Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small division” property

Average Energy ◽

Division Algorithm ◽

Prime Integer ◽

Euclidean Metric ◽

Abstract The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small remainder” property

10.21203/rs.3.rs-1053551/v4 ◽

2021 ◽

Author(s):

Ramazan Duran ◽

Murat Güzeltepe

Keyword(s):

Gaussian Noise ◽

Figure Of Merit ◽

Residue Class ◽

Signal To Noise Ratio ◽

Average Energy ◽

Division Algorithm ◽

Prime Integer ◽

Euclidean Metric ◽

Abstract The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small remainder” property

10.21203/rs.3.rs-1053551/v3 ◽

2021 ◽

Author(s):

Ramazan Duram ◽

Murat Güzeltepe

Keyword(s):

Gaussian Noise ◽

Figure Of Merit ◽

Residue Class ◽

Signal To Noise Ratio ◽

Average Energy ◽

Division Algorithm ◽

Prime Integer ◽

Euclidean Metric ◽

Abstract The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small remainder” property

10.21203/rs.3.rs-1053517/v2 ◽

2021 ◽

Author(s):

Ramazan Duram ◽

Murat Güzeltepe

Keyword(s):

Gaussian Noise ◽

Figure Of Merit ◽

Residue Class ◽

Signal To Noise Ratio ◽

Average Energy ◽

Division Algorithm ◽

Prime Integer ◽

Awgn Channel ◽

Abstract The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small division” property

10.21203/rs.3.rs-1053517/v1 ◽

2021 ◽

Author(s):

Ramazan Duram ◽

Murat Güzeltepe

Keyword(s):

Gaussian Noise ◽

Figure Of Merit ◽

Residue Class ◽

Signal To Noise Ratio ◽

Average Energy ◽

Division Algorithm ◽

Prime Integer ◽

Awgn Channel ◽

Abstract The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small remainder” property

10.21203/rs.3.rs-1053517/v3 ◽

2021 ◽

Author(s):

Ramazan Duran ◽

Murat Güzeltepe

Keyword(s):

Gaussian Noise ◽

Figure Of Merit ◽

Residue Class ◽

Signal To Noise Ratio ◽

Average Energy ◽

Division Algorithm ◽

Prime Integer ◽

Awgn Channel ◽

Abstract The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

Minimum Array Elements for Resolution of Several Direction of Arrival Estimation Methods in Various Noise-Level Environments

Journal of Telecommunications and Information Technology ◽

10.26636/jtit.2018.119417 ◽

2018 ◽

Vol 2 ◽

pp. 87-94

Author(s):

Ismail El Ouargui ◽

Said Safi ◽

Miloud Frikel

Keyword(s):

Gaussian Noise ◽

Noise Level ◽

Signal To Noise Ratio ◽

Direction Of Arrival ◽

Estimation Algorithm ◽

Doa Estimation ◽

Estimation Methods ◽

Minimum Number ◽

Informative Signals

The resolution of a Direction of Arrival (DOA) estimation algorithm is determined based on its capability to resolve two closely spaced signals. In this paper, authors present and discuss the minimum number of array elements needed for the resolution of nearby sources in several DOA estimation methods. In the real world, the informative signals are corrupted by Additive White Gaussian Noise (AWGN). Thus, a higher signal-to-noise ratio (SNR) oﬀers a better resolution. Therefore, we show the performance of each method by applying the algorithms in diﬀerent noise level environments.

Evaluasi Modulasi MFSK untuk Transmisi Data Melalui Kanal Suara GSM

Jurnal INKOM ◽

10.14203/j.inkom.308 ◽

2014 ◽

Vol 8 (1) ◽

pp. 37

Author(s):

Rika Sustika ◽

Oka Mahendra

Keyword(s):

