Uniform asymptotics of Poisson approximation to the Poisson-binomial distribution

Hwang, Hsien‐Kuei; Zacharovas, Vytas

doi:10.4213/tvp4202

“…where the inequality (a) is obtained by applying Lemma 33. From [45], we know that I λ n (t, n − t + 1) converges to φ(t − 1, λ) uniformly for λ ∈ [0, 3ρ]. For any > 0, there exists a…”

Section: B Noise Threshold Of Iterative Hdd When N < ∞mentioning

confidence: 99%

Approaching Capacity at High Rates with Iterative Hard-Decision Decoding

Jian

¹

,

Pfister

²

,

Narayanan

³

2017

IEEE Trans. Inform. Theory

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Abstract-A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., nonbinary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).

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“…In one-dimensional case, squared ℓ 2 -norm was used in the seminal paper of Franken [6] and the closeness of binomial and Poisson distributions was thoroughly investigated in [7] for an analogue of ℓ α -norm for even more general case of α ∈ (0, ∞).…”

Section: Some Known Resultsmentioning

confidence: 99%

“…Numerous papers are devoted to Poisson and compound Poisson approximations in one-dimensional case, see, for example, a survey [12]. Various metrics, such as local, Wasserstein metric, chi-square metric and analogues of ℓ p norms were used, see, for example, [2,3,7,8].…”

Section: Introductionmentioning

confidence: 99%

Compound Poisson approximations in $\ell_p$-norm for sums of weakly dependent vectors

Čekanavičius¹,

Vellaisamy²

2020

Preprint

0

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show abstract

“…From [45], we know that I λ n (t, n − t + 1) converges to φ(t − 1, λ) uniformly for λ ∈ [0, 3ρ]. For any > 0, there exists a…”

Section: B Noise Threshold Of Iterative Hdd When N < ∞mentioning

confidence: 99%

Approaching capacity at high rates with iterative hard-decision decoding

Jian

¹

,

Pfister

²

,

Narayanan

³

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Abstract-A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., nonbinary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).

show abstract

Uniform asymptotics of Poisson approximation to the Poisson-binomial distribution

Cited by 5 publications

References 31 publications

Approaching Capacity at High Rates with Iterative Hard-Decision Decoding

Approaching Capacity at High Rates with Iterative Hard-Decision Decoding

Compound Poisson approximations in $\ell_p$-norm for sums of weakly dependent vectors

Approaching capacity at high rates with iterative hard-decision decoding

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