Hash Property and Fixed-Rate Universal Coding Theorems

Muramatsu, Jun; Miyake, Shojiro

doi:10.1109/tit.2010.2046214

Cited by 11 publications

(12 citation statements)

References 17 publications

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“…First, we construct the minimum-divergence encoder g AB B defined by (1). The following construction is presented in [19]. We use the fact that the analysis of error probability in the proof of theorems is not changed if we replace the minimum-divergence encoder g AB B by…”

Section: Maximum-likelihood Decoder and Minimum-entropy Decodermentioning

confidence: 99%

Construction of Codes for the Wiretap Channel and the Secret Key Agreement From Correlated Source Outputs Based on the Hash Property

Muramatsu

Miyake

2012

IEEE Trans. Inform. Theory

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The aim of this paper is to prove coding theorems for the wiretap channel and secret key agreement based on the the notion of a hash property for an ensemble of functions. These theorems imply that codes using sparse matrices can achieve the optimal rate. Furthermore, fixed-rate universal coding theorems for a wiretap channel and a secret key agreement are also proved. Index TermsShannon theory, hash property, linear codes, sparse matrix, maximum-likelihood decoding, minimum-divergence encoding, minimum-entropy decoding, secret key agreement from correlated source outputs, wiretap channel, universal codes I. INTRODUCTIONThe aim of this paper is to prove the coding theorems for the wiretap channel (Fig. 1) introduced in [23] and secret key agreement problem (Fig. 2) introduced in [12][1]. The proof of theorems is based on the notion of a hash property for an ensemble of functions introduced in [18][19]. This notion provides a sufficient condition for the achievability of coding theorems. Since an ensemble of sparse matrices has a hash property, we can construct codes by using sparse matrices where the rate of codes is close to the optimal rate. In the construction of codes, we use minimum-divergence encoding, maximum-likelihood decoding, and minimum-entropy decoding, where we can use the approximation methods introduced in [9][5] to realize these operations.Wiretap channel coding using a sparse matrices is studied in [21] for binary erasure wiretap channels. On the other hand, our construction can be applied to any stationary memoryless channel. It should be noted here that the encoder design is based on the standard channel code presented in [14][18][19] [13]. Furthermore, we prove the fixed-rate universal coding theorem for a wiretap channel, where our construction is reliable and secure for any channel under some conditions specified by the encoding rate. Universality is not considered in [23] [21].

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Section: Maximum-likelihood Decoder and Minimum-entropy Decodermentioning

confidence: 99%

Construction of Codes for the Wiretap Channel and the Secret Key Agreement From Correlated Source Outputs Based on the Hash Property

Muramatsu

Miyake

2012

IEEE Trans. Inform. Theory

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“…We have the following lemma, where it is unnecessary to assume the linearity of functions assumed in [19] [20]. It is one of the advantages of introducing a stronger version of the hash property.…”

Section: A Formal Definitionmentioning

confidence: 99%

“…. For given µ Y |X1X2 , µ X1|X0 , µ X2|X0 , and µ X0 , assume that (R 0 , R 1 , R 2 ) satisfies (16)- (20) and the following three conditions…”

Section: Two-user Multiple Access Channel Coding: Private and Commmentioning

confidence: 99%

“…In the following, we employ a rate splitting technique to eliminate conditions (40)-(42). Assume that (R 0 , R 1 , R 2 ) satisfies conditions (16)- (20) and (40)-(42). From Theorem 3, we have the fact that there is a code with encoding rate (R 0 , R 1 , R 2 ).…”

Section: Two-user Multiple Access Channel Coding: Private and Commmentioning

confidence: 99%

“…A contribution of this paper is to construct codes based on the notion of the hash property [22] [21], which is a stronger version of that introduced in [19] [20]. Another contribution is to construct codes by using sparse matrices for a general discrete memoryless multiple access channel including asymmetric one.…”

Section: Introductionmentioning

confidence: 99%

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Construction of multiple access channel codes based on hash property

Muramatsu

Miyake

2011

2011 IEEE International Symposium on Information Theory Proceedings

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The aim of this paper is to introduce the construction of codes for a general discrete stationary memoryless multiple access channel based on the the notion of the hash property. Since an ensemble of sparse matrices has a hash property, we can use sparse matrices for code construction. Our approach has a potential advantage compared to the conventional random coding because it is expected that we can use some approximation algorithms by using the sparse structure of codes.

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DLDL: A Lightweight Hash Function Based on Double Linear Diffusion Layer

Wang

et al. 2017

2017 International Conference on Computer Technology, Electronics and Communication (ICCTEC)

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Hash Property and Fixed-Rate Universal Coding Theorems

Cited by 11 publications

References 17 publications

Construction of Codes for the Wiretap Channel and the Secret Key Agreement From Correlated Source Outputs Based on the Hash Property

Construction of Codes for the Wiretap Channel and the Secret Key Agreement From Correlated Source Outputs Based on the Hash Property

Construction of multiple access channel codes based on hash property

DLDL: A Lightweight Hash Function Based on Double Linear Diffusion Layer

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