Capacity of Classes of Gaussian Channels

Root, William L.; Varaiya, Pravin

doi:10.1137/0116114

Cited by 106 publications

(83 citation statements)

References 4 publications

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“…A similar result also appeared in [6]. This result was extended by Root and Varaiya [8] , where is the spectral norm of a matrix, i.e., the square root of the largest eigenvalue of ;…”

Section: Definitionsupporting

confidence: 53%

“…This requires channel side information at the receiver. The original proof in [8] is stronger since it does not have this assumption. One could, however, argue that the rate loss due to channel estimation is negligible when the block length goes to infinity.…”

Section: Remarkmentioning

confidence: 99%

“…Proof: The theorem for real square channel matrices first appeared in [8]. The decoding techniques used in the original proof complicate the error probability bounding.…”

Section: Definitionmentioning

confidence: 99%

“…The result will be generalized to afterwards. Following [8], we divide the proof into two steps. We will show the theorem is true when the set of the channels is finite, then extend the result to uncountably many channels by bounding the error probability of an arbitrary channel.…”

Section: Appendix Proof Of Theoremmentioning

confidence: 99%

“…Proof: This is a direct result of the Chernoff bound. For details, see [8,Lemma 5,8] and [24,Lemma 5 ].…”

Section: Lemma 1: Letmentioning

confidence: 99%

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A Study on Universal Codes With Finite Block Lengths

Shi

Wesel

2007

IEEE Trans. Inform. Theory

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Abstract-Based on random codes and typical set decoding, an alternative proof of Root and Varaiya's compound channel coding theorem for linear Gaussian channels is presented. The performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation. Although the theorem promises uniform convergence of the probability of error as the block length approaches infinity, with short block lengths the performance can differ considerably for individual channels. Simulation results show that universal performance can be a practical goal as the block lengths become large.Index Terms-Compound channel, random coding bound, sphere-packing bound (SPB), universal code.

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“…A similar result also appeared in [6]. This result was extended by Root and Varaiya [8] , where is the spectral norm of a matrix, i.e., the square root of the largest eigenvalue of ;…”

Section: Definitionsupporting

confidence: 53%

Section: Remarkmentioning

confidence: 99%

“…Proof: The theorem for real square channel matrices first appeared in [8]. The decoding techniques used in the original proof complicate the error probability bounding.…”

Section: Definitionmentioning

confidence: 99%

Section: Appendix Proof Of Theoremmentioning

confidence: 99%

“…Proof: This is a direct result of the Chernoff bound. For details, see [8,Lemma 5,8] and [24,Lemma 5 ].…”

Section: Lemma 1: Letmentioning

confidence: 99%

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