Dieter Duyck

Low-Density Graph Codes for Coded Cooperation on Slow Fading Relay Channels

We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-and-forward with a smaller outage probability than the latter. An outage probability analysis for discrete constellations shows that full diversity can be achieved only when the coding rate does not exceed a maximum value that depends on the level of cooperation. We derive a new code structure by extending the previously published full-diversity root-LDPC code, designed for the BF point-to-point channel, to exhibit a rate-compatibility property which is necessary for coded cooperation. We estimate the asymptotic performance through a new density evolution analysis and the word error rate performance is determined for finite length codes. We show that our code construction exhibits near-outage limit performance for all block lengths and for a range of coding rates up to 0.5, which is the highest possible coding rate for two cooperating users.

Analysis and construction of full-diversity joint network-LDPC codes for cooperative communications

Transmit diversity is necessary in harsh environments to reduce the required transmit power for achieving a given error performance at a certain transmission rate. In networks, cooperative communication is a well-known technique to yield transmit diversity and network coding can increase the spectral efficiency. These two techniques can be combined to achieve a double diversity order for a maximum coding rate on the Multiple-Access Relay Channel (MARC), where two sources share a common relay in their transmission to the destination. However, codes have to be carefully designed to obtain the intrinsic diversity offered by the MARC. This paper presents the principles to design a family of full-diversity LDPC codes with maximum rate. Simulation of the word error rate performance of the new proposed family of LDPC codes for the MARC confirms the full diversity.

A full-diversity joint network-channel code construction for cooperative communications

Cooperative communications is a well known technique to yield transmit diversity in a multi-user environment. Network coding can increase the spectral efficiency in networks. These two techniques can be combined to achieve a double diversity order for a maximum coding rate Rc = 2/3 on the Multiple Access Relay Channel (MARC), where two sources share a common relay in their transmission to the destination. However, codes have to be carefully designed to obtain the intrinsic channel diversity. Up till now, no full-diversity capacity-achieving code for the MARC at a coding rate Rc = 2/3 has been published. We present a strategy to produce excellent low-density parity-check (LDPC) codes with rate 2/3, i.e., exhibiting full-diversity and operating close to the outage probability limit. Simulation of the word error rate performance of the new proposed family of LDPC codes for the MARC confirms the full-diversity.

Monte Carlo solutions for blind phase noise estimation

This paper investigates the use of Monte Carlo sampling methods for phase noise estimation on additive white Gaussian noise (AWGN) channels. The main contributions of the paper are (i) the development of a Monte Carlo framework for phase noise estimation, with special attention to sequential importance sampling and Rao-Blackwellization, (ii) the interpretation of existing Monte Carlo solutions within this generic framework, and (iii) the derivation of a novel phase noise estimator. Contrary to the ad hoc phase noise estimators that have been proposed in the past, the estimators considered in this paper are derived from solid probabilistic and performance-determining arguments. Computer simulations demonstrate that, on one hand, the Monte Carlo phase noise estimators outperform the existing estimators and, on the other hand, our newly proposed solution exhibits a lower complexity than the existing Monte Carlo solutions.

Design of diversity-achieving LDPC codes for H-ARQ with cross-packet channel coding

In wireless scenarios an effective protocol to increase the reliability for time-varying channels is the hybrid automatic repeat request (H-ARQ). The H-ARQ scheme with cross-packet channel coding (CPC) is a recently published extension of H-ARQ with several advantages. No full-diversity low-density parity-check (LDPC) code design for the whole range of coding rates yielding full-diversity has been published. In this paper the authors provide a new outage behavior analysis and a new structured LDPC code ensemble achieving full-diversity for H-ARQ with CPC by exploiting the rootcheck principle. Simulation results show that the new code design outperforms the previous approaches, providing full-diversity and good coding gain, also at high coding rates.

Precoding for Outage Probability Minimization on Block Fading Channels

The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, full diversity on a block fading channel can be achieved without error-correcting code. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. Using a geometric approach, this paper establishes simple upper bounds on the outage probability, the minimization of which yields to precoding matrices that achieve very good performance. For discrete alphabets, it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing the coding gain.

EM based channel estimation in an Amplify-and-Forward relaying network

Cooperative communication offers a way to obtain spatial diversity in a wireless network without increasing hardware demands. The different cooperation protocols proposed in the literature [1] are often studied under the assumption that all channel state information is available at the destination. In a practical scenario, channel estimates need to be derived from the broadcasted signals. In this paper, we study the Amplify-and-Forward protocol and use the expectation-maximization (EM) algorithm to obtain the channel estimates in an iterative way. Our results show that the performance of the system that knows the channels can be approached at the cost of an increased computational complexity. In case a small constellation is used, a low complexity approximation is proposed with a similar performance.

Universal LDPC codes for cooperative communications

Cooperative communication is a well known technique to yield transmit diversity in the case of fading channels and to increase the spectral efficiency in the case of Gaussian channels. Error-correcting codes have to be carefully designed to achieve the promised gains. Good LDPC codes are known for fading channels and for Gaussian channels, but an LDPC code ensemble that performs well on both channels has not yet been presented in the literature. This paper merges two families of LDPC codes into a universal LDPC code ensemble for both fading channels and Gaussian channels. Furthermore, the new universal LDPC code ensemble outperforms previously proposed codes on the block fading channel, which is explained through a fading space analysis. Simulation of the word error rate performance of the new proposed family of LDPC codes shows that it performs well on both fading channels and Gaussian channels.

Rotated modulations for outage probability minimization: a fading space approach

The outage probability limit is a fundamental lower bound on the word error rate of coded communications systems. It is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, the maximum achievable coding rate yielding full-diversity can exceed the upper limit given by the standard Singleton bound. However, the effect of precoding on the coding gain is not well understood. This paper analyzes linear precoding from an information theoretical point of view and tries to optimize the coding gain. For discrete constellations, it is shown that constellation expansion together with one optimized precoding parameter is sufficient to approach the best outage achieved by a Gaussian alphabet, thus maximizing the coding gain.

Low-density parity-check coding for block fading relay channels

We study low-density parity-check (LDPC) codes with iterative decoding on block fading (BF) Relay Channels. We use coded cooperation, a variant of decode-and-forward with a smaller outage probability than the latter. We derive a new code structure by extending the previously published full-diversity root-LDPC code, designed for the BF point-to-point channel, to exhibit a rate-compatibility property which is necessary for coded cooperation. Density evolution equations are determined in order to plot the word error rate performance for infinite length codes. We show that our code construction exhibits near-outage limit performance for all block lengths and for a range of coding rates up to 0.5, which is the highest possible coding rate that achieves full-diversity on the relay channel.