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 Page 100 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1           Basic HTML Version Table of Contents View Full Version Page 100 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1 P. 100 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). (...) 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. (...) 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).
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Score: 1449131.25 - https://www.itu.int/en/publica.../files/basic-html/page100.html
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 Page 100 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1           Basic HTML Version Table of Contents View Full Version Page 100 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1 P. 100 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). (...) 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. (...) 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).
Language:English
Score: 1449131.25 - https://www.itu.int/en/publica.../files/basic-html/page100.html
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Glass Beads Groundfish Groundf ish Fish Optic Liquid Level Sensing Probes Leather Handbags 5 Cordage Butter Dairy Products Canned Hams and Canned Shoulders Butter Cookies 6 Frozen Boneless Beef 7 Dextrines and soluble or chemically treated starches derived.from potato starch 8 Tomato products Sugar Cheese Canned Tomato Paste All merchandise except that not benefited by Decree 68-581 dated June 29, 1968, as amended by Decree 68-599 dated July 6, 196&. 9 Argentina Argentina Australia Australia Austria Belgium Belgium Brazil Brazil Brazil Brazil Brazil Braz il Canada Canada Canada Canada Canada Canada Canada Canada Colombia Cuba Denmark Denmark Denmark Denmark European Communities (consisting of Franci the United Kingdom, West Germany, Luxembour Ireland, the Netherlands Denmark, Italy, and Belgium.) European Communities European Communities European Communities Finland France France Revoked 4.10.79 Revoked 5.21.80 Revoked 2.26.80 Discontinued 4.1.68 Revoked 12.6.79 Revoked 9.10.80 Revoked 4.8.80 Revoked 8.14.80(effective 1.1.80) Discontinued 2.1.69 1 2 3 4 5 6 7 8 9 SCM/4/Add. 1 Page 9 Merchandise Barley Molasses Dairy Products Canned hams and canned shoulders Country France France France France Sugar Dairy products Canned hams and canned shoulders Tomato products Spirits Dairy products Canned hams and canned shoulders Galvanized fabricated structural steel units for the erection of electrical transmission towers Canned tomatoes and canned tomato concentrates Steel welded wire mesh Ski-lifts and parts thereof Certain steel products Compressors and parts thereof Refrigerators, freezers, other refrigerating equip- ment, and parts thereof Die presses Dairy products Canned hams and canned shoulders Float glass manufactured by Societa Italiana Vetro, S.p.A. and Fabbrica Pisana, S.p.A. (...) The Netherlands The Netherlands Norway Pakistan Republic of Korea Spain Spain Spain Spa in Spain Spain 10 Revoked 10.27.78 SCM/4/Add.1 Page 10 Merchandise Amoxicillin trihydrate Fe rroalloys Oleores ins Cheese Rayon staple fiber Emmenthaler and Gruyere cheese Footwear 11 Handbags 12 Leather wearing apparel 13 Leather handbags 14 Textile mill products and men's and boys' apparel 15 Nonrubber footwear 16 Dairy products Canned hams and canned shoulders Pig, Iron Fasteners Fresh Cut Roses 11 12 13 14 15 16 Spain Spain Spain Sweden Sweden Switzerland Taiwan Taiwan Uruguay Uruguay Uruguay Uruguay West Germany West Germany Brazil India Israel Revoked 5.11.77 Revoked 11.23.77 Revoked 3.22.79 Revoked 3.22.79 Revoked 3.22.79 Revoked 3.22.79 7~~ ~~~~1 -il And t 2 A~~~~~;i, -- atI Country
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Score: 1444400.2 - https://www.wto.org/gatt_docs/English/SULPDF/91010387.pdf
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 Page 99 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1           Basic HTML Version Table of Contents View Full Version Page 99 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1 P. 99 ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1 (a) 10 0 (a) Model 2: Parallel Hamming 2xCR4 -1 10 10 0 Model 3: Parallel Hamming 5xCR 2 10 -2 -1 Fit Model 3 10 BER 10 -3 10 -2 -4 BER 10 -3 10 10 -5 -4 10 -6 10 -5 0 2 4 6 8 10 12 10 E /N (dB) b 0 -6 (b) 10 0 2 4 6 8 10 12 E /N (dB) b 0 Fig. 8 – Model 2: (a)Short‑frame OFDM communication model using MATLAB‑Simulink tools (b) BER performance plotted on BERTool ap‑ (b) plication Fig. 9 – Model 3: (a)Short‑frame OFDM communication model using Model 2: Parallel Hamming code 2*[31,26] MATLAB‑Simulink tools (b) BER performance plotted on BERTool ap‑ plication In order to improve the correction capacity of Model 1: 4.2 Comparison between parallel Hamming Simple Hamming code Model [63, 57]. (...) We use MATLAB‑Simulink tools in order to model the ence in BER performance: since parallel Hamming coding parallel Hamming code communication system 2×[31, 26] is very interesting in terms of simplicity and robustness, as shown in Fig. 8. however Reed‑Solomon is very interesting in terms of er‑ ror correction capability. Model 3: Parallel Hamming code 5*[15,11] In this scenario, we choose Model 4 where = 56/64 6 is the simple Reed‑Solomon coding rate (around 50 bits).
