Digital Signal Transmission/Symbolwise Coding with Pseudo-Ternary Codes - Revision history

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	*The actual encoding from binary  $(M_q = 2)$  to ternary  $(M = M_c = 3)$  is done by the  "linear coding network"  by the conventional subtraction		*The actual encoding from binary  $(M_q = 2)$  to ternary  $(M = M_c = 3)$  is done by the  "linear coding network"  by the conventional subtraction
	:$$c(t) ={1}/{2} \cdot \big [b(t) - K_{\rm C} \cdot b(t- N_{\~~rmC~~}\cdot T)\big] \in \{-1, \ 0, +1\}\hspace{0.05cm},$$		:$$c(t) ={1}/{2} \cdot \big [b(t) - K_{\rm C} \cdot b(t- N_{\rm C}\cdot T)\big] \in \{-1, \ 0, +1\}\hspace{0.05cm},$$

	:which can be described by the following  [[Linear_and_Time_Invariant_Systems/System_Description_in_Time_Domain#Impulse_response\|"impulse response"]]  resp.  [[Linear_and_Time_Invariant_Systems/System_Description_in_Frequency_Domain#Frequency_response_.E2.80.93_Transfer_function\|"transfer function"]]  with respect to the input signal  $b(t)$  and the output signal  $c(t)$:		:which can be described by the following  [[Linear_and_Time_Invariant_Systems/System_Description_in_Time_Domain#Impulse_response\|"impulse response"]]  resp.  [[Linear_and_Time_Invariant_Systems/System_Description_in_Frequency_Domain#Frequency_response_.E2.80.93_Transfer_function\|"transfer function"]]  with respect to the input signal  $b(t)$  and the output signal  $c(t)$:
	:$$h_{\rm C}(t) = {1}/{2} \cdot \big [\delta(t) - K_{\rm C} \cdot \delta(t- N_{\~~rmC~~}\cdot T)\big] \ \ \ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\ \ \ H_{\rm C}(f) ={1}/{2} \cdot \left [1 - K_{\rm C} \cdot {\rm e}^{- {\rm j}\hspace{0.05cm}\cdot\hspace{0.05cm} 2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}N_{\rm C}\hspace{0.05cm}\cdot \hspace{0.05cm}T}\right]\hspace{0.05cm}. $$		:$$h_{\rm C}(t) = {1}/{2} \cdot \big [\delta(t) - K_{\rm C} \cdot \delta(t- N_{\rm C}\cdot T)\big] \ \ \ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\ \ \ H_{\rm C}(f) ={1}/{2} \cdot \left [1 - K_{\rm C} \cdot {\rm e}^{- {\rm j}\hspace{0.05cm}\cdot\hspace{0.05cm} 2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}N_{\rm C}\hspace{0.05cm}\cdot \hspace{0.05cm}T}\right]\hspace{0.05cm}. $$

