Spatially-coupled codes for side-information problems

Kumar, Smita; Vem, Avinash; Narayanan, Krishna R.; Pfister, Henry D.

doi:10.1109/isit.2014.6874886

Cited by 7 publications

(24 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the boundary point, R b = 0.2764, we achieve 0.0016 bits away from the WZ limit, however the gap values of rate at the same point are 0.0396 and 0.0347 bits per channel use for the methods in [10] and [9], respectively. The equivalent gaps of distortion are, respectively, 0.007 and 0.0061 bits for the methods in [10] and [9] which are about four times more than that of the proposed method. Table 3 Simulation Results for p = 0.05 and ζ = 10-Irregular Codes (Example 5) Table 4 Simulation Results for p = 0.05-Regular Codes (Example 5) It is apparent from Figs.…”

Section: Numerical Results and Discussionmentioning

confidence: 85%

“…The coding scheme of [9] has imperfections which lead to a considerable amount of gap, such as: only regular LDGM and LDPC codes are used in that structure which might be substituted by irregular codes. Moreover, there is a possibility of failure in the algorithm of [9] that causes repetition of the encoding process. Hence, the performance of the scheme is not suitable for short length codes as a result of the attempt at encoding source sequences by such a repetitive process.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Binary Wyner–Ziv code design based on compound LDGM–LDPC structures

2018

View full text Add to dashboard Cite

Abstract:In this paper, a practical coding scheme is designed for the binary Wyner-Ziv (WZ) problem by using nested low-density generator-matrix (LDGM) and low-density paritycheck (LDPC) codes. This scheme contains two steps in the encoding procedure. The first step involves applying the binary quantization by employing LDGM codes and the second one is using the syndrome-coding technique by utilizing LDPC codes. The decoding algorithm of the proposed scheme is based on the Sum-Product (SP) algorithm with the help of a side information available at the decoder side. It is theoretically shown that the compound structure has the capability of achieving the WZ bound. The proposed method approaches this bound by utilizing the iterative message-passing algorithms in both encoding and decoding, although theoretical results show that it is asymptotically achievable.

show abstract

Section: Numerical Results and Discussionmentioning

confidence: 85%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Binary Wyner–Ziv code design based on compound LDGM–LDPC structures

2018

View full text Add to dashboard Cite

show abstract

“…The focus is on the second write of the 2-write WOM system. The first write is an instance of the Gelfand-Pinsker problem, for which we constructed capacity-achieving practical coding schemes from compound codes in an earlier article [20]. Encoding for the second write is done by the iterative quantization algorithm from a reduction to the binary erasure quantization problem.…”

Section: Discussionmentioning

confidence: 99%

“…For this problem, we have constructed lowcomplexity schemes based on spatial coupling of compound codes that were empirically shown to achieve capacity in an earlier article [20]. To find a desired codeword within a normalized distance δ from 0 n , the standard belief-propagation (BP) algorithms are not sufficient.…”

Section: E Multi-write Wom Systemmentioning

confidence: 99%

“…For the second write of the 2-write WOM system with read errors, our construction achieves any rate R < 1 − δ − h(p), where δ denotes the normalized weight of the state sequence after first write, and the codewords are protected against read errors from the binary symmetric channel with a bit-flip probability of p. In this article, the focus is mainly on the second write. For the Gelfand-Pinsker problem, we constructed practical coding schemes based on compound codes in an earlier article [20]. Empirical evidence suggests that these schemes achieve capacity for this problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatially-coupled codes for write-once memories

Kumar

Vem

Narayanan

et al. 2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Self Cite

View full text Add to dashboard Cite

The focus of this article is on low-complexity capacity-achieving coding schemes for write-once memory (WOM) systems. The construction is based on spatially-coupled compound LDGM/LDPC codes. Both noiseless systems and systems with read errors are considered. Compound LDGM/LDPC codes are known to achieve capacity under MAP decoding for the closely related Gelfand-Pinsker problem and their coset decomposition provides an elegant way to encode the messages while simultaneously providing error protection. The application of compound codes to the WOM system is new. The main result is that spatial coupling enables these codes to achieve the capacity region of the 2-write WOM system with low-complexity message-passing encoding and decoding algorithms.

show abstract

How to achieve the capacity of asymmetric channels

Mondelli

Urbanke

Hassani

2014

2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

View full text Add to dashboard Cite

We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms.The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper.The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes.The third paradigm is based on an idea of Böcherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy.Rather than focusing on the exact details of the schemes, the purpose of this tutorial is to present different coding techniques that can then be implemented with many variants. There is no absolute winner and, in order to understand the most suitable technique for a specific application scenario, we provide a detailed comparison that takes into account several performance metrics.

show abstract

Spatially-coupled codes for side-information problems

Cited by 7 publications

References 22 publications

Binary Wyner–Ziv code design based on compound LDGM–LDPC structures

Binary Wyner–Ziv code design based on compound LDGM–LDPC structures

Spatially-coupled codes for write-once memories

How to achieve the capacity of asymmetric channels

Contact Info

Product

Resources

About