Modified SNR gap approximation for resource allocation in LDPC-coded multicarrier systems

The signal-to-noise ratio (SNR) gap approximation provides a closed-form expression for the SNR required for a coded modulation system to achieve a given target error performance for a given constellation size. This approximation has been widely used for resource allocation in the context of trellis-coded multicarrier systems (e.g., for digital subscriber line communication). In this contribution, we show that the SNR gap approximation does not accurately model the relation between constellation size and required SNR in low-density parity-check (LDPC) coded multicarrier systems. We solve this problem by using a simple modification of the SNR gap approximation instead, which fully retains the analytical convenience of the former approximation. The performance advantage resulting from the proposed modification is illustrated for single-user digital subscriber line transmission

Error performance prediction of randomly shortened and punctured LDPC codes

In this contribution, we show that the word error rate (WER) performance in the waterfall region of a randomly shortened and punctured low density parity check code can be accurately predicted from the WER performance of its finitelength mother code. We derive an approximate analytical expression for the mutual information (MI) required by a daughter code to achieve a given WER, based on the MI required by the mother code, which shows that the gap to the capacity of the daughter code grows the more the code is punctured or shortened. The theoretical results are confirmed by simulations (where the random shortening and puncturing pattern is either selected independently per codeword or kept the same for all codewords) for practical codes on both the binary erasure channel and the binary-input additive white Gaussian noise channel

Modulo loss reduction in spatial multiplexing systems with Tomlinson-Harashima precoding

When a multi-user communication system over a block-fading MIMO channel utilizes Tomlinson-Harashima precoding in the downstream direction, to eliminate the interference between the spatially multiplexed data streams, the conventional detection, involving a modulo operation at the receiving terminals, is known to yield a performance degradation that becomes considerable at low SNR. In this contribution, we propose a novel detection method that exploits sending one bit of extra information per user and per frame to the receiver, which indicates whether or not the considered user can detect all its data within the frame without performing a modulo operation. Moreover, in the case of M-PAM transmission it is possible to optimize the rotation of the constellations at the transmitter, maximizing for each frame the number of users for which no modulo operation is required. Numerical results show that in the case of 2-PAM the novel detection algorithm is able to completely recover the modulo loss experienced by the conventional detection method without an increase in transmit power, and to outperform 4-QAM (with conventional or novel detection) in terms of mutual information at low SNR

Modulo loss reduction for Tomlinson-Harashima precoding in a multi-beam satellite forward link

Full frequency reuse in multi-beam satellite communication systems allows to achieve a high capacity, provided that the inter-beam co-channel interference (CCI) can be properly dealt with. Tomlinson-Harashima precoding (THP) is a popular technique applied at the basestation transmitter to cancel the interference in the forward link. However, the conventional detection of THP, involving a modulo operation at the receiver terminals, is known to suffer from modulo loss, which becomes considerable at low SNR. This contribution explores alternative detection techniques to reduce the modulo loss. We point out that by applying proper signal rotations at the basestation transmitter, these alternative detectors almost completely recover the modulo loss for 2-PAM, achieving a higher mutual information (MI) than 4-QAM at low SNR

Semi-analytical evaluation of concatenated RS/LDPC coding performance with finite block interleaving against impulsive noise

This contribution considers the word error rate (WER) performance of a concatenated coding scheme in the presence of impulsive noise (IN), which is modeled as gated white Gaussian noise, with on-and off-times governed by a 2-state Markov model. The scheme consists of a Reed-Solomon (RS) outer code and a low-density parity-check (LDPC) inner code, which are separated by a block interleaver with finite depth. The Monte Carlo (MC) simulation of the WER of such communication systems is time-consuming, especially when targeting low error rates and examining several interleaver settings. We present a semi-analytical evaluation of the WER, which relies on a simple semi-analytical statistical model for the number of byte errors in a segment of the information word after LDPC decoding. To compute the error performance of the concatenated code corresponding to different parameters of the RS code and the interleaver, we require only the WER and byte error rate (ByteER) of the inner subsystem, determined by the LDPC code and the considered constellation, in the presence of stationary white noise. We show that the semi-analytical WER of the concatenated system closely matches the WER resulting from MC simulations and use the proposed model to investigate the effect of the interleaver depth on the WER performance