	*The relative redundancy is the same for all pseudo-ternary codes.  Substituting  $M_q=2$,  $M_c=3$  and  $T_c =T_q$  into the  [[Digital_Signal_Transmission/Redundancy-Free_Coding#Symbolwise_coding_vs._blockwise_coding\|"general definition equation"]],  we obtain		*The relative redundancy is the same for all pseudo-ternary codes.  Substituting  $M_q=2$,  $M_c=3$  and  $T_c =T_q$  into the  [[Digital_Signal_Transmission/Redundancy-Free_Coding#Symbolwise_coding_vs._blockwise_coding\|"general definition equation"]],  we obtain
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	<br>		<br>
	The frequency response of the linear code network of a pseudo-ternary code is generally:		The frequency response of the linear code network of a pseudo-ternary code is generally:
	:$$H_{\rm C}(f) = {1}/{2} \cdot \big [1 - K_{\rm C} \cdot {\rm		:$$H_{\rm C}(f) = {1}/{2} \cdot \big [1 - K_{\rm C} \cdot {\rm e}^{-{\rm j}\hspace{0.03cm}\cdot \hspace{0.03cm}2\pi\hspace{0.03cm}\cdot \hspace{0.03cm}f \hspace{0.03cm}\cdot\hspace{0.03cm} N_{\rm C}\hspace{0.03cm}\cdot \hspace{0.03cm}T}\big] ={1}/{2} \cdot \big [1 - K \cdot {\rm e}^{-{\rm j}\hspace{0.03cm}\cdot \hspace{0.03cm}\alpha}\big ]\hspace{0.05cm}.$$This gives the power-spectral density  $\rm (PSD)$  of the amplitude coefficients  $(K$  and  $\alpha$  are abbreviations according to the above equation$)$::$$ {\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = \frac{\big [1 - K \cos(\alpha) + {\rm j}\cdot K \sin (\alpha) \big ] \big [1 - K \cos(\alpha) - {\rm j}\cdot K \sin (\alpha) \big ] }{4} = \text{...} = {1}/{4} \cdot \big [2 - 2 \cdot K \cdot \cos(\alpha) \big ] $$[[File:P_ID1347__Dig_T_2_4_S2b_v2.png\|right\|frame\|Power-spectral density of the AMI code\|class=fit]]:$$ \Rightarrow \hspace{0.3cm}{\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = {1}/{2} \cdot \big [1 - K_{\rm C} \cdot \cos(2\pi f N_{\rm C} T)\big ]\hspace{0.4cm}\bullet\!\!-\!\!\!-\!\!\!-\!\!\circ \hspace{0.4cm}\varphi_a(\lambda \cdot T)\hspace{0.05cm}.$$In particular,  for the power-spectral density of the AMI code  $(N_{\rm C} = K_{\rm C} = 1)$,  we obtain::$${\it \Phi}_a(f) = {1}/{2} \cdot \big [1 - \cos(2\pi f T)\big ] = \sin^2(\pi f T)\hspace{0.05cm}.$$
	e}^{-{\rm j}\hspace{0.03cm}\cdot \hspace{0.03cm}
	2\pi\hspace{0.03cm}\cdot \hspace{0.03cm}f \hspace{0.03cm}\cdot
	\hspace{0.03cm} N_{\rm C}\hspace{0.03cm}\cdot \hspace{0.03cm}T}
	\big] ={1}/{2} \cdot \big [1 - K \cdot {\rm
	e}^{-{\rm j}\hspace{0.03cm}\cdot \hspace{0.03cm}
	\alpha}
	\big ]\hspace{0.05cm}.$$This gives the power-spectral density  $\rm (PSD)$  of the amplitude coefficients  $(K$  and  $\alpha$  are abbreviations according to the above equation$)$::$$ {\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = \frac{\big [1 - K \cos
	(\alpha) + {\rm j}\cdot K \sin (\alpha) \big ] \big [1 - K \cos
	(\alpha) - {\rm j}\cdot K \sin (\alpha) \big ] }{4} = \text{...} = {1}/{4} \cdot \big [2 - 2 \cdot K \cdot \cos
	(\alpha) \big ] $$[[File:P_ID1347__Dig_T_2_4_S2b_v2.png\|right\|frame\|Power-spectral density of the AMI code\|class=fit]]:$$ \Rightarrow \hspace{0.3cm}{\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = {1}/{2} \cdot \big [1 - K_{\rm C} \cdot \cos
	(2\pi f N_{\rm C} T)\big ]
	\hspace{0.4cm}\bullet\!\!-\!\!\!-\!\!\!-\!\!\circ \hspace{0.4cm}
	\varphi_a(\lambda \cdot T)\hspace{0.05cm}.$$In particular,  for the power-spectral density of the AMI code  $(N_{\rm C} = K_{\rm C} = 1)$,  we obtain::$${\it \Phi}_a(f) = {1}/{2} \cdot \big [1 - \cos
	(2\pi f T)\big ] = \sin^2
	(\pi f T)\hspace{0.05cm}.$$

