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Information Theory and Applications (ITA) Workshop

作者： Yang, En-hui Meng, Jin Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9781467346481

New non-asymptotic random coding theorems (with error probability epsilon and finite block length n) based on Gallager parity check ensemble are established for binary input arbitrary output channels. The resulting non-asymptotic achievability bounds, when combined with non-asymptotic equipartition properties, can be easily computed. Analytically, these non-asymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as n goes to infinity with either constant or sub-exponentially decreasing epsilon. Numerically, they are also compared favourably, for finite n and epsilon of practical interest, with existing non-asymptotic achievability bounds in the literature in general.

关键词： Channel capacity non-asymptotic coding theorems non-asymptotic equipartition properties random linear codes Gallager parity check ensemble

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New nonasymptotic Channel coding theorems for Structured Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第9期61卷 4534-4553页

作者： Yang, En-Hui Meng, Jin Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

New nonasymptotic random coding theorems (with error probability epsilon and finite block length n) based on Gallager parity check ensemble and general parity check ensembles are derived in this paper. The resulting nonasymptotic achievability bounds, when combined with nonasymptotic equipartition properties developed in this paper, can be easily computed. Analytically, these nonasymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as n goes to infinity with either constant or subexponentially decreasing epsilon in the case of Gallager parity check ensemble, and to imply that low density parity check (LDPC) codes be capacity-achieving in the case of LDPC ensembles. Numerically, they are also compared favorably, for finite n and epsilon of practical interest, with existing nonasymptotic achievability bounds in the literature.

关键词： Channel capacity non-asymptotic coding theorems non-asymptotic equipartition properties random linear codes Gallager parity check ensemble LDPC code

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Jar Decoding: LDPC coding theorems for Binary Input Memoryless Channels

Jar Decoding: LDPC Coding Theorems for Binary Input Memoryle...

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IEEE International Symposium on Information Theory

作者： Yang, En-Hui Meng, Jin Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9781467325790

Recently, a new decoding rule called jar decoding was proposed, under which the decoder first forms a set of suitable size, called a jar, consisting of sequences from the channel input alphabet considered to be closely related to y(n), and then takes any codeword from the jar as the estimate of the transmitted codeword. In this paper, we show that under jar decoding, the analysis of low density parity check (LDPC) codes is much easier compared to maximum a posteriori (MAP) or maximum likelihood (ML) and Belief Propagation (BP) decoding, and new general LDPC coding theorems can be established. Specifically, it is proved that LDPC codes can approach the mutual information, with diminishing bit error probability, of any binary input memoryless channel with uniform input distribution when the average variable node degree is large. Moreover, simulation shows an interesting connection between jar decoding and BP decoding, i.e., BP decoding can be regarded as one of many ways to pick up a codeword from the jar for LDPC codes when it succeeds in outputting a codeword.

关键词： Belief propagation decoding channel capacity jar decoding low-density parity-check codes maximum a posteriori (MAP) decoding non-asymptotic coding theorems non-asymptotic equipartition properties

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coding theorems via Jar Decoding

Coding Theorems via Jar Decoding

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作者： Meng, Jin University of Waterloo

学位级别：master

In the development of digital communication and information theory, every channel decoding rule has resulted in a revolution at the time when it was invented. In the area of information theory, early channel coding theorems were established mainly by maximum likelihood decoding, while the arrival of typical sequence decoding signaled the era of multi-user information theory, in which achievability proof became simple and intuitive. Practical channel code design, on the other hand, was based on minimum distance decoding at the early stage. The invention of belief propagation decoding with soft input and soft output, leading to the birth of turbo codes and low-density-parity check (LDPC) codes which are indispensable coding techniques in current communication systems, changed the whole research area so dramatically that people started to use the term "modern coding theory'''' to refer to the research based on this decoding rule. In this thesis, we propose a new decoding rule, dubbed jar decoding, which would be expected to bring some new thoughts to both the code performance analysis and the code design. Given any channel with input alphabet X and output alphabet Y, jar decoding rule can be simply expressed as follows: upon receiving the channel output y^n ∈ Y^n, the decoder first forms a set (called a jar) of sequences x^n ∈ X^n considered to be close to y^n and pick any codeword (if any) inside this jar as the decoding output. The way how the decoder forms the jar is defined independently with the actual channel code and even the channel statistics in certain cases. Under this jar decoding, various coding theorems are proved in this thesis. First of all, focusing on the word error probability, jar decoding is shown to be near optimal by the achievabilities proved via jar decoding and the converses proved via a proof technique, dubbed the outer mirror image of jar, which is also quite related to jar decoding. Then a Taylor-type expansion of optimal channel coding rat

关键词： channel capacity non-asymptotic equipartition property channel coding jar decoding non-asymptotic coding theorems Taylor-type Expansion LDPC codes Interactive Encoding and Decoding

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