Extrinsic information transfer functions: model and erasure channel properties

Ashikhmin, Alexei; Kramer, Gerhard; Brink, Stephan ten

doi:10.1109/tit.2004.836693

Cited by 640 publications

(663 citation statements)

References 41 publications

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“…Since the channel is symmetric, it follows that (5) and (6) which is also true if contains Dirac delta functions. If a random variable satisfies (5) and (6) (5) and (6), it follows that the mutual information between and is (7) where the th conditional moment of the channel soft bit is defined by (8) Note that and therefore, the right-hand side of (7) is convergent. We also point out that the singularity of at does not affect the integral (7) since from (5) it follows that .…”

Section: -Consistency and Mutual Informationmentioning

confidence: 99%

“…As a special case, if all channels have the same distribution, the average extrinsic mutual information is (13) where the th moment is defined in (8).…”

Section: -Consistency and Mutual Informationmentioning

confidence: 99%

“…According to (7) and one can notice that the integrand is not continuous on . To avoid this problem, we use the map defined by .…”

Section: An Extremal Problem Of the Second Momentmentioning

confidence: 99%

“…A one-dimensional approximation method of density evolution, the extrinsic information transfer (EXIT) chart, originally suggested by ten Brink [6] for analyzing and designing turbo codes, was a simpler method for convergence prediction. In [7], [8], the EXIT chart method was extended for the analysis and design of LDPC codes, and a rigorous analysis of the method was conducted when the a priori channel is a binary erasure channel (BEC). VND and CND EXIT functions are defined to characterize how the mutual information contained in messages changes during the variable and check nodes processing at each iteration of the belief propagation decoding.…”

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confidence: 99%

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Extremal Problems of Information Combining

Jiang

Ashikhmin²,

Koetter

et al. 2008

IEEE Trans. Inform. Theory

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Abstract-In this paper, we study moments of soft bits of binary-input symmetric-output channels and solve some extremal problems of the moments. We use these results to solve the extremal information combining problem. Further, we extend the information combining problem by adding a constraint on the second moment of soft bits, and find the extremal distributions for this new problem. The results for this extension problem are used to improve the prediction of convergence of the belief propagation decoding of low-density parity-check (LDPC) codes, provided that another extremal problem related to the variable nodes is solved.Index Terms-Extrinsic information transfer (EXIT) functions, information combining, low-density parity-check (LDPC) codes.

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Section: -Consistency and Mutual Informationmentioning

confidence: 99%

“…As a special case, if all channels have the same distribution, the average extrinsic mutual information is (13) where the th moment is defined in (8).…”

Section: -Consistency and Mutual Informationmentioning

confidence: 99%

“…According to (7) and one can notice that the integrand is not continuous on . To avoid this problem, we use the map defined by .…”

Section: An Extremal Problem Of the Second Momentmentioning

confidence: 99%

mentioning

confidence: 99%

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Extremal Problems of Information Combining

Jiang

Ashikhmin²,

Koetter

et al. 2008

IEEE Trans. Inform. Theory

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“…Recent findings [18] have shown that the inner component of a serially concatenated Turbo scheme should be recursive and of rate 1. Thus, a recursive channel precoder [5], [6] with transfer function Gpre(D) = 1/(1 + D 2 ) as depicted in Fig.…”

Section: Equalization and Precodingmentioning

confidence: 99%

Iterative source-coded equalization: turbo error concealment for ISI channels

Schmalen

Clevorn

Vary

2007

2007 IEEE 8th Workshop on Signal Processing Advances in Wireless Communications

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In this paper, we analyze the behavior of soft decision source decoding for ISI channels and present an iterative scheme similar to Turbo equalization allowing to combat efficiently intersymbol interference effects. In a first step, we investigate the behavior of different index assignments in the quantizer and show that gains are possible by iterative processing without any channel (de)coding. In a second step, we use short block codes resulting in redundant index assignments at the transmitter. The receiver does not perform any explicit channel decoding but exploits the additional redundancy of the index assignment in the soft decision source decoder. Furthermore, we show that a very simple channel precoder permits even larger gains without any additional decoding complexity. Moreover, the extension towards a flexible multi-mode system allowing a trade-off between channel quality and quantization quality over a wide range of channel conditions is presented.

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Turbo Codes

2006

Essentials of Error‐Control Coding

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7Turbo Codes Berrou, Glavieux and Thitimajshima [1] introduced in 1993 a novel and apparently revolutionary error-control coding technique, which they called turbo coding. This coding technique consists essentially of a parallel concatenation of two binary convolutional codes, decoded by an iterative decoding algorithm. These codes obtain an excellent bit error rate (BER) performance by making use of three main components. They are constructed using two systematic convolutional encoders that are IIR FSSMs, usually known as recursive systematic convolutional (RSC) encoders, which are concatenated in parallel. In this parallel concatenation, a random interleaver plays a very important role as the randomizing constituent part of the coding technique. This coding scheme is decoded by means of an iterative decoder that makes the resulting BER performance be close to the Shannon limit.In the original structure of a turbo code, two recursive convolutional encoders are arranged in parallel concatenation, so that each input element is encoded twice, but the input to the second encoder passes first through a random interleaver [2,3]. This interleaving procedure is designed to make the encoder output sequences be statistically independent from each other. The systematic encoders are binary FSSMs of IIR type, as introduced in Chapter 6, and usually have code rate R c = 1/2. As a result of the systematic form of the coding scheme, and the double encoding of each input bit, the resulting code rate is R c = 1/3. In order to improve the rate, another useful technique normally included in a turbo coding scheme is puncturing of the convolutional encoder outputs, as introduced in Chapter 6.The decoding algorithm for the turbo coding scheme involves the corresponding decoders of the two convolutional codes iteratively exchanging soft-decision information, so that the information can be passed from one decoder to the other. The decoders operate in a soft-inputsoft-output mode; that is, both the input applied to each decoder, and the resulting output generated by the decoder, should be soft decisions or estimates [3]. Both decoders operate by utilizing what is called a priori information, and together with the channel information provided by the samples of the received sequence, and information about the structure of the code, they produce an estimate of the message bits. They are also able to produce an estimate called the extrinsic information, which is passed to the other decoder, information that in the following iteration will be used as the a priori information of the other decoder. Thus the first decoder generates extrinsic information that is taken by the second decoder as its a priori Essentials of Error-Control Coding

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Extrinsic information transfer functions: model and erasure channel properties

Cited by 640 publications

References 41 publications

Extremal Problems of Information Combining

Extremal Problems of Information Combining

Iterative source-coded equalization: turbo error concealment for ISI channels

Turbo Codes

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