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authorsara <sara.halter@gmx.ch>2021-11-06 14:11:10 +0100
committersara <sara.halter@gmx.ch>2021-11-06 14:11:10 +0100
commit84bd7ae6a6cad4d1788b16b5bb9200739dce9385 (patch)
treebfc80c3333d32f39fdabd8415df6a005dce4cf98 /hardware/QPSK
parentscr tests (diff)
parentMerge branch 'master' of github.com:NaoPross/Fading (diff)
downloadFading-84bd7ae6a6cad4d1788b16b5bb9200739dce9385.tar.gz
Fading-84bd7ae6a6cad4d1788b16b5bb9200739dce9385.zip
Merge remote-tracking branch 'origin/master'
Diffstat (limited to '')
-rwxr-xr-xhardware/QPSK/qpks.py199
-rw-r--r--hardware/QPSK/qpsk.grc209
2 files changed, 314 insertions, 94 deletions
diff --git a/hardware/QPSK/qpks.py b/hardware/QPSK/qpks.py
index aa9b943..f89ac12 100755
--- a/hardware/QPSK/qpks.py
+++ b/hardware/QPSK/qpks.py
@@ -166,7 +166,7 @@ class qpks(gr.top_block, Qt.QWidget):
)
self.uhd_usrp_sink_0.set_clock_source('external', 0)
self.uhd_usrp_sink_0.set_center_freq(2.4e9, 0)
- self.uhd_usrp_sink_0.set_normalized_gain(0.3, 0)
+ self.uhd_usrp_sink_0.set_normalized_gain(0.35, 0)
self.uhd_usrp_sink_0.set_antenna('TX/RX', 0)
self.uhd_usrp_sink_0.set_samp_rate(samp_rate)
self.uhd_usrp_sink_0.set_time_unknown_pps(uhd.time_spec())
@@ -278,88 +278,6 @@ class qpks(gr.top_block, Qt.QWidget):
self.plots_grid_layout_2.setRowStretch(r, 1)
for c in range(0, 1):
self.plots_grid_layout_2.setColumnStretch(c, 1)
- self.qtgui_time_raster_sink_x_0 = qtgui.time_raster_sink_b(
- samp_rate,
- 256,
- 256,
- [],
- [],
- "",
- 1
- )
-
- self.qtgui_time_raster_sink_x_0.set_update_time(0.10)
- self.qtgui_time_raster_sink_x_0.set_intensity_range(-1, 1)
- self.qtgui_time_raster_sink_x_0.enable_grid(False)
- self.qtgui_time_raster_sink_x_0.enable_axis_labels(True)
-
- labels = ['', '', '', '', '',
- '', '', '', '', '']
- colors = [0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0]
- alphas = [1.0, 1.0, 1.0, 1.0, 1.0,
- 1.0, 1.0, 1.0, 1.0, 1.0]
-
- for i in range(1):
- if len(labels[i]) == 0:
- self.qtgui_time_raster_sink_x_0.set_line_label(i, "Data {0}".format(i))
- else:
- self.qtgui_time_raster_sink_x_0.set_line_label(i, labels[i])
- self.qtgui_time_raster_sink_x_0.set_color_map(i, colors[i])
- self.qtgui_time_raster_sink_x_0.set_line_alpha(i, alphas[i])
-
- self._qtgui_time_raster_sink_x_0_win = sip.wrapinstance(self.qtgui_time_raster_sink_x_0.pyqwidget(), Qt.QWidget)
- self.plots_grid_layout_3.addWidget(self._qtgui_time_raster_sink_x_0_win, 1, 0, 1, 1)
- for r in range(1, 2):
- self.plots_grid_layout_3.setRowStretch(r, 1)
- for c in range(0, 1):
- self.plots_grid_layout_3.setColumnStretch(c, 1)