	The graph shows		The graph shows

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2026-03-16T13:46:51Z

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← Older revision		Revision as of 15:46, 16 March 2026
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	*The  "non-linear pre-encoder"  obtains the precoded symbols  $b_\nu$,  which are also binary,  by a modulo–2 addition  ("antivalence")  between the symbols  $q_\nu$  and  $K_{\rm C} \cdot b_{\nu-N_{\rm C}} $:		*The  "non-linear pre-encoder"  obtains the precoded symbols  $b_\nu$,  which are also binary,  by a modulo–2 addition  ("antivalence")  between the symbols  $q_\nu$  and  $K_{\rm C} \cdot b_{\nu-N_{\rm C}} $:
	:$$q_\nu \in \{-1, +1\},\hspace{0.1cm} K_{\rm C} \in \{-1,		:$$q_\nu \in \{-1, +1\},\hspace{0.1cm} K_{\rm C} \in \{-1,+1\}\hspace{0.3cm}\Rightarrow \hspace{0.3cm}b_\nu \in \{-1,+1\}\hspace{0.05cm}.$$
	+1\}\hspace{0.3cm}\Rightarrow \hspace{0.3cm}b_\nu \in \{-1,
	+1\}\hspace{0.05cm}.$$
	*Like the source symbols  $q_\nu$,  the symbols  $b_\nu$  are statistically independent of each other.  Thus,  the pre-encoder does not add any redundancy.  However,  it allows a simpler realization of the decoder and prevents error propagation after a transmission error.<br>		*Like the source symbols  $q_\nu$,  the symbols  $b_\nu$  are statistically independent of each other.  Thus,  the pre-encoder does not add any redundancy.  However,  it allows a simpler realization of the decoder and prevents error propagation after a transmission error.<br>

	*The actual encoding from binary  $(M_q = 2)$  to ternary  $(M = M_c = 3)$  is done by the  "linear coding network"  by the conventional subtraction		*The actual encoding from binary  $(M_q = 2)$  to ternary  $(M = M_c = 3)$  is done by the  "linear coding network"  by the conventional subtraction
	:$$c(t) ={1}/{2} \cdot \big [b(t) - K_{\rm C} \cdot b(t- N_{\rm		:$$c(t) ={1}/{2} \cdot \big [b(t) - K_{\rm C} \cdot b(t- N_{\rmC}\cdot T)\big] \in \{-1, \ 0, +1\}\hspace{0.05cm},$$
	C}\cdot T)\big] \in \{-1, \ 0, +1\}\hspace{0.05cm},$$

	:which can be described by the following  [[Linear_and_Time_Invariant_Systems/System_Description_in_Time_Domain#Impulse_response\|"impulse response"]]  resp.  [[Linear_and_Time_Invariant_Systems/System_Description_in_Frequency_Domain#Frequency_response_.E2.80.93_Transfer_function\|"transfer function"]]  with respect to the input signal  $b(t)$  and the output signal  $c(t)$:		:which can be described by the following  [[Linear_and_Time_Invariant_Systems/System_Description_in_Time_Domain#Impulse_response\|"impulse response"]]  resp.  [[Linear_and_Time_Invariant_Systems/System_Description_in_Frequency_Domain#Frequency_response_.E2.80.93_Transfer_function\|"transfer function"]]  with respect to the input signal  $b(t)$  and the output signal  $c(t)$:
	:$$h_{\rm C}(t) = {1}/{2} \cdot \big [\delta(t) - K_{\rm C} \cdot \delta(t- N_{\rm		:$$h_{\rm C}(t) = {1}/{2} \cdot \big [\delta(t) - K_{\rm C} \cdot \delta(t- N_{\rmC}\cdot T)\big] \ \ \ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\ \ \ H_{\rm C}(f) ={1}/{2} \cdot \left [1 - K_{\rm C} \cdot {\rm e}^{- {\rm j}\hspace{0.05cm}\cdot\hspace{0.05cm} 2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}N_{\rm C}\hspace{0.05cm}\cdot \hspace{0.05cm}T}\right]\hspace{0.05cm}. $$
	C}\cdot T)\big] \ \ \ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\ \ \ H_{\rm C}(f) ={1}/{2} \cdot \left [1 - K_{\rm C} \cdot {\rm e}^{- {\rm j}\hspace{0.05cm}\cdot\hspace{0.05cm} 2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}N_{\rm C}\hspace{0.05cm}\cdot \hspace{0.05cm}T}\right]\hspace{0.05cm}. $$

