A dirty paper coding scheme for the Multiple Input Multiple Output Broadcast Channel

Dirty paper coding (DPC) is known to achieve the capacity region of a Gaussian Multiple Input Multiple Output-Broadcast channel (MIMO-BC). Practical DPC schemes using finite length codes are still being actively studied. In this paper, we design a zero-forcing DPC (ZF-DPC) scheme using trellis shaping and Low Density Parity Check (LDPC) codes for a MIMO-BC with two transmit antennas and two users (receivers), each with one antenna. This is an extension of an earlier design for the single antenna Gaussian broadcast channel. One of the important aspects of the DPC code design is the introduction of a one block delay that enables the channel encoder (and decoder) and the shaping encoder (and decoder) to operate independently. In the ZF-DPC method, the MIMO precoder ensures that one user has no interference. The other user uses DPC to combat interference. The performance of this method is compared using simulations with the capacity limit and simpler precoder based methods like Minimum Mean Square Error-Vector Perturbation (MMSE-VP) and zero-forcing beamforming (ZF-BF).

I. Introduction

In the cellular downlink, base stations and mobiles use multiple antennas in order to increase spectral efficiency. This downlink channel is a non-degraded Multiple Input Multiple Output Broadcast (MIMO-BC) channel. The sum capacity for the non-degraded Gaussian-MIMO broadcast channel was derived in [1] and shown to be achieved using Dirty Paper Coding (DPC). Later, in [2], it was shown that the DPC rate region coincides with the capacity region. Practical code designs for DPC have been studied in [3] [4] [5] [6] [7]. In the designs in [3] [4] [5] [6], joint shaping and coding encoders (or iterative decoders) are required at the transmitter (or receiver). In [7], for the single antenna Gaussian broadcast channel, joint encoding and iterative decoding between the shaping and channel codes are avoided by introducing a one-codeword delay at the transmitter and the shaping of symbols from current message bits combined with parity bits from the previous codeword. In this work, we design codes for the MIMO-BC using this idea from [7].