- self.qtgui_histogram_sink_x_0 = qtgui.histogram_sink_f(
- 1024*4,
- 20,
- -1,
- 1,
- "Sent",
- 1
- )
-
- self.qtgui_histogram_sink_x_0.set_update_time(0.10)
- self.qtgui_histogram_sink_x_0.enable_autoscale(True)
- self.qtgui_histogram_sink_x_0.enable_accumulate(False)
- self.qtgui_histogram_sink_x_0.enable_grid(False)
- self.qtgui_histogram_sink_x_0.enable_axis_labels(True)
-
-
- labels = ['', '', '', '', '',
- '', '', '', '', '']
- widths = [1, 1, 1, 1, 1,
- 1, 1, 1, 1, 1]
- colors = ["blue", "red", "green", "black", "cyan",
- "magenta", "yellow", "dark red", "dark green", "dark blue"]
- styles = [1, 1, 1, 1, 1,
- 1, 1, 1, 1, 1]
- markers= [-1, -1, -1, -1, -1,
- -1, -1, -1, -1, -1]
- alphas = [1.0, 1.0, 1.0, 1.0, 1.0,
- 1.0, 1.0, 1.0, 1.0, 1.0]
-
- for i in range(1):
- if len(labels[i]) == 0:
- self.qtgui_histogram_sink_x_0.set_line_label(i, "Data {0}".format(i))
- else:
- self.qtgui_histogram_sink_x_0.set_line_label(i, labels[i])
- self.qtgui_histogram_sink_x_0.set_line_width(i, widths[i])
- self.qtgui_histogram_sink_x_0.set_line_color(i, colors[i])
- self.qtgui_histogram_sink_x_0.set_line_style(i, styles[i])
- self.qtgui_histogram_sink_x_0.set_line_marker(i, markers[i])
- self.qtgui_histogram_sink_x_0.set_line_alpha(i, alphas[i])
-
- self._qtgui_histogram_sink_x_0_win = sip.wrapinstance(self.qtgui_histogram_sink_x_0.pyqwidget(), Qt.QWidget)
- self.plots_grid_layout_3.addWidget(self._qtgui_histogram_sink_x_0_win, 0, 0, 1, 1)
- for r in range(0, 1):
- self.plots_grid_layout_3.setRowStretch(r, 1)
- for c in range(0, 1):
- self.plots_grid_layout_3.setColumnStretch(c, 1)
self.qtgui_freq_sink_x_1_0_1_0 = qtgui.freq_sink_c(
1024, #size
firdes.WIN_BLACKMAN_hARRIS, #wintype
@@ -580,6 +498,110 @@ class qpks(gr.top_block, Qt.QWidget):
self.plots_grid_layout_1.setRowStretch(r, 1)
for c in range(0, 1):
self.plots_grid_layout_1.setColumnStretch(c, 1)
+ self.qtgui_eye_sink_x_1 = qtgui.eye_sink_c(
+ 1024, #size
+ samp_rate, #samp_rate
+ "", #name
+ 1 #number of inputs
+ )
+ self.qtgui_eye_sink_x_1.set_update_time(0.10)
+ self.qtgui_eye_sink_x_1.set_samp_per_symbol(sps)
+ self.qtgui_eye_sink_x_1.set_y_axis(-1, 1)
+
+ self.qtgui_eye_sink_x_1.set_y_label('Amplitude', "")
+
+ self.qtgui_eye_sink_x_1.enable_tags(True)
+ self.qtgui_eye_sink_x_1.set_trigger_mode(qtgui.TRIG_MODE_FREE, qtgui.TRIG_SLOPE_POS, 0.0, 0, 0, "")
+ self.qtgui_eye_sink_x_1.enable_autoscale(False)
+ self.qtgui_eye_sink_x_1.enable_grid(False)
+ self.qtgui_eye_sink_x_1.enable_axis_labels(True)
+ self.qtgui_eye_sink_x_1.enable_control_panel(False)
+
+
+ labels = ['Signal 1', 'Signal 2', 'Signal 3', 'Signal 4', 'Signal 5',
