Memoryless channel
A communication channel for which the statistical properties of the output signal at a time are determined only by the input signal transmitted at this moment
of time (and consequently do not depend on the signal transmitted prior to or after the moment
). More precisely, a discrete-time communication channel whose input and output signals are given by random sequences
and
with values in spaces
and
, respectively, is called a memoryless channel if for any natural number
and any sets
,
,
, the equality
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holds, where . If furthermore the conditional probabilities
do not depend on
, then the channel is called a homogeneous memoryless channel.
If one denotes by the transmission rate of the channel (cf. Transmission rate of a channel) for a segment of length
of a homogeneous memoryless channel, then
. If
and
are finite (or countable) sets, a homogeneous memoryless channel is completely determined by the matrix of transition probabilities
, where
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For references see , – cited in Communication channel.
Memoryless channel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Memoryless_channel&oldid=47821