On information rates for mismatched decoders

Merhav, Neri; Kaplan, G.; Lapidoth, Amos; Shitz, Shlomo Shamai

doi:10.1109/18.340469

Cited by 323 publications

(67 citation statements)

References 23 publications

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“…An information-theoretic analysis of the NLS channel is cumbersome because of a complicated signal-noise interaction caused by the interplay between the nonlinearity and the dispersion [2]. In general, capacity analyses of optical fibers are performed either by considering simplified channels, or by evaluating mismatched decoding lower bounds [3] via simulations (see [4] and ( [5], Sec. I) for excellent literature reviews).…”

Section: Introductionmentioning

confidence: 99%

Accuracy Assessment of Nondispersive Optical Perturbative Models through Capacity Analysis

Keykhosravi¹,

Durisi²,

Agrell³

2019

Entropy

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A number of simplified models, based on perturbation theory, have been proposed for the fiber-optical channel and have been extensively used in the literature. Although these models are mainly developed for the low-power regime, they are used at moderate or high powers as well. It remains unclear to what extent the capacity of these models is affected by the simplifying assumptions under which they are derived. In this paper, we consider single-channel data transmission based on three continuous-time optical models: (i) a regular perturbative channel, (ii) a logarithmic perturbative channel, and (iii) the stochastic nonlinear Schrödinger (NLS) channel. To obtain analytically tractable discrete-time models, we consider zero-dispersion fibers and a sampling receiver. We investigate the per-sample capacity of these models. Specifically, (i) we establish tight bounds on the capacity of the regular perturbative channel; (ii) we obtain the capacity of the logarithmic perturbative channel; and (iii) we present a novel upper bound on the capacity of the zero-dispersion NLS channel. Our results illustrate that the capacity of these models departs from each other at high powers because these models yield different capacity pre-logs. Since all three models are based on the same physical channel, our results highlight that care must be exercised in using simplified channel models in the high-power regime.

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Section: Introductionmentioning

confidence: 99%

Accuracy Assessment of Nondispersive Optical Perturbative Models through Capacity Analysis

Keykhosravi¹,

Durisi²,

Agrell³

2019

Entropy

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“…Lapidoth [59] showed that -capacity can equal the channel capacity even if the above lower bound is strictly smaller. Other recent works addressing the problem of -capacity or its special case of zero undetected error capacity include Merhav, Kaplan, Lapidoth, and Shamai [67], Ahlswede, Cai, and Zhang [9], as well as Telatar and Gallager [77].…”

Section: Related Further Resultsmentioning

confidence: 99%

The method of types [information theory]

Csiszár

1998

IEEE Trans. Inform. Theory

328

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The method of types is one of the key technical tools in Shannon Theory, and this tool is valuable also in other fields. In this paper, some key applications will be presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method, and a wide selection of further applications will be surveyed. These range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems. While the method of types is suitable primarily for discrete memoryless models, its extensions to certain models with memory will also be discussed.Index Terms-Arbitrarily varying channels, choice of decoder, counting approach, error exponents, extended type concepts, hypothesis testing, large deviations, multiuser problems, universal coding.

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“…(2.5) For equally likely codewords, this decoder finds the most likely codeword as long as the metric q(x, y) is a bijective (thus strictly increasing) function of the transition probability P Y |X (y|x) of the memoryless channel. Instead, if the decoding metric q(x, y) is not a bijective function of the channel transition probability, we have a mismatched decoder [41,59,84].…”

Section: Channel Model: Encoding and Decodingmentioning

confidence: 99%

“…As suggested in the previous chapter, BICM can be viewed as a coded modulation scheme with a mismatched decoding metric. We study the achievable information rates of coded modulation systems with a generic decoding metric [41,59,84] and determine the so-called generalized mutual information. We also provide a general coding theorem based on Gallager's analysis of the error probability by means of the random coding error exponent [39], thus giving an achievable rate and a lower bound to the random coding error exponent.…”

Section: Information-theoretic Foundationsmentioning

confidence: 99%

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Bit-Interleaved Coded Modulation

Fàbregas¹,

Martínez²,

Caire³

2007

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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 signalspace 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 work 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 monograph, 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.6 Applications 122 6.

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On information rates for mismatched decoders

Cited by 323 publications

References 23 publications

Accuracy Assessment of Nondispersive Optical Perturbative Models through Capacity Analysis

Accuracy Assessment of Nondispersive Optical Perturbative Models through Capacity Analysis

The method of types [information theory]

Bit-Interleaved Coded Modulation

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