The technology of error-correcting codes

Berlekamp, Elwyn R.

doi:10.1109/proc.1980.11696

Cited by 216 publications

(88 citation statements)

References 19 publications

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“…In addition to PCE, the symbol error probability P s , and the bit error prob ability Pb, are also important measures in evaluating system 78 performance [17]. An exact expression for either P, or P b is in general difficult to evaluate, since it depends to a large extent on the operation of the decoding algorithm.…”

Section: An Upper Bound To the Symbol And Bit Error Probabilitiesmentioning

confidence: 99%

“…To evaluate the performance of non-interleaved concate nated codes recall that the probability P, (m, n) of m erro neous received symbols at the input to the RS decoder is given by Equation (17). The generating series Fe and Fe for the sets of error symbols that produces a correct and erro neous received RS symbol for the outer channel are:…”

Section: Cecilio Pimentel Generating Series For Error Statistics Of Bmentioning

confidence: 99%

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Generating Series for Error Statistics of Block Codes on Channels with Memory

Pimentel¹

1998

JCIS

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-We present an analytical method for evaluating the performance of non-interleaved forward error correcting codes on channels that exhibit statistical dependence in the occurrence of errors. We consider a model for such a chan nel based on the probabilistic function of a Markov chain, also known as finite state channel (FSC) model. The main idea is to apply combinatorial methods to derive simple ex pressions for the probability of the number of symbol errors produced by the channel in terms of a coefficient in a formal power series. These methods are used to derive expressions for the codeword error probability of various practical cod ing schemes, including nonbinary block codes and the con catenation of two block codes. The general expressions are specialized for a Gilbert-Elliott channel with known model parameters, and numerical results are derived.Resumo -Apresentamos um rnetodo analftico para calcu lar 0 desempenho de c6digos corretores de erro em canais que exibem dependencia estatistica na sequencia de erro. Con sideramos um modelo para tais canais baseado em funcoes probabilfsticas de uma Cadeia de Markov, tambem conhecido como modelo de canais de estados finitos (FSC). A ideia cen tral consiste em aplicar metodos enumerativos para derivar expressces para a probabilidade de erro em tennos de coe ficientes especfficos de urna serie de potencia formal. Este metodo e aplicado para calcular 0 desempenho de varies esquemas de codificacao, incluindo c6digos nao binaries e c6digos concatenados.

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Section: An Upper Bound To the Symbol And Bit Error Probabilitiesmentioning

confidence: 99%

Section: Cecilio Pimentel Generating Series For Error Statistics Of Bmentioning

confidence: 99%

Generating Series for Error Statistics of Block Codes on Channels with Memory

Pimentel¹

1998

JCIS

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“…The advantages of concatenated codes using ReedSolomon outer codes and either short block codes or shortconstraint-length convolutional codes as inner codes are well documented [1], and such codes are widely used. The novel feature of our work is the required imbalance in the numbers of ones and zeroes in the codewords.…”

mentioning

confidence: 99%

“…The probability of decoding the inner code incorrectly depends on the details of the distance structure, which is complicated. We obtain an approximation to this error probability using the tangential union bound described in [1], a bound believed to be tight.…”

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confidence: 99%

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An Error-Control Code with an Imbalance of Ones and Zeros to Provide a Residual Carrier Component

Berlekamp

Currie²,

McEliece

et al. 1986

MILCOM 1986 - IEEE Military Communications Conference: Communications-Computers: Teamed for the 90's

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We consider in this paper a direct sequence spreadspectrum communication system employing an errorcontrol code having an imbalance of ones and zeroes. The primary motivation for using such a code is to provide a carrier component for synchronization as an alternative to the transmisson of a separate pilot tone. We evaluate the performance of this system when a concatenated code whose inner code is a constant-weight subcode of the (24, 12) extended Golay code and whose outer code is a ReedSolomon code. We consider the effects of both white Gaussian noise and burst jamming, and we evaluate several decoding algorithms with different complexities and different coding gains. Near-maximum-likelihood decoding can be realized at the lowest data rates of interest, while successively less complicated algorithms achieving corresponding smaller coding gains must be used as the data rate increases. The performance of this system compares favorably with that of a more conventional pilottone system.

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Gallager bounds on the performance of maximum‐likelihood decoded linear binary block codes in AWGN interference

Yousefi

2006

Trans Emerging Tel Tech

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SUMMARYPerformance evaluation of maximum-likelihood (ML) soft-decision-decoded binary block codes is usually carried out using bounding techniques. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). In this method, Gallager bisects the error probability to the joint probability of error and noise residing in a region < (here referred to as the Gallager region) plus joint probability of error and noise residing in the complement of < (also referred to as regions of many and few errors, respectively); where < is a volume around the transmitted codeword. In this tutorial review, a comprehensive study of a number of upper bounds on the error probability of ML decoding of binary codes based on GFBT is provided. For some bounds, their applicability to other schemes is also pointed out and argued. We also provide an overview of bounds based on Gallager's second bounding technique (GSBT) and discuss some of their relations and interconnections.

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The technology of error-correcting codes

Cited by 216 publications

References 19 publications

Generating Series for Error Statistics of Block Codes on Channels with Memory

Generating Series for Error Statistics of Block Codes on Channels with Memory

An Error-Control Code with an Imbalance of Ones and Zeros to Provide a Residual Carrier Component

Gallager bounds on the performance of maximum‐likelihood decoded linear binary block codes in AWGN interference

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