[show abstract][hide abstract] ABSTRACT: Multiple antenna (MIMO) devices are widely used to increase reliability and
information bit rate. Optimal error rate performance (full diversity and large
coding gain), for unknown channel state information at the transmitter and for
maximal rate, can be achieved by approximately universal space-time codes, but
comes at a price of large detection complexity, infeasible for most practical
systems. We propose a new coded modulation paradigm: error-correction outer
code with space-only but time-varying precoder (as inner code). We refer to the
latter as Ergodic Mutual Information (EMI) code. The EMI code achieves the
maximal multiplexing gain and full diversity is proved in terms of the outage
probability. Contrary to most of the literature, our work is not based on the
elegant but difficult classical algebraic MIMO theory. Instead, the relation
between MIMO and parallel channels is exploited. The theoretical proof of full
diversity is corroborated by means of numerical simulations for many MIMO
scenarios, in terms of outage probability and word error rate of LDPC coded
systems. The full-diversity and full-rate at low detection complexity comes at
a price of a small coding gain loss for outer coding rates close to one, but
this loss vanishes with decreasing coding rate.
[show abstract][hide abstract] ABSTRACT: Multiple antennas are used to increase reliability and bit rate for a given bandwidth. For a fixed transmission rate, discrete input alphabets and without channel state information at the transmitter, optimal space-time codes (STCs) achieving both gains (full rate and full diversity) are well known. However, the complexity of maximum likelihood decoding increases exponentially with the number of space and time dimensions of the STC. Previous work reducing the complexity of decoding STCs has focused on the decoding algorithm, because the dimensions of the STC cannot be reduced without losing rate or diversity for uncoded communication. However, for coded communication (assuming the presence of an outer code), the dimensions of the STC may be reduced. We propose a new full-rate and full-diversity suboptimal time-varying space-only code, adding a new dimension to the work on complexity reduction. Full diversity is proved in terms of the outage probability.
[show abstract][hide abstract] ABSTRACT: In wireless communications, the block fading (BF) channel is an important channel model. A key quality indicator in coded transmission is the word error rate (WER), which is the fraction of packets that cannot be decoded correctly at the receiver. We study Low-Density Parity-Check (LDPC) coded modulation with precoding, with the aim to minimize the WER on BF channels without channel state information at the transmitter. In the literature, it was not yet known how to optimize the system parameters for this channel model, mainly due to the fading gain distribution. One of the existing approaches to combining coding and modulation is bit-interleaved coded modulation with iterative decoding (BICM-ID). This work uses precoding to optimize BICM-ID with LDPC codes for BF channels, and is a continuation of previous work that used precoding to minimize the outage probability limit. We present the selection of the precoding matrix, the mapping function and the error-correcting code yielding a WER that closely approaches this minimum outage probability. Using a geometric approach, the off-line system optimization effort for the BF channel is limited to at most B+1 times the effort for Gaussian channels, where B is the number of blocks in the BF channel.
[show abstract][hide abstract] ABSTRACT: 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.
IEEE Transactions on Information Theory 03/2011; · 2.62 Impact Factor
[show abstract][hide abstract] ABSTRACT: The block fading (BF) channel is a useful model for various communication systems in urban environments. Full-diversity error-correcting codes are required to approach the physical limits of the performance on BF channels. Low-density parity-check (LDPC) codes are good error-correcting codes, but full-diversity standard random LDPC codes for the BF channel are not known yet. We design full-diversity random LDPC ensembles at infinite block length by optimizing the threshold in multiple points in the fading space, which takes into account the randomness of the fading. However, this is not sufficient to achieve full-diversity at finite block length, because of stopping sets. We therefore propose a method to generate full-diversity code instances at finite length so that stopping sets over information bits are avoided. The asymptotic and finite length word error rate performance is verified by means of density evolution and Monte Carlo simulations, respectively, confirming that full-diversity standard random LDPC codes exist and perform well.
[show abstract][hide abstract] ABSTRACT: We study precoding for the outage probability minimization of block fading (BF) channels and BF relay channels. Recently, an upper bound on the outage probability with precoding was established for BF channels, but only for high instantaneous SNR. This upper bound is much easier to minimize than the actual outage probability, so that optimal precoding matrices can be determined without much computational effort. Here, we provide a proof for the upper bound on the outage probability at low instantaneous SNR. Next, the structure of the precoding matrix is simplified so that it can be easily constructed for an arbitrary number of blocks in the BF channel. Finally, we apply this technique to cooperative communications.
[show abstract][hide abstract] ABSTRACT: For a given channel instance and a fixed LDPC ensemble, a stability outage event is defined by the density evolution being unstable at the origin. The probability of such an event, referred to as Stability Outage Probability, is a useful lower bound for the word error rate. We formulate the stability outage probability for block fading channels and we introduce the stability diversity order. As a direct application, we show how the class of capacity-achieving ensembles on the erasure channel is bounded away from the outage limit on a block fading channel.