	*The relative redundancy is the same for all pseudo-ternary codes.  Substituting  $M_q=2$,  $M_c=3$  and  $T_c =T_q$  into the  [[Digital_Signal_Transmission/Redundancy-Free_Coding#Symbolwise_coding_vs._blockwise_coding\|"general definition equation"]],  we obtain		*The relative redundancy is the same for all pseudo-ternary codes.  Substituting  $M_q=2$,  $M_c=3$  and  $T_c =T_q$  into the  [[Digital_Signal_Transmission/Redundancy-Free_Coding#Symbolwise_coding_vs._blockwise_coding\|"general definition equation"]],  we obtain
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	e}^{-{\rm j}\hspace{0.03cm}\cdot \hspace{0.03cm}		e}^{-{\rm j}\hspace{0.03cm}\cdot \hspace{0.03cm}
	\alpha}		\alpha}
	\big ]\hspace{0.05cm}.$$		\big ]\hspace{0.05cm}.$$This gives the power-spectral density  $\rm (PSD)$  of the amplitude coefficients  $(K$  and  $\alpha$  are abbreviations according to the above equation$)$::$$ {\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = \frac{\big [1 - K \cos

	This gives the power-spectral density  $\rm (PSD)$  of the amplitude coefficients  $(K$  and  $\alpha$  are abbreviations according to the above equation$)$:
	:$$ {\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = \frac{\big [1 - K \cos
	(\alpha) + {\rm j}\cdot K \sin (\alpha) \big ] \big [1 - K \cos		(\alpha) + {\rm j}\cdot K \sin (\alpha) \big ] \big [1 - K \cos
	(\alpha) - {\rm j}\cdot K \sin (\alpha) \big ] }{4} = \text{...} = {1}/{4} \cdot \big [2 - 2 \cdot K \cdot \cos		(\alpha) - {\rm j}\cdot K \sin (\alpha) \big ] }{4} = \text{...} = {1}/{4} \cdot \big [2 - 2 \cdot K \cdot \cos
	(\alpha) \big ] $$		(\alpha) \big ] $$[[File:P_ID1347__Dig_T_2_4_S2b_v2.png\|right\|frame\|Power-spectral density of the AMI code\|class=fit]]:$$ \Rightarrow \hspace{0.3cm}{\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = {1}/{2} \cdot \big [1 - K_{\rm C} \cdot \cos
	[[File:P_ID1347__Dig_T_2_4_S2b_v2.png\|right\|frame\|Power-spectral density of the AMI code\|class=fit]]
	:$$ \Rightarrow \hspace{0.3cm}{\it \Phi}_a(f) = \| H_{\rm C}(f)\|^2 = {1}/{2} \cdot \big [1 - K_{\rm C} \cdot \cos
	(2\pi f N_{\rm C} T)\big ]		(2\pi f N_{\rm C} T)\big ]
	\hspace{0.4cm}\bullet\!\!-\!\!\!-\!\!\!-\!\!\circ \hspace{0.4cm}		\hspace{0.4cm}\bullet\!\!-\!\!\!-\!\!\!-\!\!\circ \hspace{0.4cm}
	\varphi_a(\lambda \cdot T)\hspace{0.05cm}.$$		\varphi_a(\lambda \cdot T)\hspace{0.05cm}.$$In particular,  for the power-spectral density of the AMI code  $(N_{\rm C} = K_{\rm C} = 1)$,  we obtain::$${\it \Phi}_a(f) = {1}/{2} \cdot \big [1 - \cos

