Channel coding: The road to channel capacity

Forney, G. David; Costello, Daniel J.

doi:10.1109/jproc.2007.895188

Cited by 309 publications

(196 citation statements)

References 113 publications

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“…Various efficient techniques for encoding random LDPC codes have been proposed, see Ping et al [26] for example, but none of these techniques simplifies the storage requirements. The simplicity of the encoder and decoder structure has led to many algebraically constructed LDPC codes being adopted as industry standards [5]. 4.…”

Section: Algebraic Constructionsmentioning

confidence: 99%

“…Let the [64800, 48600] LDPC code that we will construct be denoted by C 1 . A protograph code, which has parameter [540, 405], is constructed using the PEG algorithm with a good variable vertex degree distributions obtained from Urbanke [34], Λ λ 1 (x) = 0.00185185x + 0.248148x 2 for zigzag matrix +0.55x 3 + 0.0592593x 5 + 0.0925926x 8 (12.10), and H u is an irregular matrix satisfying Λ λ 1 (x) above. In order to construct a [64800, 48600] LDPC code C 1 , we need to expand the protograph code by a factor of Q = 120.…”

Section: Construction Of Quasi-cyclic Codes Using a Protographmentioning

confidence: 99%

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LDPC Codes

Tomlinson¹,

Tjhai²,

Ambroze³

et al. 2017

Error-Correction Coding and Decoding

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LDPC codes are linear block codes whose parity-check matrix-as the name implies-is sparse. These codes can be iteratively decoded using the sum product [9] or equivalently the belief propagation [24] soft decision decoder. It has been shown, for example by Chung et al. [3], that for long block lengths, the performance of LDPC codes is close to the channel capacity. The theory of LDPC codes is related to a branch of mathematics called graph theory. Some basic definitions used in graph theory are briefly introduced as follows.Definition 12.1 (Vertex, Edge, Adjacent and Incident) A graph, denoted by G(V, E), consists of an ordered set of vertices and edges.• (Vertex) A vertex is commonly drawn as a node or a dot. The set V (G) consists of vertices of G(V, E) and if v is a vertex of G(V, E), it is denoted as v ∈ V (G). The number of vertices of V (G) is denoted by |V (G)|. • (Edge) An edge (u, v) connects two vertices u ∈ V (G) and v ∈ V (G) and it is drawn as a line connecting vertices u and v. The set E(G) contains pairs of elements of

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Section: Algebraic Constructionsmentioning

confidence: 99%

Section: Construction Of Quasi-cyclic Codes Using a Protographmentioning

confidence: 99%

LDPC Codes

Tomlinson¹,

Tjhai²,

Ambroze³

et al. 2017

Error-Correction Coding and Decoding

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show abstract

“…A chaos-based image encryption scheme was introduced in [20]. An image is first converted to a binary data stream by masking these data with a random keystream generated by the chaos-based PRKG, the corresponding encrypted image is formed.…”

Section: Some Image Encryption Schemesmentioning

confidence: 99%

“…Nowadays source compression and channel coding techniques are necessary for transmitting images efficiently [20], source coding is needed to remove as much redundancy as possible and to combat the errors introduced by noisy channels, channel coding is often employed to add controlled redundancy. Therefore, using characteristics of channels and compressed bit stream may be interested in practical systems.…”

Section: Combine Source and Channel Codingmentioning

confidence: 99%

Image Security With Different Techniques Of Cryptography And Coding: A Survey

Mursi¹,

Eldin²,

Ahmed³

et al. 2014

IOSRJCE

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“…Forward error correction (FEC) [4] has already become a vital part of optical transport network standards and has evolved in several generations [5]. CM schemes are known [6]- [8] to be superior to conventional FEC techniques with independent FEC and modulation designs, in the sense of requiring less signal power for the same amount of redundancy and the same bit-error ratio (BER). Also, the joint design provides more freedom in the trade-off between digital signal processing complexity and transparent reach.…”

Section: Introductionmentioning

confidence: 99%

Rate-Adaptive Coded Modulation for Fiber-Optic Communications

Beygi

Agrell

Kahn

et al. 2014

J. Lightwave Technol.

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Abstract-Rate-adaptive optical transceivers can play an important role in exploiting the available resources in dynamic optical networks, in which different links yield different signal qualities. We study rate-adaptive joint coding and modulation, often called coded modulation (CM), addressing non-dispersion-managed (non-DM) links, exploiting recent advances in channel modeling of these links. We introduce a four-dimensional CM scheme, which shows a better tradeoff between digital signal processing complexity and transparent reach than existing methods. We construct a rate-adaptive CM scheme combining a single low-density paritycheck code with a family of three signal constellations and using probabilistic signal shaping. We evaluate the performance of the proposed CM scheme for single-channel transmission through long-haul non-DM fiber-optic systems with electronic chromaticdispersion compensation. The numerical results demonstrate improvement of spectral efficiency over a wide range of transparent reaches, an improvement over 1 dB compared to existing methods.Index Terms-Fiber-optic communications, four-dimensional set partitioning, non-dispersion managed links, nonlinear channel model, probabilistic shaping, rate-adaptive coded modulation.

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Channel coding: The road to channel capacity

Cited by 309 publications

References 113 publications

LDPC Codes

LDPC Codes

Image Security With Different Techniques Of Cryptography And Coding: A Survey

Rate-Adaptive Coded Modulation for Fiber-Optic Communications

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