Performance Analysis of Linear Codes under Maximum-Likelihood Decoding A Tutorial (Foundations and Trends(R) in Communications and Information Theory) by Igal Sason

Cover of: Performance Analysis of Linear Codes under Maximum-Likelihood Decoding | Igal Sason

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Subjects:

  • Communications engineering / telecommunications,
  • Technology,
  • Technology & Industrial Arts,
  • Science/Mathematics,
  • Information Theory,
  • Telecommunications,
  • Computers-Information Theory,
  • Technology / Telecommunications,
  • Coding theory,
  • Decoders (Electronics),
  • Error-correcting codes (Information theory)

Book details

The Physical Object
FormatPaperback
Number of Pages236
ID Numbers
Open LibraryOL8811999M
ISBN 101933019328
ISBN 109781933019321

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Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial focuses on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding.

Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer.

Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial focuses on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding.

Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their Cited by: Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial Article (PDF Available) in Foundations and Trends® in Communications and Information Theory 3(1/2).

Performance Analysis of Linear Codes Under Maximum-likelihood Decoding: A Tutorial. Abstract. The preferred citation for this publication is I.

Sason and S. Shamai, Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial, Foun-dation and Trends R in Communications and Information Theory, vol 3, no 1/2, pp 1–, Printed on acid-free paper ISBN: c I. Sason and S. Shamai All rights Cited by: The preferred citation for this publication is I.

Sason and S. Shamai, Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial, Foun-dation and Trends°R in Communications and Information Theory, vol 3, no 1/2, pp 1–, Printed on acid-free paper ISBN: °c I.

Sason and S. Shamai All rights. This article is focused on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for.

Performance analysis of linear codes under maximum likelihood decoding at low rates. Performance Analysis of Raptor Codes Under Maximum Likelihood Decoding Abstract: In this paper, we analyze the maximum likelihood decoding performance of Raptor codes with a systematic low-density generator-matrix code as the pre-code.

By investigating the rank of the product of two random coefficient matrices, we derive upper and lower bounds. Performance of space-time block codes can be improved using the coordinate interleaving of the input symbols from rotated M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) constellations.

This paper is on the performance analysis of coordinate-interleaved space-time codes, which are a subset of single-symbol maximum likelihood decodable linear space-time block.

Maximum Likelihood Decoding The ML decoding rule implicitly divides the received vectors into decoding regions known as Voronoi regions. TheVoronoiregion(i.e.,decisionregion)forthecodeword xn 1 2CisthesubsetofYn defined by V(xn 1), fyn 1 2Y njW(yn 1 jx n 1) >W(yn 1 jxe n 1) 8ex n 1 2C;ex n 1 6= x n 1 g: Inthiscase.

Get this from a library. Performance analysis of linear codes under maximum-likelihood decoding: a tutorial. [Igal Sason; Shlomo Shamai] -- This article is focused on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding.

Though the ML decoding algorithm is prohibitively complex for most practical. Other topics studied are related to fundamental and simple block codes, the algebra of linear block codes, binary cyclic codes and BCH codes, decoding techniques for binary BCH codes, nonbinary BCH codes and Reed-Solomon codes, the performance of linear block codes with bounded-distance decoding an introduction to convolutional codes, maximum.

Having covered the techniques of hard and soft decision decoding, its time to illustrate the most important concept of Maximum Likelihood Decoding. Maximum Likelihood Decoding: Consider a set of possible codewords (valid codewords – set) generated by an encoder in the transmitter side.

We pick one codeword out of this set (call Read more Maximum Likelihood Decoding. Key words Product codes, split enumerator, weight enumerator, maximum likelihood performance 1 Introduction Linear product codes are widely used in many commu-nication and data storage systems.

Elias has introduced product codes and suggested decoding them in an it-erative fashion. The product code of two linear block codes is a linear block code. In this chapter, we discussed the performance of codes under hard and soft decision decoding.

For hard decision decoding, the performance of codes in the binary symmetric channel was discussed and numerically evaluated results for the bounded distance decoder compared to the full decoder were presented for a range of codes whose coset leader weight distribution is known.

In maximum-likelihood decoding of a convolutional code, we must find the code sequence x(D) that gives the maximum-likelihood P(y(D)|x(D)) for the given received sequence y(D).The Viterbi algorithm is a method for obtaining the path of the trellis that corresponds to the maximum-likelihood code sequence.

Consider the two paths x(D) and x'(D) in the trellis that diverge at node level 0 and. of block and convolutional codes in terms of maximum-likelihood analytical upper bounds. Section V is devoted to the presentation of a new iterative decoding algorithm and to its application to some significant codes.

Performance comparison between SCCC’s and PCCC’s under suboptimum iterative decoding algorithms are presented in Section IV. Toshiyasu Matsushima's research works with citations and 1, reads, including: Bayes code for two-dimensional auto-regressive hidden Markov model and its application to lossless image.

These bounds are applied to various ensembles of turbo-like codes, focusing especially on repeat-accumulate codes and their recent variations which possess low encoding and decoding complexity and exhibit remarkable performance under iterative decoding.

Since the work of Shannon [], Maximum likelihood (ML) decoders have been it was established in the s that ML decoding of arbitrary linear codes is an NP-complete problem [], instead of seeking a universal, code book independent decoder, most codes are co-designed and developed with a specific decoder that is often an approximation of a ML decoder [3, 4].

an arbitrary code (linear or nonlinear) using maximum likelihood decoding is studied on binary erasure channels (BECs) with arbitrary erasure probability 0linear codes, which are equivalent to a concatenation of several Hadamard linear codes.

