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Convolutional Codes
◊ The encoder for a convolutional code also accepts k-bit blocks of the information sequence
u and produces an encoded sequence (code word) v of n-symbol blocks.
◊ Each encoded block depends not only on the corresponding k-bit message block at the same
time unit, but also on m previous message blocks. Hence the encoder has a memory order of
m message blocks. Hence, the encoder has a memory order of m.
◊ The set of encoded sequences produced by a k-input, n-output encoder of memory order m
is called an (n, k, m) convolutional y ( , , ) code.
◊ The ratio R=k/n is called the code rate.
◊ Since the encoder contains memory, it must be implemented with a sequential logic circuit.
◊ Binary convolutional encoder with k=1, n=2, and m=2
◊ Memorylesschannels are called random-error channels.
Transition probability diagrams for binary symmetric channel (BSC).1.5 Types of Errors 1.5
Types of Errors
◊ On channels with memory, the noise is not independent from Transmission to transmission
◊ Channel with memory are called burst-error channels.
Simplified model of a channel with memory.1.6 Error Control Strategies 1.6 Error Control
Strategies
◊ Error control for a one-way system must be accomplished using
Forward error correction (FEC) that is by employing error- forward error correction (FEC),
that is, by employing error correcting codes that automatically correct errors detected at the
receiver.
◊ Error control for a two-way system can be accomplished using error detection and
retransmission, called automatic repeat request (ARQ).
This is also know as the backward error correction (BEC).
◊ In an ARQ system, when errors are detected at the receiver, a request is sent
For the transmitter to repeat the message and this continues until the message for the
transmitter to repeat the message, and this continues until the message is received correctly.
◊ The major advantage of ARQ over FEC is that error detection requires much simpler
decoding equipment than does error correction.
151.6 Error Control Strategies 1.6 Error Control Strategies