Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial

Sason, Igal; Shamai, Shlomo

doi:10.1561/9781933019796

Cited by 70 publications

(120 citation statements)

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“…Finally, we conclude this chapter with a brief section outlining possible extensions of the union bound for BICM to the region beyond the cutoff rate. We chiefly use the results reported in Sason and Shamai's monograph on improved bounds beyond the cutoff rate [101].…”

Section: Error Probability Analysismentioning

confidence: 99%

“…Spurred by the appearance of turbo-codes [11] and the rediscovery of LDPC codes [69], there has been renewed interest in the past decade in the derivation of improved bounds for a region above the cutoff rate. A comprehensive review can be found in the monograph by Sason and Shamai [101]. In this section, we briefly discuss such bounds for BICM.…”

Section: Bounds and Approximations Above The Cutoff Ratementioning

confidence: 99%

“…This effect translates into a reduced rate of decay of the error probability with SNR. We have then reviewed improved bounds to the error probability like the Duman-Salehi and the tangential-sphere bound [101]. We have given the expression of the former for a general decoding metric, while the latter is an approximate bound based on the Gaussian approximation of the tail of the decoding score distribution.…”

Section: Concluding Remarks and Related Workmentioning

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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Section: Error Probability Analysismentioning

confidence: 99%

Section: Bounds and Approximations Above The Cutoff Ratementioning

confidence: 99%

Section: Concluding Remarks and Related Workmentioning

confidence: 99%

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Bit-Interleaved Coded Modulation

Fàbregas¹,

Martínez²,

Caire³

2007

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“…Upper bounds on the maximum a posteriori (MAP) decoding error probability, as a key technique for evaluating the performance of the binary linear codes over additive white Gaussian noise (AWGN) channels, bring a profound impact on the reliable transmission of the next-generation mobile communication systems since they can be used to not only predict the performance without resorting to computer simulations but also guide the design of coding [1]. In order to improve the looseness of the union bound in the low signal-to-noise ratio (SNR) region, many improved upper bounds, on the bit error probability [2][3][4][5] and on the frame error probability [2][3][4][6][7][8][9][10][11][12][13][14][15], are proposed.…”

Section: Introductionmentioning

confidence: 99%

“…In order to improve the looseness of the union bound in the low signal-to-noise ratio (SNR) region, many improved upper bounds, on the bit error probability [2][3][4][5] and on the frame error probability [2][3][4][6][7][8][9][10][11][12][13][14][15], are proposed. As surveyed in [1], the improved upper bounds on the bit error probability [2][3][4] are based on Gallager's first bounding technique (GFBT):…”

Section: Introductionmentioning

confidence: 99%

Upper Bound on the Bit Error Probability of Systematic Binary Linear Codes via Their Weight Spectra

Liu

Zhang

Wang

et al. 2020

Discrete Dynamics in Nature and Society

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In this paper, upper bound on the probability of maximum a posteriori (MAP) decoding error for systematic binary linear codes over additive white Gaussian noise (AWGN) channels is proposed. The proposed bound on the bit error probability is derived with the framework of Gallager’s first bounding technique (GFBT), where the Gallager region is defined to be an irregular high-dimensional geometry by using a list decoding algorithm. The proposed bound on the bit error probability requires only the knowledge of weight spectra, which is helpful when the input-output weight enumerating function (IOWEF) is not available. Numerical results show that the proposed bound on the bit error probability matches well with the maximum-likelihood (ML) decoding simulation approach especially in the high signal-to-noise ratio (SNR) region, which is better than the recently proposed Ma bound.

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Seek and decode: Random access with physical‐layer network coding and multiuser detection

Cocco

Pfletschinger

Navarro

2016

Trans. Emerging Tel. Tech.

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We present a novel cross layer approach to random access (RA) that combines physical-layer network coding (PLNC) with multiuser detection (MUD). PLNC and MUD are applied jointly at the physical level in order to extract any linear combination of messages experiencing a collision. The set of combinations extracted from a whole frame is then processed by the receiver to recover the original packets. A simple pre-coding stage at the transmitting terminals allows the receiver to further increase system diversity. We derive an analytical bound on the system throughput and present simulation results for the decoding at the physical level as well as several performance measures at frame level in block fading channels, namely throughput, packet loss rate and energy efficiency. The results we present are promising and suggest that a cross layer approach leveraging on the joint use of PLNC and MUD can significantly improve the performance of RA systems.

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Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial

Cited by 70 publications

References 0 publications

Bit-Interleaved Coded Modulation

Bit-Interleaved Coded Modulation

Upper Bound on the Bit Error Probability of Systematic Binary Linear Codes via Their Weight Spectra

Seek and decode: Random access with physical‐layer network coding and multiuser detection

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