Methodical instructions
Calculation of a signal BPSK (QPSK) bandwidth should be made under recommendations from the Module 1. Using of an error-control codes with code rate Rcode leads to increasing of a occupied frequency band of the signal KF = 1/Rcode times (see Chapter 9). On the other hand, a control ability of a code increases with a decreasing of a code rate. Therefore the problem of a code parameters optimisation consists in a choice of a code with a rate at which the frequency band of the coded signal does not exceed the given pass band of transmission channel Fch. If the demanded pass band for the transmission of a coded MPSK signal with rate R is equal to FMPSK, and the code rate is chosen equal to Rcode the pass band of channel which is necessary for transmission a coded MPSK signal will be equal
.
Then
from a inequality (
)
it is received a simple condition for
choice of code rate:
Rcode > . (B.1)
The told is illustrated by figure B.1. The expanding of a frequency band of a coded signal is proportional to factor of a band expansion. By the process of a decreasing of a code rate (increasing of Kf) the frequency band extends and reaches values of a given channel frequency band Fch. On the same figure the line A‑gain = f(Rcode) is shown. Intersection of a curve band with boundary given value Fch defines the admissible factor of a channel frequency band expansion Kf = 1/Rcode and, accordingly, of code rate .
The first stage of a choice of a error-control code is the choice of a class of codes (a class block or convolution codes). Using materials of Chapters 8 and 11 it is recommended to justify with deep arguments for a choice of convolution codes for using in project. Among decoding algorithms on a latitude of practical application the in the lead place occupies Viterbi algorithm. It is recommended to apply Viterbi algorithm in project. In section of the project with a substantiation of application of this algorithm it is necessary to give information about realisation complexity of an algorithm. Among the codes selected by criterion of a rate according to the formula (B.1) there can be codes with various length of code constraint length (and, accordingly, with various decoder complexity). The noise immunity of decoding is characterised by A-gain. In code tables of a values A-gain are not reduced at certain level of error probability. At the same time, magnitude of A-gain is upper estimation of a real gain. Therefore at choice of a codes it is recommended to use A-gain which values are available from the Attachment A. Among the selected candidates of codes it is necessary to apply code ensuring maximum A-gain and meeting maximum requirements on code rate and minimum complexity of decoder.
Definitive data about error probability on decoder output it is necessary to get by the calculations the decoding bit error probability for chosen code from the signal to noise ratio. In case of representation failure to meet requirements it is recommended to apply a code with more value of A-gain.