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Score: 1421712.7 - https://www.itu.int/en/publica...1/files/basic-html/page99.html
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 Page 99 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1           Basic HTML Version Table of Contents View Full Version Page 99 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1 P. 99 ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1 (a) 10 0 (a) Model 2: Parallel Hamming 2xCR4 -1 10 10 0 Model 3: Parallel Hamming 5xCR 2 10 -2 -1 Fit Model 3 10 BER 10 -3 10 -2 -4 BER 10 -3 10 10 -5 -4 10 -6 10 -5 0 2 4 6 8 10 12 10 E /N (dB) b 0 -6 (b) 10 0 2 4 6 8 10 12 E /N (dB) b 0 Fig. 8 – Model 2: (a)Short‑frame OFDM communication model using MATLAB‑Simulink tools (b) BER performance plotted on BERTool ap‑ (b) plication Fig. 9 – Model 3: (a)Short‑frame OFDM communication model using Model 2: Parallel Hamming code 2*[31,26] MATLAB‑Simulink tools (b) BER performance plotted on BERTool ap‑ plication In order to improve the correction capacity of Model 1: 4.2 Comparison between parallel Hamming Simple Hamming code Model [63, 57]. (...) We use MATLAB‑Simulink tools in order to model the ence in BER performance: since parallel Hamming coding parallel Hamming code communication system 2×[31, 26] is very interesting in terms of simplicity and robustness, as shown in Fig. 8. however Reed‑Solomon is very interesting in terms of er‑ ror correction capability. Model 3: Parallel Hamming code 5*[15,11] In this scenario, we choose Model 4 where = 56/64 6 is the simple Reed‑Solomon coding rate (around 50 bits).
Language:English
Score: 1421712.7 - https://www.itu.int/en/publica...1/files/basic-html/page99.html
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We calculate Bit Error Rate (BER) as a function of the Model 1: Simple Hamming code [63, 57] energy per bit to noise power spectral density ratio ( ). 0 6 2. (...) For in‑ stance, we consider the Hamming code [ , ] with coding We generate the BER data for a simple Hamming code rate = / where represents the code length and communication system model [63, 57]. (...) In the following, we will com‑ • Model 2: We cut the message on 2 times when we pare to the concatenation of several encoders/decoders are coding with Hamming coding rate = 26/31; with shorter coding rates in order to prove that parallel 4 Since in Model 2, the Hamming code has length 62 Hamming has better performances than Hamming sim‑ and dimension 52, we have to append only 2 zeros to ple, while keeping the same simplicity of implementation. 50 information bits before encoding. 82 © International Telecommunication Union, 2021     93     94     95     96     97     98     99     100     101     102     103          
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Score: 1418555.3 - https://www.itu.int/en/publica...1/files/basic-html/page98.html
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We calculate Bit Error Rate (BER) as a function of the Model 1: Simple Hamming code [63, 57] energy per bit to noise power spectral density ratio ( ). 0 6 2. (...) For in‑ stance, we consider the Hamming code [ , ] with coding We generate the BER data for a simple Hamming code rate = / where represents the code length and communication system model [63, 57]. (...) In the following, we will com‑ • Model 2: We cut the message on 2 times when we pare to the concatenation of several encoders/decoders are coding with Hamming coding rate = 26/31; with shorter coding rates in order to prove that parallel 4 Since in Model 2, the Hamming code has length 62 Hamming has better performances than Hamming sim‑ and dimension 52, we have to append only 2 zeros to ple, while keeping the same simplicity of implementation. 50 information bits before encoding. 82 © International Telecommunication Union, 2021     93     94     95     96     97     98     99     100     101     102     103          
Language:English
Score: 1418555.3 - https://www.itu.int/en/publica...1/files/basic-html/page98.html
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 Page 96 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1           Basic HTML Version Table of Contents View Full Version Page 96 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1 P. 96 ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1 The number of redundancy bits are generated using the 10 0 following formula: 2 = + + 1, (2) -2 where, represents the number of redundancy bits and 10 the number of information data bits. Hamming CR 1 For example, if we calculate the number of redundancy BER Fit Hamming CR bits for a = 11 bits then it comes to add = 4 redun‑ Hamming CR 1 dancy bits. These parity/redundancy bits ( , , , ) 10 -4 Fit Hamming CR 2 8 1 2 4 are added to the information bits ( , ..., ) at the Hamming CR 2 1 11 transmitter (Hamming encoder) and then removed at the 4 Fit Hamming CR receiver (Hamming decoder) which is able to detect and 4 correct errors. 