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

Sason, Igal; Shamai, Shlomo

doi:10.1561/0100000009

Cited by 119 publications

(136 citation statements)

References 168 publications

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“…For a detailed review of the ML performance bounds, see [21]. Here, we adapt a version of the bound in [12] given by…”

Section: Performance Upper Boundsmentioning

confidence: 99%

Randomized Convolutional Codes for the Wiretap Channel

Nooraiepour¹,

Duman²

2017

IEEE Trans. Commun.

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Abstract-We study application of convolutional codes to the randomized encoding scheme introduced by Wyner as a way of confusing the eavesdropper over a wiretap channel. We describe optimal and practical sub-optimal decoders for the main and the eavesdropper's channels, and estimate the security gap, which is used as the main metric. The sub-optimal decoder works based on the trellis of the code generated by a convolutional code and its dual, where one encodes the data bits and the other encodes the random bits. By developing a code design metric, we describe how these two generators should be selected for optimal performance over a Gaussian wiretap channel. We also propose application of serially concatenated convolutional codes to this setup so as to reduce the resulting security gaps. Furthermore, we provide an analytical characterization of the system performance by extending existing lower and upper bounds for coded systems to the current randomized convolutional coding scenario. We illustrate our findings via extensive simulations and numerical examples, which show that the newly proposed coding scheme can outperform the other existing methods in the literature in terms of security gap.

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“…For a detailed review of the ML performance bounds, see [21]. Here, we adapt a version of the bound in [12] given by…”

Section: Performance Upper Boundsmentioning

confidence: 99%

Randomized Convolutional Codes for the Wiretap Channel

Nooraiepour¹,

Duman²

2017

IEEE Trans. Commun.

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“…In order to get the tightest bound within the form (19), one needs to optimize the radius r. This optimization is carried by setting to zero the derivative of the RHS of (19) w.r.t. r, which yields the following optimization equations ( [14]):…”

Section: The Tangential-sphere Boundmentioning

confidence: 99%

“…In [15, Appendix C], Sason and Shamai derive an upper bound on the bit error probability by replacing the distance spectrum {A k } in (19) and (21) with the sequence {A ′ k }, and show some properties on the resulting bound on the bit error probability.…”

Section: The Tangential-sphere Boundmentioning

confidence: 99%

“…where 0 ≤ ρ ≤ 1 and λ ≥ 0 (see [8,19]; in order to make the presentation self-contained, it will be introduced shortly in the next section as part of the preliminary material). Here, ψ m N (y) is an arbitrary probability tilting measure (which may depend on the transmitted codeword c m ), and p N (y|c) designates the transition probability measure of the channel.…”

Section: Introductionmentioning

confidence: 99%

“…We conclude our discussion in Section 6. For an extensive tutorial paper on performance bounds of linear codes, the reader is referred to [19].…”

Section: Introductionmentioning

confidence: 99%

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Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

Twitto

Sason

Shamai

2006

2006 IEEE International Symposium on Information Theory

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The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and outputsymmetric communication channel, and their effectiveness is exemplified for various ensembles of turbo-like codes over the AWGN channel. An expurgation of the distance spectrum of binary linear block codes further tightens the resulting upper bounds.

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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 119 publications

References 168 publications

Randomized Convolutional Codes for the Wiretap Channel

Randomized Convolutional Codes for the Wiretap Channel

Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

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

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