Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference

Forney, Jr. G.D.

doi:10.1109/tcom.1972.1091101

Cited by 102 publications

(35 citation statements)

References 2 publications

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“…Note that this was expected, since the matrix multiplication in (4) is actually a matched filtering [1], [33], [34]. Reminiscent of the notation used for ISI channels which, as shown in the following, is a particular case of the very general model (1), we will call y and x as Forney and Ungerboeck observation models, respectively [33], [34]. The system model corresponding to (1) is…”

Section: Maximum-a-posteriori Symbol Detectionmentioning

confidence: 99%

SISO Detection Over Linear Channels With Linear Complexity in the Number of Interferers

Colavolpe

Fertonani

Piemontese

2011

IEEE J. Sel. Top. Signal Process.

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Abstract-We consider detection over linear channels impaired by additive white Gaussian noise. For this general model, which describes a large variety of scenarios, novel detection algorithms are derived by applying the sum-product algorithm to a suitablydesigned factor graph. Being soft-input soft-output (SISO) in nature, the proposed detectors can be adopted in turbo processing without additional modifications. Among various applications, we focus on channels with known intersymbol interference, on frequency-division-multiplexed systems where adjacent signals are allowed to overlap in frequency to increase the spectral efficiency, and on code division multiple access systems. When compared with the existing interference-cancellation algorithms, the proposed schemes result very appealing in terms of tradeoff between performance and computational complexity. Particularly, the proposed schemes can approach or even outperform the performance provided by much more complex algorithms.

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Section: Maximum-a-posteriori Symbol Detectionmentioning

confidence: 99%

SISO Detection Over Linear Channels With Linear Complexity in the Number of Interferers

Colavolpe

Fertonani

Piemontese

2011

IEEE J. Sel. Top. Signal Process.

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“…In [9,2], a lower bound was derived on the symbol error probability achieved by the Viterbi equalizer for an ISI channel when no a priori information is available. By following the reasoning of [9,2], we can derive expressions of tight lower bounds on the BER of the a posteriori LLRs at the output of the MAP sequence equalizer when it is fed with a priori LLRs.…”

Section: Gaussian Approximation At the Output Of The Equalizermentioning

confidence: 99%

“…By following the reasoning of [9,2], we can derive expressions of tight lower bounds on the BER of the a posteriori LLRs at the output of the MAP sequence equalizer when it is fed with a priori LLRs. We can show that…”

Section: Gaussian Approximation At the Output Of The Equalizermentioning

confidence: 99%

A Proof of Convergence of the MAP Turbo-Detector to the AWGN Case

Sellami

Roumy

Fijalkow

2008

IEEE Trans. Signal Process.

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In this paper, we consider a coded transmission over a frequency selective channel. We propose to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We show that the densities of the extrinsic Log Likelihood Ratios (LLRs) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to perform a one-dimensional (1-D) analysis of the turbo-detector. By deriving the analytical expressions of the extrinsic LLR distributions under the Gaussian approximation, we prove that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded Additive White Gaussian Noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency selective channel. EDICS:• PERF Performance analysis and bounds• CEST Channel estimation and equalization• MODL Modulation and encoding * This work was supported by the INRIA-DGRSRT program under Grant 05 I 17 and by the EU 6th framework program, via the NEWCOM network of excellence under project 507325. Parts of this paper were presented at the SPAWC'05 and EUSIPCO'06 conferences.

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“…The decoder is therefore called the genie decoder. The main motivation for us to investigate the genie decoder is to get a BEP performance lower bound, since the genie-aided decoding should outperform these without a genie aid [29]. Also, as we will show, the performance bound for the genie decoder is quite straightforward to evaluate, and it is tight for practical BEP regions (below 10 −2 ).…”

Section: A Genie-aided Decodermentioning

confidence: 90%

“…We assume the sink knows the error pattern of each finalhop codeword from a genie [29]. The decoder is therefore called the genie decoder.…”

Section: A Genie-aided Decodermentioning

confidence: 99%

Optimal Decoding and Performance Analysis of a Noisy Channel Network with Network Coding

Xiao

Aulin

2009

IEEE Trans. Commun.

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Abstract-We investigate sink decoding approaches and performance analysis for a network with intermediate node encoding (coded network). The network consists of statistically independent noisy channels. The sink bit error probability (BEP) is the performance measure. First, we investigate soft-decision decoding without statistical information on the upstream channels (the channels not directly connected to the sink). Numerical results show that the decoder cannot significantly improve the performance from a hard-decision decoder. We develop union bounds for analysis. The bounds show the asymptotic (regarding SNR: signal-to-noise ratio) performance of the decoder. Using statistical information about the upstream channels, we can find the error patterns of final hop channels (channels directly connected to sinks). With the error patterns, maximum-likelihood (ML) decoding can be performed, and a significant improvement in the BEP is obtained. To evaluate the union bound for the ML decoder, we use an equivalent point procedure. It is reduced to the least-squares problem with a linear constraint in the mediumto-high SNR region. With deterministic knowledge of the errors in the upstream channels, a genie-aided decoder can further improve the performance. We give the union bound for the genie decoder, which is straightforward to evaluate. By analyzing these decoders, we find that knowledge about the upstream channels is essential for good sink decoding.Index Terms-Network coding, noisy channel, optimal decoding, bit error probability, transmitted energy and analysis bounds.

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Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference

Cited by 102 publications

References 2 publications

SISO Detection Over Linear Channels With Linear Complexity in the Number of Interferers

SISO Detection Over Linear Channels With Linear Complexity in the Number of Interferers

A Proof of Convergence of the MAP Turbo-Detector to the AWGN Case

Optimal Decoding and Performance Analysis of a Noisy Channel Network with Network Coding

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