1
CHAPTER 10
Error Detection and Correction
Solutions to Oddnumbered Review Questions and Exercises
Review Questions
1.
In a
single bit error
only one bit of a data unit is corrupted; in a
burst error
more
than one bit is corrupted (not necessarily contiguous).
3.
In
forward error correction
, the receiver tries to correct the corrupted codeword;
in
error detection by retransmission
, the corrupted message is discarded (the
sender needs to retransmit the message).
5.
The
Hamming distance
between two words (of the same size) is the number of
differences between the corresponding bits. The Hamming distance can easily be
found if we apply the XOR operation on the two words and count the number of 1s
in the result. The
minimum Hamming distance
is the smallest Hamming distance
between all possible pairs in a set of words.
7.
a.
The only relationship between the size of the codeword and dataword is the one
based on the definition:
n = k + r
., where
n
is the size of the codeword,
k
is the
size of the dataword, and
r
is the size of the remainder.
b.
The
remainder
is always
one bit smaller
than the
divisor
.
c.
The
degree
of the generator polynomial is
one less than
the size of the
divisor
.
For example, the CRC32 generator (with the polynomial of degree 32) uses a
33bit divisor.
d.
The
degree
of the generator polynomial is the
same as
the size of the remainder
(length of checkbits). For example, CRC32 (with the polynomial of degree 32)
creates a remainder of 32 bits.
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 Winter '09
 multiple
 Hamming Code, Error detection and correction, error detection, codeword, d. Dataword, dataword

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