Page 97 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

manages to converge to no errors for = 8dB, 10 0
3
0
which represents the noise level that we will ind in the Hamming Simple CR 2
real PLC channel. -1 Fit Hamming Simple CR 2
10
Reed-Solomon CR
2
Fit Reed-Solomon CR
3.3 Discussion and comparison 10 -2 2
As we discussed before, the complexity and the capacity
of error correction of the chosen ECC are the most impor‑ BER 10 -3
tant criteria: the ECC has to be effective and fairly easy to
implement at the same time. 10 -4
The capacity of error correction of each ECC is known and
depends on its structure and their way of coding the in‑ 10 -5
formation. Table 3 summarizes the detection and correc‑
tion capability of each ECC scheme. We denoted here by 10 -6
6
SED/DED/MED: the Single/Double/Multiple Error Detec‑ 0 2 4 E /N (dB) 8 10 12
tion, and by SEC/DEC/MEC: the Single/Double/Multiple b 0
Error Correction. Fig. 5 – Comparing the simple Hamming code to the Reed‑Solomon code

Table 3 – The capability of error detection or/and error correction for parallel Hamming coding in order to increase the error
each ECC.
correction capability of our model.
ECC SED SEC DED DEC MED MEC
4. PARALLEL HAMMING CODING RE‑

Hamming x x SULTS USING MATLAB‑SIMULINK AND
code BERTOOL
Extended
x x x In this Section, we have selected only a few of the most il‑
Hamming
Reed‑ lustrative and interesting scenarios to be presented here.
Solomon x x x x x x In order to plot the Bit Error Rate (BER) function of the
which is given in equation (1), we have used the Mat‑
Code 0
BCH Code x x x x x x lab tools called ”BERTOOL”.

While the Hamming code can be implemented creating 4.1 BER performance analyser for MATLAB‑
just two fairly simple modules (encoder/decoder) based Simulink models
on XOR gates, the Reed‑Solomon code requires a higher
number of blocks. In fact, the Reed Solomon encoder Here, we use the Bit Error Rate (BER) analysis GUI (called
needs: Adder in Galois Field, Multiplier in Galois Field, BERTool) from Matlab application. The BERTool appli‑
Multiplex and Registers [13]. The Reed‑Solomon decoder cation is able to analyze the BER performance of differ‑
needs algorithms to decode the code word such as: Syn‑ ent communications systems as a function of signal‑to‑
drome calculator; Berlekamp‑Massey algorithm (or Eu‑ noise ratio given in equation (1). It analyzes perfor‑
0
clid algorithm)which inds the location of the errors by mance either with Monte‑Carlo simulations of MATLAB
creating an error locator polynomial; Chien Search Algo‑ functions and MATLAB‑Simulink models or with theoreti‑
rithm which inds the roots of the previous polynomial; cal closed‑form expressions for selected types of commu‑
Forney’s algorithm where the symbol’s error values are nication systems[14].
found and corrected. Thus, these blocks are complex and
use multiplications (or RAM memory if we use tables).
Here, we have simulated in Fig. 5 the Hamming code and
the Reed‑Solomon code for the same coding rate in
2
order to compare their BER performance.
The Hamming and Reed‑Solomon codes have proved to
be a good compromise between ef iciency and complex‑
ity. Hamming is very easy to implement and does not con‑
sume many resources, and it is a robust ECC, but the Bit
Error Rate (BER) performance (in Fig. 5) shows that it is
not the most effective ECC. Reed‑Solomon is more opti‑
mal to eliminate errors, but it is also more complex than
the Hamming code.
In the following Section, we will propose a new model of Fig. 6 – Bertool Interface: steps to plot the BER vs EB/No simulations

© International Telecommunication Union, 2021 81