Coded diversity on block-fading channels

Malkamaki, E.; Leib, H.

doi:10.1109/18.749028

Cited by 189 publications

(135 citation statements)

References 14 publications

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“…This assumption leads to the capacity versus outage problem which focuses on the tradeoff between the outage probability and the supportable rate; see, for example, [12], [13]. The practice of ignoring data received during an 0018-9448/$20.00 © 2006 IEEE outage is supported by the fact that the outage probability matches well the error probability of actual codes [14], [15]. Consequently, we characterize the performance of a system design based on the concept of average reliable throughput (ART), defined as the average data rate assuming zero rate when the channel is in outage [2].…”

Section: Introductionmentioning

confidence: 96%

“…On the other hand, if , outage within is inevitable and the corresponding optimum power allocation is the truncated channel inversion (14) where is a subset of better channel states in , i.e., and implies . Moreover, the set is chosen to satisfy the average power constraint (15) Note that is not defined for and . This is due to the fact that, in the vicinity of , the channel is too poor to support any positive rate.…”

Section: System Model and Problem Formulationmentioning

confidence: 99%

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Adaptive transmission with finite code rates

Lin¹,

Yates

Spasojević

2006

IEEE Trans. Inform. Theory

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Abstract-This work examines a transmission system which adapts a finite set of code rates and a continuously varying transmit power. We propose a technique for finding the average reliable throughput (ART)-maximizing policy satisfying an average power constraint for a slow fading additive white Gaussian noise (AWGN) channel. ART is a measure motivated by the information outage and can, for example, be argued to characterize the long-term average throughput of a data packet transmission system with a transmit queue and a feedback protocol which requests retransmission of erroneously received packets.Given the size of the code rate set , the ART-maximizing policy has the following properties.1. For a given set of code rates, the optimum allocation policy suggests quantizing the fading state space into a set of +1 corresponding intervals. For each quantization interval the optimal policy specifies a minimum transmitted power assignment which guarantees zero information outage. The optimum average power assignments across quantization intervals have a waterfilling relationship with respect to the interval channel quality measure. The joint optimization of quantization intervals and thecorresponding rate assignments are shown to have multiple local maxima. Nevertheless, this optimization problem can be reduced to a simple one-dimensional search over a parameter which determines the outage interval. Numerical results show that, in a Rayleigh-fading channel, there is only a 1-dB gap between the ergodic capacity and the throughput of a two-rate adaptive transmission system when the throughput is less than 6 bits/s/Hz. A special case of our optimal policy assignment is the optimal power and rate policy for an adaptive -QAM system. Index Terms-Adaptive coded modulation, adaptive transmission, average reliable throughput (ART), bit loading, block-fading channels, delayed constrained communications, information outage, -QAM.

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Section: Introductionmentioning

confidence: 96%

Section: System Model and Problem Formulationmentioning

confidence: 99%

Adaptive transmission with finite code rates

Lin¹,

Yates

Spasojević

2006

IEEE Trans. Inform. Theory

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“…The corresponding information-theoretic limit is the outage probability, and the design of efficient coded modulation schemes for the block-fading channel is based on approaching the outage probability. In [46], it was proved that the outage probability for sufficiently large snr behaves as 6) where d sb is the slope of the outage probability in a log-log scale and is given by the Singleton bound [61,70] …”

Section: Block-fadingmentioning

confidence: 99%

“…In order to apply our results on error exponents and error probability, we need to follow the approach of Malkämaki and Leib [70] and derive the error exponent for a particular channel realization. Then, the error probability (and not the error exponent) is averaged over the channel realizations.…”

Section: Block-fadingmentioning

confidence: 99%

“…In the fully interleaved MIMO channel, this metric can be used to characterize the mismatched decoding error exponents, capacity and error probability. In the quasi-static channel, we would need to compute the error exponent using the metric (6.9) at every channel realization, and derive the corresponding error probability as done in [70] in block-fading channels. Note, however, that the size of X j,t b is exponential with the number of transmit antennas, which can make decoding very complex.…”

Section: Mimomentioning

confidence: 99%

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Bit-Interleaved Coded Modulation

Fàbregas

Martinez

Caire

2007

FNT in Communications and Information Theory

186

165

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The principle of coding in the signal space follows directly from Shannon's analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal with errors introduced at the demodulator of the underlying waveform channel. The correct perspective of signal-space coding, although never out of sight of information theorists, was brought back into the focus of coding theorists and system designers by Imai's and Ungerböck's pioneering works on coded modulation. More recently, powerful families of binary codes with a good tradeoff between performance and decoding complexity have been (re-)discovered. Bit-Interleaved Coded Modulation (BICM) is a pragmatic approach combining the best out of both worlds: it takes advantage of the signal-space coding perspective, whilst allowing for the use of powerful families of binary codes with virtually any modulation format. BICM avoids the need for the complicated and somewhat less flexible design typical of coded modulation. As a matter of fact, most of today's systems that achieve high spectral efficiency such as DSL, Wireless LANs, WiMax and evolutions thereof, as well as systems based on low spectral efficiency orthogonal modulation, feature BICM, making BICM the de-facto general coding technique for waveform channels.The theoretical characterization of BICM is at the basis of efficient coding design techniques and also of improved BICM decoders, e.g., those based on the belief propagation iterative algorithm and approximations thereof. In this text, we review the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. This framework allows an accurate analysis without any particular assumptions on the length of the interleaver or independence between the multiple bits in a symbol. We further consider the sensitivity of the BICM capacity with respect to the signal-to-noise ratio (SNR), and obtain a wideband regime (or low-SNR regime) characterization. We review efficient tools for the error probability analysis of BICM that go beyond the standard approach of considering infinite interleaving and take into consideration the dependency of the coded bit observations introduced by the modulation. We also present bounds that improve upon the union bound in the region beyond the cutoff rate, and are essential to characterize the performance of modern randomlike codes used in concatenation with BICM. Finally, we turn our attention to BICM with iterative decoding, we review extrinsic information transfer charts, the area theorem and code design via curve fitting. We conclude with an overview of some applications of BICM beyond the classical coherent Gaussian channel. List of Abbreviations, Acronyms, and SymbolsRatio between average bit energy and noise spectral densityReliability function at rate R E bicm 0 (ρ, s) BICM random coding exponent E cm 0 (ρ) CM random coding exponent ...

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