Analysis of Low-Density Parity-Check Codes for the Gilbert–Elliott Channel

Eckford, Andrew W.; Kschischang, Frank R.; Pasupathy, S.

doi:10.1109/tit.2005.856934

Cited by 66 publications

(77 citation statements)

References 15 publications

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“…FSMC models enable implementation of mathematically tractable channel estimation and data decoding algorithms for time-varying fading channels [35], [37]. Decoding algorithms for conventional turbo codes and low-density parity-check (LDPC) codes have been modified in [30], [31], and [32], respectively, to take into account FSMC state estimation, and it is shown that information rates higher than the memoryless channel capacity become possible. More recently, successive decoding is proposed for fading channels modeled by FSMCs that takes channel memory into account [33].…”

Section: Historical Background On Applications Of Fsmc Models For Fadmentioning

confidence: 99%

“…Incorporating the GEC and FSMC model into the message passing in LDPC decoding has been studied in [34] and [31], respectively and superior error rate performance compared to decoding techniques that do not take channel statistics into account is shown. In [32], density evolution analysis is extended from memoryless channels to the GEC, which can be used to determine the region of GEC parameters over which LDPC decoding is successful.…”

Section: Proposed Techniquesmentioning

confidence: 99%

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Finite-state Markov modeling of fading channels - a survey of principles and applications

Sadeghi

Kennedy

Rapajic

et al. 2008

IEEE Signal Process. Mag.

422

313

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In late 1950s and early 1960s, Gilbert and Elliott at Bell Labs were modeling burst-noise telephone circuits with a very simple two-state channel model with memory. This simple model allowed them to evaluate channel capacity and error rate performance through bursty wireline telephone circuits. However, it took another 30 years for the so-called Gilbert-Elliott channel (GEC) and its generalized finite-state Markov channel (FSMC) to be applied in the design of second-generation (2G) wireless communication systems. Since the mid 1990s, the GEC and FSMC models have been widely used for modeling wireless flat-fading channels in a variety of applications, ranging from modeling channel error bursts to decoding at the receiver. FSMC models are versatile, and with suitable choices of model parameters, can capture the essence of time-varying fading channels. This article's goal is to provide an in-depth understanding of the principles of FSMC modeling of fading channels with its applications in wireless communication systems. Digital Object Identifier 10.1109/MSP.2008 [ Parastoo Sadeghi, Rodney A. Kennedy, Predrag B. Rapajic, and Ramtin Shams ] While the emphasis is on frequency nonselective or flat-fading channels, this understanding will be useful for future generalizations of FSMC models for frequency-selective fading channels. The target audience of this article include both theory-and practice-oriented researchers who would like to design accurate channel models for evaluating the performance of wireless communication systems in the physical or media access control layers, or those who would like to develop more efficient and reliable transceivers that take advantage of the inherent memory in fading channels. Both FSMC models and flat-fading channels will be formally introduced. However, a background in time-varying fading communication channels is beneficial.We consider the FSMC modeling of fading channels from five distinct viewpoints. First, we provide a brief history of FSMC models and the FSMC modeling of flat-fading channels. Second, we define the parameters of FSMC models and discuss how these parameters can be derived from flat-fading channel statistics. We point out the trade-offs between model accuracy and complexity. Third, we categorize applications of FSMC models for fading channels into four categories and discuss the FSMC model applicability and accuracy in each application. We pay special attention to the effect of FSMC memory order on the model accuracy. Fourth, we consider the information-theoretical aspects of FSMC models and the FSMC modeling of fading channels. Finally, we present open questions and directions for future research. For easier access to the technical contents, the reader can refer to the "List of Acronyms" and "Notational Conventions." THE HISTORY OF FSMC 1957-1968: DEVELOPMENT OF FSMC MODELSThe study of finite-state communication channels with memory dates back to the work by Shannon in 1957 [1]. In [1], Shannon proved coding theorems for finite-state channels (FSCs) with discret...

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Section: Historical Background On Applications Of Fsmc Models For Fadmentioning

confidence: 99%

Section: Proposed Techniquesmentioning

confidence: 99%

Finite-state Markov modeling of fading channels - a survey of principles and applications

Sadeghi

Kennedy

Rapajic

et al. 2008

IEEE Signal Process. Mag.

422

313

View full text Add to dashboard Cite

show abstract

“…2 Lemma 4: Let C be an (n, M, d) binary linear quasi-perfect code to be used over the Markov noise channel. Assume that…”

Section: Decoding Of Quasi-perfect Codesmentioning

confidence: 99%

“…3 In light of the above result and Lemma 2, we next propose the following complete decoder that improves over MD decoding. It includes SMD decoding and exploits 2 Recall that the ML and MD decoders are complete decoders -i.e., they always select a codeword to decode the received word -while the SML and SMD decoders are incomplete decoders as they declare a decoding failure when there are more than one codeword with minimal decoding metric. 3 In contrast, recall that for the BSC(p) with p < 1/2, SML and SMD decoding are equivalent for all binary codes (the same equivalence also holds between ML and MD decoding).…”

Section: Decoding Of Quasi-perfect Codesmentioning

confidence: 99%

“…Progress has been achieved on the statistical and information theoretic modeling of channels with memory (e.g., see [1], [6], [10], [11]), as well as on the design of effective iterative decoders for such channels (e.g., see [2], [3], [7], [8]). However, little is known about the structure of optimal maximum likelihood (ML) decoders for such channels.…”

Section: Introductionmentioning

confidence: 99%

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On Decoding Binary Quasi-Perfect Codes Over Markov Noise Channels

Al-Lawati¹,

Alajaji²

2007

2007 10th Canadian Workshop on Information Theory (CWIT)

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Abstract-We study the decoding problem when a binary linear quasi-perfect code is transmitted over a binary channel with additive Markov noise. After examining the properties of the channel block transition distribution, we show a near equivalence relationship between strict maximum likelihood and strict minimum Hamming distance decoding for a range of channel parameters and the code's minimum distance. As a result, an improved minimum distance decoder is proposed and simulations illustrating its benefits are provided.

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Decoding of Product Codes in Discrete and Semi-continuous Channels with Memory

Fominykh,

Ovchinnikov

2024

Lecture Notes in Computer Science

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Analysis of Low-Density Parity-Check Codes for the Gilbert–Elliott Channel

Cited by 66 publications

References 15 publications

Finite-state Markov modeling of fading channels - a survey of principles and applications

Finite-state Markov modeling of fading channels - a survey of principles and applications

On Decoding Binary Quasi-Perfect Codes Over Markov Noise Channels

Decoding of Product Codes in Discrete and Semi-continuous Channels with Memory

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