Page 100 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1

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

Table 4 – ECCs comparison in terms of complexity of implementation
and capacity of correction

ECCs Advantages Disadvantages

10 -2
Very effective
especially with
BER burst errors; Complex and
Simple High correction need more re‑
-4
10 sources (LUT)
Model1: Hamming CR Reed‑ capacity: can
5
Model 2: Parallel Hamming 2 CR Solomon correct mul‑ than Hamming
4
Model 4: Reed-Solomon Simple CR tiple errors code.
6
Model 3: Parallel Hamming 5 CR simultane‑
2
-6 ously.
10
0 2 4 6 8 10
E /N (dB)
b 0
Easy to imple‑
Fig. 10 – Comparing simple, parallel Hamming and Reed‑Solomon codes ment;
for the same total size (around 50 bits).
Parallel Correction Not the most ef‑
pecially through our PLC channel, we have an average er‑ Ham‑ capacity: cor‑ fective in terms
ror probability almost equal to 3 errors for a packet of 50 ming 5 × rect 5 of 10 of BER.
detected errors
bits. That ’s why, Model 3 seems to be slightly better, es‑ [15, 11]
for a 50 bits
pecially towards the end, which can seem logical given the packet.
fact that Model 3 can have a correction of up to 5 errors,
while Model 2 can only correct 2 errors.
Even if the Reed‑Solomon code is apparently more ef i‑ shown in Fig. 10, the curve of Model 3, which represents a
cient, we can see at the end of the Reed‑Solomon simula‑ new design of parallel Hamming coding, is closer to Reed‑
tion curve that the BER converges suddenly to zero: this Solomon than the other models of Hamming coding.
is due to the complexity of the Reed‑Solomon algorithm, For these reasons, we have chosen parallel Hamming
MATLAB‑Simulink tools couldn’t simulate for long peri‑ 5×encoder/decoder (Model 3) to be implemented
2
ods of time and we could only send a inite amount of bits next in VHDL in order to show that this solution uses a few
before it made the simulation stop. The two last points of resources and has a higher capability of correcting com‑
the Reed‑Solomon simulation curve are stagnant because pared to the simple Hamming code.
it’s the limit of the simulation given its complexity.
5. IMPLEMENTATION OF PARALLEL HAM‑
However, Hamming curves (for Model 1, Model 2 and
−6
Model 3) can go to lower values of BER ≤ 10 , which MING ENCODER/DECODER
proves that it’s easier and robust.
In this Section, we will analyse and validate the low com‑
To give an order of magnitude: for Model 1 (simple Ham‑ plexity of Model 3 by implementing the design of the par‑
ming code), we simulated 2 million bits (for each value of allel enCOde/DECoder (CODEC) on an FPGA mock‑up and

), while for Model 4 (simple Reed‑Solomon) we could simulating this design on VHDL code.
0
only simulate 700 thousand bits which shows the com‑
plexity of the Reed‑Solomon code when compared to the 5.1 Parallel Hamming CODEC design
Hamming code.
As we discussed before, the idea here is to make a trade‑
Concerning their performance, in Fig. 10, we remark that
Reed‑Solomon is better, especially for ≥ 8 dB and with off between Hamming simplicity of implementation and
0 Reed Solomon’s capacity of correction and performance.
a high value of there are few errors to be corrected. In fact, with parallel Hamming encoder/decoder (Model
0
Nevertheless, this gain in effectiveness for Reed‑Solomon 3), we will consume ive times more resources than with
has a cost in complexity when compared to Model 3 of the simple one Hamming encoder/decoder, but we will have
Parallel Hamming coding. a notable improvement in terms of BER performance.

Based on the previous analysis, we have discussed and In Fig. 11, Hamming encoder/decoder [15, 11] module
validated via simulations the trade‑off between complex‑ is the base module to create our parallel Hamming en‑
ity (Hamming is the easiest to code) and error correction coder/decoder (Model 3), which is composed of 5× Ham‑
capability (Reed‑Solomon being the most effective). Table ming encoders/decoders [15, 11] added to Demux/Mux to
4 summarizes the advantages and disadvantages of each concatenate the messages respectively.
ECC. Therefore, we have chosen to improve the correction The encoder/decoder circuit to compute the parity bits of
capacity of the Hamming code instead of decreasing the the Hamming encoder/decoder (11, 15) is shown in Fig.
complexity cost for the Reed‑Solomon code since we have 11. These parity bits ( , , , ) are added to the in‑
2
4
8
1

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