Lattice Coding and Decoding for Multiple-Antenna Ergodic Fading Channels

Abstract

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.

On the design of multi-dimensional irregular repeat-accumulate lattice codes

“…. , g L ] T is added to the interleaved sequence z via z ⊕ g in an element-wise manner, where "⊕" is the modulo-lattice addition defined in (7). Note that each element of g is randomly and uniformly chosen from the set of coset leaders Ψ such that a linear code constraint is met, which will be introduced later.…”

“…This paper was presented in part at the IEEE International Symposium on Information Theory (ISIT) in 2017 [1]. such as index coding [4], cooperative communications [5], multiple access [6], multiple antenna systems [7] and so on. It is believed that lattice codes will play a crucial role in future communication systems.…”

Algebraic lattice codes for linear fading channels

“…From now on, we will fix A k to be the set of all diagonal matrices in M k (C) having determinant with absolute value 1. Note that with this choice, if rh A k (L k ) ≥ 2kc then Corollary 1 holds for any channel of the form (11).…”

“…As far as we know this was the first result achieving constant gap to MIMO capacity with lattice codes. In [11] the authors corrected and generalized [10] and improved on our gap in the case of Rayleigh fading MIMO channels.…”

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

“…Under ergodic fading and CSIR only, Luzzi and Vehkalahti [26] recently showed that a class of lattices belonging to a family of division algebra codes achieve rates within a constant gap to capacity, however, this gap can be large. In [27], a lattice coding scheme was proposed whose decoder does not depend on the fading realizations, achieving rates within a constant gap to capacity. The results in both [26], [27] are limited to channels with isotropic fading, i.e., the optimal input covariance matrix is a scaled identity.…”