Mobile Communication ◽

Bit Error Rate ◽

Error Rate ◽

Gaussian Noise ◽

Linear Prediction ◽

Signal To Noise Ratio ◽

Signal To Noise ◽

Global System ◽

Shift Keying

Pada tulisan ini, dievaluasi performansi skema modulasi MFSK (M-ary Frequency Shift Keying) untuk aplikasi pengiriman data melalui kanal suara GSM (Global System for Mobile Communication). Parameter yang dievaluasi berupa kesalahan bit trasmisi yang dinyatakan dengan laju kesalahan bit atau bit error rate (BER). Evaluasi ini dilakukan untuk menentukan besarnya orde M yang akan dipilih pada aplikasi pengiriman data digital melalui kanal suara GSM. Pada proses simulasi, data digital dikodekan menjadi simbol-simbol lalu dimodulasi menggunakan modulator MFSK menjadi data menyerupai pembicaraan (suara). Suara yang dihasilkan dikodekan dengan algoritma CELP (Code Excited Linear Prediction), kemudian dikirimkan melalui udara yang dimodelkan sebagai kanal AWGN (Additive White Gaussian Noise). Di sisi penerima, sinyal terima yang menyerupai suara ini didemodulasi dan dikonversi kembali menjadi data digital. Dari simulasi menggunakan Eb/No (signal to noise ratio) sebesar 6 dB, diperoleh laju bit 2,5 kbps dengan BER 2,01 x 10-3 untuk M=4, 2,22 x 10-3 untuk M=8, dan 1,87 x 10-3 untuk M=16.

Pemodelan Non-uniform Coded-Modulation pada Kanal Akustik Bawah Air di Lingkungan Perairan Dangkal

INOVTEK POLBENG ◽

10.35314/ip.v9i1.890 ◽

2019 ◽

Vol 9 (1) ◽

pp. 38

Author(s):

Sholihah Ayu Wulandari ◽

Tri Budi Santoso ◽

I Gede Puja Astawa ◽

Muhamad Milchan

Keyword(s):

Error Rate ◽

Gaussian Noise ◽

Signal To Noise Ratio ◽

Measurement Data ◽

Coded Modulation ◽

Bch Code ◽

Ieee 802.11A ◽

Shift Keying ◽

Binary Information

In this paper, presented an OFDM performance evaluation with the Non-uniform Coded-Modulation in the underwater acoustic channel in shallow water. A row of binary information is encoded by BCH code (7.4) for error correction and combined with Non-uniform modulation which is the result of modification of the subcarrier arrangement of the OFDM standard IEEE 802.11a. Modeling uses 52 subcarriers consisting of 4 pilots and 48 subcarrier data which are divided into three parts, i.e.: 24 subcarrier data with 16-Quadrature Amplitude Modulation (16-QAM) modulation, 12 subcarrier data with Quadrature phase-shift keying (QPSK) modulation and 12 other data subcarriers with Binary key-shift keying (BPSK) modulation. The channel type used describes the Additive White Gaussian Noise (AWGN) condition and is the result of measurement data. The analysis is done in terms of Signal-to-Noise-Ratio (SNR) and Bit Error Rate (BER) show that the value of the error rate of 0.001, modulation of BPSK, QPSK, 16-QAM, and Non-uniform modulation required the power each 5 dB, 8.5 dB, 10.3 dB, and 7.9 dB. However, the proposed system is able to suppress the required power up to 6 dB. The proposed system also shows better performance than fixed modulation and Non-uniform Modulation, which in this case with low power to achieve the same error rate. In addition, the proposed system has a coding gain of 1.9 dB compared to a non-uniform modulation system. Real testing is also done with measurement data at Mangrove estuary, Surabaya. The results show performance similar to simulations performed on Gaussian noise channels.

Encrypted message transmission in a QO-STBC encoded MISO wireless Communication system under implementation of low complexity ML decoding algorithm

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY ◽

10.24297/ijct.v2i1.2617 ◽

2012 ◽

Vol 2 (2) ◽

pp. 53-58

Author(s):

Shaikh Enayet Ullah ◽

Md. Golam Rashed ◽

Most. Farjana Sharmin

Keyword(s):

Fading Channels ◽

Gaussian Noise ◽

Communication System ◽

Channel Coding ◽

Signal To Noise Ratio ◽

Text Message ◽

Low Complexity ◽

White Gaussian Noise ◽

Message Transmission

In this paper, we made a comprehensive BER simulation study of a quasi- orthogonal space time block encoded (QO-STBC) multiple-input single output(MISO) system. The communication system under investigation has incorporated four digital modulations (QPSK, QAM, 16PSK and 16QAM) over an Additative White Gaussian Noise (AWGN) and Raleigh fading channels for three transmit and one receive antennas. In its FEC channel coding section, three schemes such as Cyclic, Reed-Solomon and Â½-rated convolutionally encoding have been used. Under implementation of merely low complexity ML decoding based channel estimation and RSA cryptographic encoding /decoding algorithms, it is observable from conducted simulation test on encrypted text message transmission that the communication system with QAM digital modulation and Â½-rated convolutionally encoding techniques is highly effective to combat inherent interferences under Raleigh fading and additive white Gaussian noise (AWGN) channels. It is also noticeable from the study that the retrieving performance of the communication system degrades with the lowering of the signal to noise ratio (SNR) and increasing in order of modulation.