10 -6 0 2 4 6 8 10 12 Bit po‑ E /N (dB) b 0 sition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Encoded Fig. 3 – BER performance of the Hamming code for different coding rates data 1 2 1 4 2 3 4 8 5 6 7 8 9 10 11 1 , 2 , 4 bits frequently we have = 2 to use them as binary codes, x x x x x x x x 1 2 x x x x x x x x each element being represented as a binary m‑tuple. x x x x x x x x x 4 In terms of complexity, the Reed–Solomon encoder is x x x x x x x x fairly simple in terms of blocks and only involves multipli‑ 8 Table 2 – The encoded bits for Hamming code [15, 11] ers and adders in the Galois Field. (...) BER Reed-Solomon CR 1 Fit Reed-Solomon CR 1 The theoretical point of view “the longer the code, the bet‑ 10 -4 Reed-Solomon CR ter the error performance” is proved in Fig. 3 and Fig. 4. 2 Fit Reed-Solomon CR Fig. 3 shows that the coding rate is crucial to obtain a good Reed-Solomon CR 2 performance. When ≤ 9 dB, the Hamming code curve 3 0 Fit Reed-Solomon CR with the coding rate is very close to the Hamming -6 3 4 code curve with the coding rate in terms of BER. 10 0 2 4 6 8 10 12 2 E /N (dB) b 0 3.2 The Reed‑Solomon code Fig. 4 – BER performance of the Reed‑Solomon code for different coding rates 1 , 2 , 3 The Reed‑Solomon code operates on a block of data treated as a set of inite‑ ield elements called symbols.
Language:English
Score: 1418402.9 - https://www.itu.int/en/publica...1/files/basic-html/page96.html
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 Page 96 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1           Basic HTML Version Table of Contents View Full Version Page 96 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1 P. 96 ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1 The number of redundancy bits are generated using the 10 0 following formula: 2 = + + 1, (2) -2 where, represents the number of redundancy bits and 10 the number of information data bits. Hamming CR 1 For example, if we calculate the number of redundancy BER Fit Hamming CR bits for a = 11 bits then it comes to add = 4 redun‑ Hamming CR 1 dancy bits. These parity/redundancy bits ( , , , ) 10 -4 Fit Hamming CR 2 8 1 2 4 are added to the information bits ( , ..., ) at the Hamming CR 2 1 11 transmitter (Hamming encoder) and then removed at the 4 Fit Hamming CR receiver (Hamming decoder) which is able to detect and 4 correct errors. 10 -6 0 2 4 6 8 10 12 Bit po‑ E /N (dB) b 0 sition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Encoded Fig. 3 – BER performance of the Hamming code for different coding rates data 1 2 1 4 2 3 4 8 5 6 7 8 9 10 11 1 , 2 , 4 bits frequently we have = 2 to use them as binary codes, x x x x x x x x 1 2 x x x x x x x x each element being represented as a binary m‑tuple. x x x x x x x x x 4 In terms of complexity, the Reed–Solomon encoder is x x x x x x x x fairly simple in terms of blocks and only involves multipli‑ 8 Table 2 – The encoded bits for Hamming code [15, 11] ers and adders in the Galois Field. (...) BER Reed-Solomon CR 1 Fit Reed-Solomon CR 1 The theoretical point of view “the longer the code, the bet‑ 10 -4 Reed-Solomon CR ter the error performance” is proved in Fig. 3 and Fig. 4. 2 Fit Reed-Solomon CR Fig. 3 shows that the coding rate is crucial to obtain a good Reed-Solomon CR 2 performance. When ≤ 9 dB, the Hamming code curve 3 0 Fit Reed-Solomon CR with the coding rate is very close to the Hamming -6 3 4 code curve with the coding rate in terms of BER. 10 0 2 4 6 8 10 12 2 E /N (dB) b 0 3.2 The Reed‑Solomon code Fig. 4 – BER performance of the Reed‑Solomon code for different coding rates 1 , 2 , 3 The Reed‑Solomon code operates on a block of data treated as a set of inite‑ ield elements called symbols.
Language:English
Score: 1418402.9 - https://www.itu.int/en/publica...1/files/basic-html/page96.html
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Based on this analysis, we propose a new design of parallel Hamming coding. On the one hand, we validate this new model of parallel Hamming coding with numerical results using MATLAB‑Simulink tools and BERTool Application which makes easier the Bit Error Rate (BER) performance simulations. On the other hand, we implement the design of this new model on an FPGA mock‑up and we show that this solution of a parallel Hamming encoder/decoder uses a few resources (LUTs) and has a higher capability of correcting when compared to the simple Hamming code. Keywords – error correcting codes, FPGA, Hamming code, parallel Hamming coding, OFDM communication systems, Reed‑Solomon code, short‑frame, sensor’s network, VHDL simulation 1.
Language:English
Score: 1413052.3 - https://www.itu.int/en/publica...1/files/basic-html/page93.html
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