+ 'Signal 6', 'Signal 7', 'Signal 8', 'Signal 9', 'Signal 10']
+ widths = [1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1]
+ colors = ['blue', 'blue', 'blue', 'blue', 'blue',
+ 'blue', 'blue', 'blue', 'blue', 'blue']
+ alphas = [1.0, 1.0, 1.0, 1.0, 1.0,
+ 1.0, 1.0, 1.0, 1.0, 1.0]
+ styles = [1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1]
+ markers = [-1, -1, -1, -1, -1,
+ -1, -1, -1, -1, -1]
+
+
+ for i in range(2):
+ if len(labels[i]) == 0:
+ if (i % 2 == 0):
+ self.qtgui_eye_sink_x_1.set_line_label(i, "Eye [Re{{Data {0}}}]".format(round(i/2)))
+ else:
+ self.qtgui_eye_sink_x_1.set_line_label(i, "Eye [Im{{Data {0}}}]".format(round((i-1)/2)))
+ else:
+ self.qtgui_eye_sink_x_1.set_line_label(i, labels[i])
+ self.qtgui_eye_sink_x_1.set_line_width(i, widths[i])
+ self.qtgui_eye_sink_x_1.set_line_color(i, colors[i])
+ self.qtgui_eye_sink_x_1.set_line_style(i, styles[i])
+ self.qtgui_eye_sink_x_1.set_line_marker(i, markers[i])
+ self.qtgui_eye_sink_x_1.set_line_alpha(i, alphas[i])
+
+ self._qtgui_eye_sink_x_1_win = sip.wrapinstance(self.qtgui_eye_sink_x_1.pyqwidget(), Qt.QWidget)
+ self.plots_grid_layout_3.addWidget(self._qtgui_eye_sink_x_1_win, 1, 0, 1, 1)
+ for r in range(1, 2):
+ self.plots_grid_layout_3.setRowStretch(r, 1)
+ for c in range(0, 1):
+ self.plots_grid_layout_3.setColumnStretch(c, 1)
+ self.qtgui_eye_sink_x_0 = qtgui.eye_sink_c(
+ 1024, #size
+ samp_rate, #samp_rate
+ "", #name
+ 1 #number of inputs
+ )
+ self.qtgui_eye_sink_x_0.set_update_time(0.10)
+ self.qtgui_eye_sink_x_0.set_samp_per_symbol(sps)
+ self.qtgui_eye_sink_x_0.set_y_axis(-1, 1)
+
+ self.qtgui_eye_sink_x_0.set_y_label('Amplitude', "")
+
+ self.qtgui_eye_sink_x_0.enable_tags(True)
+ self.qtgui_eye_sink_x_0.set_trigger_mode(qtgui.TRIG_MODE_FREE, qtgui.TRIG_SLOPE_POS, 0.0, 0, 0, "")
+ self.qtgui_eye_sink_x_0.enable_autoscale(False)
+ self.qtgui_eye_sink_x_0.enable_grid(False)
+ self.qtgui_eye_sink_x_0.enable_axis_labels(True)
+ self.qtgui_eye_sink_x_0.enable_control_panel(False)
+
+
+ labels = ['Signal 1', 'Signal 2', 'Signal 3', 'Signal 4', 'Signal 5',
+ 'Signal 6', 'Signal 7', 'Signal 8', 'Signal 9', 'Signal 10']
+ widths = [1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1]
+ colors = ['blue', 'blue', 'blue', 'blue', 'blue',
+ 'blue', 'blue', 'blue', 'blue', 'blue']
+ alphas = [1.0, 1.0, 1.0, 1.0, 1.0,
+ 1.0, 1.0, 1.0, 1.0, 1.0]
+ styles = [1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1]
+ markers = [-1, -1, -1, -1, -1,
+ -1, -1, -1, -1, -1]
+
+
+ for i in range(2):
+ if len(labels[i]) == 0:
+ if (i % 2 == 0):