[show abstract][hide abstract] ABSTRACT: Expectation-maximization (EM) based iterative algorithms are investigated in order to estimate the impulse response of a frequency-selective multipath channel in a coded OFDM system. Two ways of choosing the EM complete data are compared: a complete data built from observations and transmitted symbols (CL-EM) and a complete data chosen by decomposing noise and observation components (NCD-EM). Both CL-EM and NCD-EM algorithms are derived for a coded OFDM system. The rate of convergence of both EM algorithms is theoretically determined. It is found that the rate of convergence of CL-EM is independent from the number of channel taps at high signal-to-noise ratio (SNR), while that of NCD-EM varies with the number of taps. It is shown that CL-EM converges in a few iterations. Furthermore, considering the complexity per iteration, CL-EM has a lower complexity than its counterpart. We also establish a Cramer-Rao bound (CRB) for coded OFDM transmission. Simulation results show that CL-EM has a good performance-complexity trade-off and it achieves the CRB.
[show abstract][hide abstract] ABSTRACT: The block fading channel model is very useful for many systems in urban environments. When striving for high performance implying high rate, full-diversity and excellent coding gain, coded modulations have to be used. When linear precoding is used, error-correcting codes can focus on achieving a high coding gain and are not constrained in coding rate so that no bandwidth is sacrificed. However, optimal precoding schemes for coded modulations on block fading channels are not known because of the inability to deal with the randomness of the fading gains. We study coded modulations for block fading channels in the fading space. This geometric approach yields more insight and allows to take into account the randomness of the fading. It can be used to generate the system parameters so that the word error rate performance approaches the outage probability closely.
Communications and Vehicular Technology in the Benelux (SCVT), 2010 17th IEEE Symposium on; 12/2010
[show abstract][hide abstract] ABSTRACT: This paper<sup>1</sup> presents our investigation on iterative decoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in  and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes. Also, we show analytically that, in the case of 2 fading blocks, the iterative threshold γ<sup>*</sup><sub>root</sub> of Root-LDPC codes is proportional to (α<sub>1</sub>α<sub>2</sub>)<sup>-1</sup>, where α<sub>1</sub> and α<sub>2</sub> are corresponding fading gains. From this result, the full diversity property of Root-LDPC codes immediately follows.
[show abstract][hide abstract] ABSTRACT: 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.
Turbo Codes and Iterative Information Processing (ISTC), 2010 6th International Symposium on; 10/2010
[show abstract][hide abstract] ABSTRACT: We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not perform well under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.
IEEE Transactions on Information Theory 10/2010; · 2.62 Impact Factor
[show abstract][hide abstract] ABSTRACT: We study irregular binary turbo codes over nonergodic block-fading channels. We first propose an extension of channel multiplexers initially designed for regular turbo codes. We then show that, using these multiplexers, irregular turbo codes that exhibit a small decoding threshold over the ergodic Gaussian-noise channel perform very close to the outage probability on block-fading channels, from both density evolution and finite-length perspectives.
Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on; 07/2010
[show abstract][hide abstract] ABSTRACT: In this paper, we consider the problem of coding for the half-duplex nonorthogonal amplify-and-forward (NAF) cooperative channel where the transmitter to relay and the interrelay links are highly reliable. We derive bounds on the diversity order of the NAF protocol that are achieved by a distributed space-time bit-interleaved coded modulation (D-ST-BICM) scheme under iterative APP detection and decoding. These bounds lead to the design of space-time precoders that ensure maximum diversity order and high coding gains. The word error rate performance of D-ST-BICM are also compared to outage probability limits.
IEEE Transactions on Information Theory 07/2010; · 2.62 Impact Factor
[show abstract][hide abstract] ABSTRACT: We study irregular binary turbo codes over non-ergodic block-fading channels. We first propose an extension of channel multiplexers initially designed for regular turbo codes. We then show that, using these multiplexers, irregular turbo codes that exhibit a small decoding threshold over the ergodic Gaussian-noise channel perform very close to the outage probability on block-fading channels, from both density evolution and finite-length perspectives. Comment: to be presented at the IEEE International Symposium on Information Theory, 2010
[show abstract][hide abstract] ABSTRACT: This paper derives approximations allowing the estimation of outage probability for standard irregular LDPC codes and full-diversity Root-LDPC codes used over nonergodic block-fading channels. Two separate approaches are discussed: a numerical approximation, obtained by curve fitting, for both code ensembles, and an analytical approximation for Root-LDPC codes, obtained under the assumption that the slope of the iterative threshold curve of a given code ensemble matches the slope of the outage capacity curve in the high-SNR regime.
[show abstract][hide abstract] ABSTRACT: 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.
IEEE International Symposium on Information Theory, ISIT 2010, June 13-18, 2010, Austin, Texas, USA, Proceedings; 01/2010