Many universal decoding algorithms have been proposed for the decoding of linear binary block codes. The decoding algorithms in [4, 5] are based on the testing and re-encoding of the information bits as initially considered by Dorsch.

In particular, a list of the likely transmitted codewords is generated using the reliabilities of the. parallel channel binary linear code independent parallel channel optimized tilting measure turbo-like code gallager bound new bound low encoding iterative decoding repeat-accumulate code memoryless parallel channel performance analysis asymptotic case improved inner bound special case attainable channel region single channel exhibit remarkable.

Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for soft-decision decoding methods which require a generator matrix with a particular structure such as trellis decoding, multistage decoding, or algebraic-based soft-decision.

algorithm [21], and the mRRD performance was obtained using parallel mRRD decoder [17]. We have a gap of dB to achieve maximum likelihood performance with our proposed decoder. Note, that the overall decoding time of our decoder is substantially smaller than the mRRD’s decoding time for the (63,36) code, with a factor of up to IEEE TRANSACTIONS ON INFORMATION THEORY, VOL.

51, NO. 3, MARCH Using Linear Programming to Decode Binary Linear Codes Jon Feldman, Martin J. Wainwright, Member, IEEE, and David R. Karger, Associate Member, IEEE Abstract—A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear.

their excellent performance under sum-product(SP) decoding (or message-passingdecoding). The primary research focus in this area to date has been on binary LDPC codes. Finite-length analysis of such LDPC codes under SP decoding is a difficult ta sk.

An approach to such an. This book has been written as lecture notes for students who need a grasp of the basic principles of linear codes. The scope and level of the lecture notes are considered suitable for under-graduate students of Mathematical Sciences at the Faculty of Mathematics, Natural Sciences and Information Technologies at the University of Primorska.

A new soft decision maximum-likelihood decoding algorithm, which generates the minimum set of candidate codewords by efficiently applying the algebraic decoder is proposed. As a result, the decoding complexity is reduced without degradation of performance.

The new algorithm is tested and verified by simulation results. This chapter provides design, analysis, construction, and performance of the turbo codes, serially concatenated codes, and turbo-like codes including the design of interleavers in concatenation of codes. Also this chapter describes the iterative decoding algorithms for these codes.

Lectures 2: The Maximum-Likelihood Decoding Performance of Error-Correcting Codes slides notes (working draft updated 11/21/13) Lectures Factor Graphs and Probabilistic Graphical Models slides lec4_scribe lec5_scribe. Lectures Gallager's Ensemble of LDPC Codes lec6_scribe lec7_scribe.

Density Evolution Handout with Exercises. 68 CHAPTER 6. LINEAR BLOCK CODES: ENCODING AND SYNDROME DECODING where | represents the horizontal “stacking” (or concatenation) of two matrices with the same number of rows.

⌅ Maximum-Likelihood (ML) Decoding Given a binary symmetric channel with bit-flip probability ", our goal is to develop a maximum-likelihood (ML) decoder. For a linear block code, an.

Topics. This book is mainly centered around algebraic and combinatorial techniques for designing and using error-correcting linear block codes.

It differs from previous works in this area in its reduction of each result to its mathematical foundations, and its clear exposition of. ￿ Maximum-Likelihood (ML) Decoding Given a binary symmetric channel with bit-flip probability ε, our goal is to develop a maximum-likelihood (ML) decoder.

For a linear block code, an ML decoder takes n re-ceived bits as input and returns the most likely k-bit message among the 2k possible mes-sages. the maximum likelihood (ML) decoding problem is to deter-mine the closest codeword (in Hamming distance). It is well known that ML decoding for general binary linear codes is NP-hard [2], which motivates the study of sub-optimal but practical algorithms for decoding.

LP decoding We now describe how the problem of optimal decoding. perfect codes. MacWilliams’ Theorem and performance In this section we relate weight enumerators to code performance. This leads to a rst proof of MacWilliams’ Theorem.

For easy of exposition, we shall restrict ourselves to the consideration of binary linear codes on the BSC(p) throughout this section. Let Cbe a binary [n;k] linear code. Belief Propagation Decoding The wlanHTDataRecover function implements the BP algorithm based on the decoding algorithm presented in [2].

0 bitmap image on the analysis and application of ldpc codes outline the error-control paradigm ldpc codes the code graph and iterative decoding decoding of ldpc codes slide 7 slide 8.

A code f Fk q F n q is a linear code if u Fkq, c u uG(row-vector convention), where G Fk n q. ∈ is a generator matrix ×} Proposition c∈C ⇔c row span of G c ∈ KerH; for some H F(n−k)×n q s.t. HG T 0: Note: For linear codes, the ⇔ co ∈ debook is a k-dimensional ∈ linear subspace = of Fn q (ImGor KerH).

The matrix His. A tight performance analysis is derived based on the theory of ordered statistics for this new approach.

Enhanced Box and Match Algorithm for Reliability-Based Soft-Decision Decoding of Linear Block Codes Wenyi Jin, Fossorier, M. Details; Contributors; code is about dB away from that of maximum likelihood decoding (MLD) at the word. book may be reproduced without prior permission from the author.

This book is set in LATEX. Performance of ML Decoding of Turbo Codes Performance analysis of differential detectors in Rayleigh flat fading chan.The obtained results offer a very powerful tool to reach near the maximum likelihood (ML) decoding performance in several cases such as lattice codes decoding over the Gaussian and Rayleigh fading channels, multiuser detection, uncoded multi-antenna systems detection and space-time codes decoding, and vector quantization.Performance analysis of linear codes under maximum-likelihood decoding: a tutorial I Sason, S Shamai Foundations and Trends® in Communications and Information Theory 3 (),

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