+ self.qtgui_eye_sink_x_0.set_line_label(i, "Eye [Re{{Data {0}}}]".format(round(i/2)))
+ else:
+ self.qtgui_eye_sink_x_0.set_line_label(i, "Eye [Im{{Data {0}}}]".format(round((i-1)/2)))
+ else:
+ self.qtgui_eye_sink_x_0.set_line_label(i, labels[i])
+ self.qtgui_eye_sink_x_0.set_line_width(i, widths[i])
+ self.qtgui_eye_sink_x_0.set_line_color(i, colors[i])
+ self.qtgui_eye_sink_x_0.set_line_style(i, styles[i])
+ self.qtgui_eye_sink_x_0.set_line_marker(i, markers[i])
+ self.qtgui_eye_sink_x_0.set_line_alpha(i, alphas[i])
+
+ self._qtgui_eye_sink_x_0_win = sip.wrapinstance(self.qtgui_eye_sink_x_0.pyqwidget(), Qt.QWidget)
+ self.top_grid_layout.addWidget(self._qtgui_eye_sink_x_0_win)
self.qtgui_const_sink_x_2 = qtgui.const_sink_c(
1024, #size
"Locked", #name
@@ -814,7 +836,7 @@ class qpks(gr.top_block, Qt.QWidget):
log=False)
self.digital_constellation_decoder_cb_0 = digital.constellation_decoder_cb(qpsk_const)
self.digital_cma_equalizer_cc_0 = digital.cma_equalizer_cc(eq_ntaps, eq_mod, eq_gain, int(sps / 2))
- self.blocks_uchar_to_float_0 = blocks.uchar_to_float()
+ self.blocks_null_sink_0 = blocks.null_sink(gr.sizeof_char*1)
self.blocks_file_source_0 = blocks.file_source(gr.sizeof_char*1, '/home/god/Documents/Fading/hardware/QPSK/lena512color.tiff', True, 0, 0)
self.blocks_file_source_0.set_begin_tag(pmt.PMT_NIL)
@@ -823,9 +845,7 @@ class qpks(gr.top_block, Qt.QWidget):
##################################################
# Connections
##################################################
- self.connect((self.blocks_file_source_0, 0), (self.blocks_uchar_to_float_0, 0))
self.connect((self.blocks_file_source_0, 0), (self.digital_constellation_modulator_0, 0))
- self.connect((self.blocks_uchar_to_float_0, 0), (self.qtgui_histogram_sink_x_0, 0))
self.connect((self.digital_cma_equalizer_cc_0, 0), (self.digital_costas_loop_cc_0, 0))
self.connect((self.digital_cma_equalizer_cc_0, 0), (self.qtgui_const_sink_x_1_0, 0))
self.connect((self.digital_cma_equalizer_cc_0, 0), (self.qtgui_freq_sink_x_1_0_1, 0))
@@ -836,10 +856,11 @@ class qpks(gr.top_block, Qt.QWidget):
self.connect((self.digital_constellation_modulator_0, 0), (self.uhd_usrp_sink_0, 0))
self.connect((self.digital_costas_loop_cc_0, 0), (self.digital_constellation_decoder_cb_0, 0))
self.connect((self.digital_costas_loop_cc_0, 0), (self.qtgui_const_sink_x_2, 0))
+ self.connect((self.digital_costas_loop_cc_0, 0), (self.qtgui_eye_sink_x_1, 0))
self.connect((self.digital_costas_loop_cc_0, 0), (self.qtgui_freq_sink_x_1_0_1_0, 0))
self.connect((self.digital_costas_loop_cc_0, 0), (self.qtgui_time_sink_x_2_0_0, 0))
self.connect((self.digital_diff_decoder_bb_0, 0), (self.digital_map_bb_0, 0))