	In particular,  for the power-spectral density of the AMI code  $(N_{\rm C} = K_{\rm C} = 1)$,  we obtain:
	:$${\it \Phi}_a(f) = {1}/{2} \cdot \big [1 - \cos
	(2\pi f T)\big ] = \sin^2		(2\pi f T)\big ] = \sin^2
	(\pi f T)\hspace{0.05cm}.$$		(\pi f T)\hspace{0.05cm}.$$
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	[[File:P_ID1348__Dig_T_2_4_S3b_v1.png\|right\|frame\|Power-spectral density of the duobinary code\|right\|class=fit]]		[[File:P_ID1348__Dig_T_2_4_S3b_v1.png\|right\|frame\|Power-spectral density of the duobinary code\|right\|class=fit]]

	:$${\it \Phi}_a(f) ={1}/{2} \cdot \big [1 + \cos		:$${\it \Phi}_a(f) ={1}/{2} \cdot \big [1 + \cos(2\pi f T)\big ] = \cos^2(\pi f T)\hspace{0.05cm},$$
	(2\pi f T)\big ] = \cos^2		:$$ {\it \Phi}_s(f) = s_0^2 \cdot T \cdot \cos^2(\pi f T)\cdot {\rm si}^2(\pi f T)= s_0^2 \cdot T \cdot {\rm si}^2(2 \pi f T) \hspace{0.05cm}.$$
	(\pi f T)\hspace{0.05cm},$$
	:$$ {\it \Phi}_s(f) = s_0^2 \cdot T \cdot \cos^2
	(\pi f T)\cdot {\rm si}^2
	(\pi f T)= s_0^2 \cdot T \cdot {\rm si}^2
	(2 \pi f T) \hspace{0.05cm}.$$

	The graph shows the power-spectral density		The graph shows the power-spectral density
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	*In the section quoted above,  the symbol error probability of the 4B3T code for the parameter  $10 \cdot \lg \hspace{0.05cm}(s_0^2 \cdot T/N_0) = 13 \ \rm dB$  was calculated as follows:		*In the section quoted above,  the symbol error probability of the 4B3T code for the parameter  $10 \cdot \lg \hspace{0.05cm}(s_0^2 \cdot T/N_0) = 13 \ \rm dB$  was calculated as follows:
	:$${ \sigma_d}/{s_0} = 0.145 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}		:$${ \sigma_d}/{s_0} = 0.145 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}p_{\rm S} = {4}/{3} \cdot {\rm Q} \left( \frac{s_0/2}{ \sigma_d} \right) \approx{4}/{3} \cdot {\rm Q} \left( 3.45 \right) = 3.7 \cdot 10^{-4}\hspace{0.05cm}.$$
	p_{\rm S} = {4}/{3} \cdot {\rm Q} \left( \frac{s_0/2}{ \sigma_d} \right) \approx
	{4}/{3} \cdot {\rm Q} \left( 3.45 \right) = 3.7 \cdot 10^{-4}
	\hspace{0.05cm}.$$
	*Using a pseudo-ternary code results in a larger error probability because here the noise rms value is not reduced compared to redundancy-free binary coding:		*Using a pseudo-ternary code results in a larger error probability because here the noise rms value is not reduced compared to redundancy-free binary coding:
	:$${ \sigma_d}/{s_0} = 0.167 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}		:$${ \sigma_d}/{s_0} = 0.167 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}p_{\rm S} = {4}/{3} \cdot {\rm Q} \left( \frac{s_0/2}{ \sigma_d} \right) \approx{4}/{3} \cdot {\rm Q} \left( 3 \right) = 1.8 \cdot 10^{-3}\hspace{0.05cm}.$$
	p_{\rm S} = {4}/{3} \cdot {\rm Q} \left( \frac{s_0/2}{ \sigma_d} \right) \approx
	{4}/{3} \cdot {\rm Q} \left( 3 \right) = 1.8 \cdot 10^{-3}
	\hspace{0.05cm}.$$
	*When the Nyquist condition is satisfied,  the AMI and duobinary codes do not differ in terms of error probability despite completely different eye diagrams.  But as will be shown in the section  [[Digital_Signal_Transmission/Intersymbol_Interference_for_Multi-Level_Transmission#Eye_opening_for_the_pseudo_ternary_codes\|"Eye opening for the pseudo-ternary codes"]],  the error behavior of these codes differs extremely whenever  [[Digital_Signal_Transmission/Ursachen_und_Auswirkungen_von_Impulsinterferenzen\|"intersymbol interference"]]  plays a role.<br>		*When the Nyquist condition is satisfied,  the AMI and duobinary codes do not differ in terms of error probability despite completely different eye diagrams.  But as will be shown in the section  [[Digital_Signal_Transmission/Intersymbol_Interference_for_Multi-Level_Transmission#Eye_opening_for_the_pseudo_ternary_codes\|"Eye opening for the pseudo-ternary codes"]],  the error behavior of these codes differs extremely whenever  [[Digital_Signal_Transmission/Ursachen_und_Auswirkungen_von_Impulsinterferenzen\|"intersymbol interference"]]  plays a role.<br>

