Precoding for Word Error Rate Minimization of LDPC Coded Modulation on Block Fading Channels

Duyck, Dieter; Boutros, Joseph J.; Moeneclaey, Marc

doi:10.1109/twc.2012.051712.111142

Cited by 5 publications

(11 citation statements)

References 35 publications

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“…11(a) and 9 are the same for both constellations, except for an upward translation of 3 dB. 7 The 8-QAM constellations have the same form as in Fig. 8(a).…”

Section: A Numerical Results Formentioning

confidence: 96%

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Precoding for Outage Probability Minimization on Block Fading Channels

Duyck

Boutros

Moeneclaey

2013

IEEE Trans. Inform. Theory

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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.Index Terms-Block fading channels, multidimensional mapping, precoding, outage probability.

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“…11(a) and 9 are the same for both constellations, except for an upward translation of 3 dB. 7 The 8-QAM constellations have the same form as in Fig. 8(a).…”

Section: A Numerical Results Formentioning

confidence: 96%

“…The condition for being orthogonal is , or the eigenvalues of must have a squared magnitude of 1. It is easy to find that (6) Now, it follows that (7) As the eigenvalues must have a magnitude of 1, we have . In order to obtain a real-valued , we take real-valued (i.e., or ) and (i.e., ) for .…”

Section: System Modelmentioning

confidence: 99%

Precoding for Outage Probability Minimization on Block Fading Channels

Duyck

Boutros

Moeneclaey

2013

IEEE Trans. Inform. Theory

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“…For the toy example, we consider a classical system model with two flat non-ergodic parallel channels with Rayleigh fading and BPSK symbols at the precoder input (see for example [6], [12]), which allows a geometric illustration. The system model is…”

Section: Toy Examplementioning

confidence: 99%

“…III, we have explained that the non-ergodic MIMO channel is equivalent to a parallel channel with a random precoder. To the authors' best knowledge, only [12] presented a tool to optimize the degree distributions of an LDPC code for parallel Rayleigh faded channels with precoding. We therefore utilized the techniques from [12] to generate the degree distributions of the LDPC code.…”

Section: A Ldpc Code Optimization For the Emi Codementioning

confidence: 99%

“…We briefly describe the techniques developed in [12], where coded modulations (including the precoding matrix, the mapping function and the error-correcting code) were optimized to yield a WER closely approaching the outage probability. The off-line optimization, done using a geometric approach, was limited to at most B + 1 times the effort for Gaussian channels, where B is the number of parallel channels, here min(n T , n R ).…”

Section: A Ldpc Code Optimization For the Emi Codementioning

confidence: 99%

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Time-varying space-only codes

Duyck

Moeneclaey

Yang

et al. 2012

2012 IEEE International Symposium on Information Theory Proceedings

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International audienceMultiple antennas are used to increase reliability and bit rate for a given bandwidth. For a fixed transmission rate, discrete input alphabets and no 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. Despite praiseworthy efforts to reduce the decoding complexity, optimal STCs are not used in practice in the case of more than two transmit antennas because of complexity reasons. It is generally accepted that reducing the dimension of the STC leads to a reduced diversity order. We show that this is not true for coded communication, assuming the presence of an outer error-correcting code with any coding rate. We propose a new class of full-rate full-diversity STCs; more specifically, time-varying space-only codes. This new class is referred to as EMI codes. Full diversity is proven in terms of outage probability, for the case where the number of receive antennas is larger than or equal to the number of transmit antennas, and is numerically verified in terms of outage and word error probability using LDPC codes

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