Titlebook: Codes, Systems, and Graphical Models; Brian Marcus,Joachim Rosenthal Conference proceedings 2001 Springer Science+Business Media New York

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https://doi.org/10.1007/978-3-030-83236-0when decoded with a simple erasure decoder described in the paper. We will prove a necessary property called . for a sequence of degree distributions to be capacity-achieving, and will comment on possible applications to the design of capacity-achieving sequences on other communication channels.

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Ehab Al-Shaer,Mohammad Ashiqur Rahmant resembles the classical union bound, but unlike the union bound, our method is powerful enough to prove Shannon’s theorem for the ensemble of random linear codes. We apply our method to find numerical thresholds for the ensembles of low-density parity-check codes, and “repeat-accumulate” codes.

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Capacity-Achieving Sequenceswhen decoded with a simple erasure decoder described in the paper. We will prove a necessary property called . for a sequence of degree distributions to be capacity-achieving, and will comment on possible applications to the design of capacity-achieving sequences on other communication channels.

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BSC Thresholds for Code Ensembles Based on “Typical Pairs” Decodingt resembles the classical union bound, but unlike the union bound, our method is powerful enough to prove Shannon’s theorem for the ensemble of random linear codes. We apply our method to find numerical thresholds for the ensembles of low-density parity-check codes, and “repeat-accumulate” codes.

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On Testing Data-Intensive Software Systems in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes.

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https://doi.org/10.1007/978-3-030-83236-0tail-biting trellis of the Golay code [2] is used for exampIes. Although in this case no pseudocodeword is found with effective weight less than the minimum Hamming weight of the Golay code on an AWGN channel, it is shown by example that the minimum effective pseudocodeword weight can be less than the minimum codeword weight.

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conference

Connections Between Linear Systems and Convolutional Codes in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes.

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