Maintenance script: Add German interlanguage link

2026-03-16T12:26:50Z

Add German interlanguage link

← Older revision		Revision as of 14:26, 16 March 2026
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	{{Display}}		{{Display}}
			[[de:Digitalsignalübertragung/Symbolweise_Codierung_mit_Pseudoternärcodes]]

Noah at 22:47, 22 March 2023

2023-03-22T22:47:12Z

← Older revision		Revision as of 00:47, 23 March 2023
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	*The system comparison is made under  "peak constraint".  Therefore,  we use the rectangular basic transmission pulse.<br>		*The system comparison is made under  "peak constraint".  Therefore,  we use the rectangular basic transmission pulse.<br>

	*The overall frequency response shows a cosine ~~rolloff~~ with best possible rolloff factor  $r = 0.8$.		*The overall frequency response shows a raised cosine with best possible rolloff factor  $r = 0.8$.

	*The noise power  $\sigma_d^2$  is thus  $12\%$  larger than with the matched filter  (global optimum).		*The noise power  $\sigma_d^2$  is thus  $12\%$  larger than with the matched filter  (global optimum).

Hwang at 00:00, 13 November 2022

2022-11-13T00:00:09Z

← Older revision		Revision as of 02:00, 13 November 2022
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	*With the 4B3T code,  you can see clearly more lines in the eye diagram than in the two left pictures.  The redundancy-free ternary code would give almost the same result.<br>		*With the 4B3T code,  you can see clearly more lines in the eye diagram than in the two left pictures.  The redundancy-free ternary code would give almost the same result.<br>

	*On the ~~page~~ quoted above,  the symbol error probability of the 4B3T code for the parameter  $10 \cdot \lg \hspace{0.05cm}(s_0^2 \cdot T/N_0) = 13 \ \rm dB$  was calculated as follows:		*In the section quoted above,  the symbol error probability of the 4B3T code for the parameter  $10 \cdot \lg \hspace{0.05cm}(s_0^2 \cdot T/N_0) = 13 \ \rm dB$  was calculated as follows:
	:$${ \sigma_d}/{s_0} = 0.145 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}		:$${ \sigma_d}/{s_0} = 0.145 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}
	p_{\rm S} = {4}/{3} \cdot {\rm Q} \left( \frac{s_0/2}{ \sigma_d} \right) \approx		p_{\rm S} = {4}/{3} \cdot {\rm Q} \left( \frac{s_0/2}{ \sigma_d} \right) \approx

Guenter at 15:21, 24 August 2022

2022-08-24T15:21:47Z

← Older revision		Revision as of 17:21, 24 August 2022
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	*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.		*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.

	[[File:~~Dig_T_2_4_S1_v1_neu~~.png\|right\|frame\|Block diagram  (above)  and equivalent circuit  (below)  of a pseudo-ternary encoder ~~'''Korrektur'''~~\|class=fit]]		[[File:EN_Dig_T_2_4_S1_v23.png\|right\|frame\|Block diagram  (above)  and equivalent circuit  (below)  of a pseudo-ternary encoder\|class=fit]]

Guenter at 11:29, 13 July 2022

2022-07-13T11:29:50Z

← Older revision		Revision as of 13:29, 13 July 2022
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	*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.		*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.

