fading distributions. For the MIMO channel under Rayleigh fading, the rate achieved is within a gap to capacity that does not depend on the signal-to-noise ratio (SNR), and diminishes with the number of receive antennas. The analysis is extended to the K-user MAC where similar results hold. Achieving a small gap to capacity while limiting the use of CSIR to the equalizer highlights the scope for efficient decoder implementations, since decision regions are fixed, i.e., independent of channel realizations.

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.