Modulo Loss Research Articles

SNR maximization and modulo loss reduction for Tomlinson-Harashima precoding

Compared to linear precoding, Tomlinson-Harashima precoding (THP) requires less transmit power to eliminate the spatial interference in a multi-user downlink scenario involving a multi-antenna transmitter and geographically separated receivers. However, THP gives rise to certain performance losses, referred to as modulo loss and power loss. Based on the observation that part of the users can omit the modulo operation at the receiver during an entire frame, we present an alternative detector, which reduces the modulo loss compared to the conventional detector. In addition, this contribution compares several existing and novel algorithms for selecting the user ordering and the rotation of the constellations at the transmitter, to increase the SNR at the detector and decrease the modulo loss for the alternative detector. Compared to the better of linear precoding and THP with conventional detector, the optimized alternative detector achieves significant gains (up to about 4 dB) for terrestrial wireless communication, whereas smaller gains (up to about 1 dB) are obtained for multi-beam satellite communication.

Modulo Loss Reduction for Vector Perturbation Systems

In this letter, we present an improved precoding technique which reduces a modulo loss in vector perturbation with low complexity. Instead of searching perturbation vectors in the infinite lattice, the proposed scheme restricts the search range by utilizing the distribution of the perturbation vector depending on transmitted data. As a result, we can achieve significant complexity savings at the transmitter while providing better performance compared to the original vector perturbation.

Near-Capacity Dirty-Paper Code Design: A Source-Channel Coding Approach

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper examines near-capacity dirty-paper code designs based on source–channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat–accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity. </para>

Power and modulo loss tradeoff with expanded soft demapper for LDPC coded GMD-THP MIMO systems

Tomlinson-Harashima precoding (THP) can be combined with geometric mean decomposition (GMD) to decouple a multiple-input multiple-output (MIMO) channel into multiple single-input single-output (SISO) subchannels with identical signal-to-noise ratios (SNRs). The combined system is called GMD-THP MIMO system. As all subchannels for this system have identical SNRs, it is more convenient to design modulation/demodulation and coding/decoding schemes than other MIMO systems that have different SNRs among the subchannels. In this paper, we consider low-density parity-check (LDPC) coded GMD-THP MIMO systems. Modulo operation at the receiver is needed for THP decoding but it may generate modulo errors. These modulo errors cause the log likelihood ratio (LLR) values provided by conventional soft demapper to be very inaccurate. We propose an expanded soft demapper scheme to reduce the inaccuracy of the LLR values, by which significant performance improvement can be achieved for LDPC decoding. Furthermore, THP introduces power loss and modulo loss into the system. These two losses are related to the size of the modulo boundaries and therefore we derive the expressions for these two losses as functions of the modulo size factor. With these expressions, we find the optimal modulo size factor which achieves the minimum combined losses through doing a tradeoff between power loss and modulo loss. Computer simulations are presented to show that the tradeoff indeed improves the performance of the LDPC coded GMD-THP systems.