A Proof of Random Channel Coding Theorem for Channel Capacity of Additive Correlated Gaussian Noise Channels

2021 ◽  
Vol 46 (1) ◽  
pp. 53-56
Author(s):  
Kyuhyuk Chung
Keyword(s):  
Channel Capacity ◽  
Gaussian Noise ◽  
Channel Coding ◽  
Gaussian Noise Channels

Information Theory and Channel Coding

2021 ◽  
pp. 427-541
Author(s):  
Stevan Berber
Keyword(s):  
Information Theory ◽  
Channel Capacity ◽  
Gaussian Noise ◽  
Channel Coding ◽  
Signal Transmission ◽  
Convolutional Codes ◽  
Turbo Coding ◽  
Supplementary Material ◽  
Measure Entropy ◽  
Hard Decision

Chapter 9 presents the fundamentals of information theory and coding, which are required for understanding of the information measure, entropy and limits in signal transmission including the definition and derivative of the communication channel capacity. The coding theorem is separtelly presented. The chapter contains a part that defines the entropy of continuous and discrete Gaussian and uniform stochastic processes. The results of this unique analysis is essential to understand the notion of the continuous and discrete white Gaussian noise process. The block and convolutional codes, including hard decision Viterbi algorihthm are presented. The theory of iterative and turbo coding is presented in a form of a Project in the supplementary material, where several topics are defined and the related solutions are offered.

On the capacity of additive white mixture Gaussian noise channels

2019 ◽  
Vol 30 (7) ◽  
pp. e3585
Author(s):  
Mohsen Sheikh-Hosseini ◽  
Ghosheh Abed Hodtani
Keyword(s):  
Gaussian Noise ◽  
Gaussian Noise Channels

The Capacity of the White Gaussian Noise Channel

1990 ◽  
Vol 4 (3) ◽  
pp. 345-353
Author(s):  
Jerome R. Bretienbach
Keyword(s):  
Channel Capacity ◽  
Gaussian Noise ◽  
White Gaussian Noise ◽  
General Sense ◽  
Infinite Dimensional ◽  
Band Limited ◽  
Arbitrary Noise ◽  
Noise Sequence

The capacity of the white Gaussian noise (WGN) channel is widely stated asS/N0nats/unit time. This conclusion is commonly derived either formally, or from the capacity,Wln(l +S/N0W), of the corresponding band-limited channel with bandwidthW, by takingW→8. In this paper, the WGN channel capacity is instead found directly by treating WGN as an arbitrary noise sequence that whitens in a general sense. In addition, the coding theorems proved make explicit the class of allowable receivers, either finite- or infinite-dimensional correlation receivers, or unconstrained. The capacities for these three receiver classes are found to be, respectively:S/N0forS> 0, and 0 forS= 0; and 8 for allS≥ 0. In those cases where the capacity is infinite, actual transmitter–receiver pairs are specified that achieve capacity.

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