	[[File:Dig_T_2_4_S1_v1_neu.png\|right\|frame\|Block diagram  (above)  and equivalent circuit  (below)  of a pseudo-ternary encoder\|class=fit]]		[[File:Dig_T_2_4_S1_v1_neu.png\|right\|frame\|Block diagram  (above)  and equivalent circuit  (below)  of a pseudo-ternary encoder '''Korrektur'''\|class=fit]]

Guenter at 16:13, 8 July 2022

2022-07-08T16:13:10Z

← Older revision		Revision as of 18:13, 8 July 2022
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	*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.		*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.

	[[File:Dig_T_2_4_S1_v1_neu.png\|right\|frame\|Block diagram and equivalent circuit of a pseudo-ternary encoder\|class=fit]]		[[File:Dig_T_2_4_S1_v1_neu.png\|right\|frame\|Block diagram  (above)  and equivalent circuit  (below)  of a pseudo-ternary encoder\|class=fit]]

Guenter at 14:56, 8 July 2022

2022-07-08T14:56:28Z

← Older revision		Revision as of 16:56, 8 July 2022
Line 20:		Line 20:
	*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.		*In the right graph an equivalent circuit is given,  which is very suitable for an analysis of these codes.

	[[File:~~EN_Dig_T_2_4_S1~~.png\|right\|frame\|Block diagram and equivalent circuit of a pseudo-ternary encoder ~~'''Korrektur''' untereinander D+E~~\|class=fit]]		[[File:Dig_T_2_4_S1_v1_neu.png\|right\|frame\|Block diagram and equivalent circuit of a pseudo-ternary encoder\|class=fit]]

Guenter at 15:32, 3 June 2022

2022-06-03T15:32:01Z

← Older revision		Revision as of 17:32, 3 June 2022
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	Typical for symbolwise coding is that		Typical for symbolwise coding is that
	*the symbol duration  $T$  of the ~~encoder '''KORREKTUR:~~ encoded~~'''~~ signal  (and of the transmitted signal)  matches the bit duration  $T_{\rm B}$  of the binary source signal,  and		*the symbol duration  $T$  of the encoded signal  (and of the transmitted signal)  matches the bit duration  $T_{\rm B}$  of the binary source signal,  and

	*encoding and decoding do not lead to major time delays,  which are unavoidable when block codes are used.<br><br>		*encoding and decoding do not lead to major time delays,  which are unavoidable when block codes are used.<br><br>
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	:* the likewise binary signal  $b(t)$  after the pre-encoder,  and		:* the likewise binary signal  $b(t)$  after the pre-encoder,  and

	:* the ~~encoder '''KORREKTUR:~~ encoded~~'''~~ signal  $c(t) = s(t)$  of the AMI code.		:* the encoded signal  $c(t) = s(t)$  of the AMI code.


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	#The binary value  "+1"  of the source signal  $q(t)$   ⇒   symbol  $\rm H$  is alternately represented by  $a_\nu = +1$  and  $a_\nu = -1$.  <br><br>		#The binary value  "+1"  of the source signal  $q(t)$   ⇒   symbol  $\rm H$  is alternately represented by  $a_\nu = +1$  and  $a_\nu = -1$.  <br><br>

	This ensures that the AMI ~~encoder '''KORREKTUR:~~ encoded~~'''~~ signal does not contain any   "long sequences"<br>		This ensures that the AMI encoded signal does not contain any   "long sequences"<br>
	*   $ \langle c_\nu \rangle = \langle \text{...}, +1, +1, +1, +1, +1, \text{...}\rangle$   resp.		*   $ \langle c_\nu \rangle = \langle \text{...}, +1, +1, +1, +1, +1, \text{...}\rangle$   resp.
	*   $ \langle c_\nu \rangle = \langle \text{...}, -1, -1, -1, -1, -1, \text{...}\rangle$,		*   $ \langle c_\nu \rangle = \langle \text{...}, -1, -1, -1, -1, -1, \text{...}\rangle$,