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Unformatted text preview: CHAPTER 8
CODING AND ERROR CONTROL
A N SWERS
NSWERS TO Q UESTIONS 8.1 A parity bit appended to an array of binary digits to make the sum of all the binary
digits, including the parity bit, always odd (odd parity) or always even (even
parity).
8.2 The CRC is an error detecting code in which the code is the remainder resulting
from dividing the bits to be checked by a predetermined binary number.
8.3 The CRC has more bits and therefore provides more redundancy. That is, it
provides more information that can be used to detect errors.
8.4 Modulo 2 arithmetic, polynomials, and digital logic.
8.5 It is possible. You could design a code in which all codewords are at least a distance
of 3 from all other codewords, allowing all singlebit errors to be corrected. Suppose
that some but not all codewords in this code are at least a distance of 5 from all
other codewords. Then for those particular codewords, but not the others, a doublebit error could be corrected.
8.6 An (n, k) block code encodes k data bits into nbit codewords.
8.7 An (n, k, K) code processes input data k bits at a time and produces an output of n
bits for each incoming k bits. The current output of n bits is a function of the last K ×
k input bits.
8.8 A trellis is a diagram that shows the state transitions over time in a convolutional
code.
8.9 Detection of errors and retransmission of frames that are received in error.
8.10 GobackN ARQ is a form of error control in which a destination station sends a
negative acknowledgment (NAK) when it receives an error. The source station
receiving the NAK will retransmit the frame in error plus all succeeding frames
transmitted in the interim. A N SWERS
NSWERS TO PROBLEMS 8.1 Any arithmetic scheme will work if applied in exactly the same way to the forward
and reverse process. The modulo 2 scheme is easy to implement in circuitry. It also
yields a remainder one bit smaller than binary arithmetic.
8.2 a. We have:
Pr [single bit in error] = 10–3
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This note was uploaded on 02/20/2012 for the course ENC 3250 taught by Professor Dr.timothycerner during the Fall '11 term at UNF.
 Fall '11
 Dr.TimothyCerner

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