Very noisy channels, reliability functions, and exponentially optimum codes

A very noisy channel (VNC), is a discrete-input memoryless channel whose capacity is close to zero. Very noisy channels are of interest, since they serve as models for some important physical channels. There are two distinct classes of VNCs: Reiffen's class I (Reiffen, 1963) and Majani's c...

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Bibliographic Details
Published in:IEEE transactions on information theory 1994-05, Vol.40 (3), p.647-661
Main Authors: Sangmin Lee, Winick, K.A.
Format: Article
Language:English
Subjects:
Additive white noise
Area measurement
AWGN
Channel capacity
Communications
Energy measurement
Gaussian noise
Network address translation
Optical detectors
Optical noise
Signal to noise ratio
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Summary:A very noisy channel (VNC), is a discrete-input memoryless channel whose capacity is close to zero. Very noisy channels are of interest, since they serve as models for some important physical channels. There are two distinct classes of VNCs: Reiffen's class I (Reiffen, 1963) and Majani's class II (Majani, 1987). It is shown that the reliability function is known exactly for both classes of VNCs, by extending the results previously obtained only for class I. It is then shown that an exponentially optimum code can be constructed for a channel if it can be modeled as repeated uses of a binary-input class I VNC, a binary-input/binary-output class II VNC or a class II very noisy binary erasure channel. The theory developed is illustrated by considering the direct detection optical channel used with polarization modulation. The capacity, reliability function, and exponentially optimum code, for this channel, are derived.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.335878