- self.connect((self.digital_map_bb_0, 0), (self.qtgui_time_raster_sink_x_0, 0))
+ self.connect((self.digital_map_bb_0, 0), (self.blocks_null_sink_0, 0))
self.connect((self.digital_pfb_clock_sync_xxx_0, 0), (self.digital_cma_equalizer_cc_0, 0))
self.connect((self.digital_pfb_clock_sync_xxx_0, 0), (self.qtgui_const_sink_x_0_0, 0))
self.connect((self.digital_pfb_clock_sync_xxx_0, 0), (self.qtgui_freq_sink_x_1_0, 0))
@@ -859,6 +880,8 @@ class qpks(gr.top_block, Qt.QWidget):
def set_sps(self, sps):
self.sps = sps
self.set_rrc_taps(firdes.root_raised_cosine(self.nfilts, self.nfilts, 1.0/float(self.sps), self.excess_bw, 45*self.nfilts))
+ self.qtgui_eye_sink_x_0.set_samp_per_symbol(self.sps)
+ self.qtgui_eye_sink_x_1.set_samp_per_symbol(self.sps)
def get_nfilts(self):
return self.nfilts
@@ -886,6 +909,8 @@ class qpks(gr.top_block, Qt.QWidget):
def set_samp_rate(self, samp_rate):
self.samp_rate = samp_rate
+ self.qtgui_eye_sink_x_0.set_samp_rate(self.samp_rate)
+ self.qtgui_eye_sink_x_1.set_samp_rate(self.samp_rate)
self.qtgui_freq_sink_x_1.set_frequency_range(0, self.samp_rate)
self.qtgui_freq_sink_x_1_0.set_frequency_range(0, self.samp_rate)
self.qtgui_freq_sink_x_1_0_0.set_frequency_range(0, self.samp_rate)
diff --git a/hardware/QPSK/qpsk.grc b/hardware/QPSK/qpsk.grc
index 69c2915..fd17712 100644
--- a/hardware/QPSK/qpsk.grc
+++ b/hardware/QPSK/qpsk.grc
@@ -205,7 +205,7 @@ blocks:
bus_sink: false
bus_source: false
bus_structure: null
- coordinate: [1776, 692.0]
+ coordinate: [1832, 692.0]
rotation: 0
state: disabled
- name: blocks_file_source_0
@@ -246,7 +246,7 @@ blocks:
bus_structure: null
coordinate: [1832, 800.0]
rotation: 0
- state: disabled
+ state: enabled
- name: blocks_uchar_to_float_0
id: blocks_uchar_to_float
parameters:
@@ -261,7 +261,7 @@ blocks:
bus_structure: null
coordinate: [792.0, 192]
rotation: 90
- state: true
+ state: disabled
- name: blocks_vector_source_x_0
id: blocks_vector_source_x
parameters:
@@ -936,9 +936,203 @@ blocks:
bus_sink: false
bus_source: false
bus_structure: null
- coordinate: [1372.0, 720]
+ coordinate: [1380.0, 720]
rotation: 90
state: true
+- name: qtgui_eye_sink_x_0
+ id: qtgui_eye_sink_x
+ parameters:
+ affinity: ''
+ alias: ''
+ alpha1: '1.0'
+ alpha10: '1.0'
+ alpha2: '1.0'
+ alpha3: '1.0'
+ alpha4: '1.0'
+ alpha5: '1.0'
+ alpha6: '1.0'
+ alpha7: '1.0'
+ alpha8: '1.0'
+ alpha9: '1.0'
+ autoscale: 'False'
+ axislabels: 'True'
+ color1: blue
+ color10: blue
+ color2: blue
+ color3: blue
+ color4: blue
+ color5: blue
+ color6: blue
+ color7: blue
+ color8: blue
+ color9: blue
+ comment: ''
+ ctrlpanel: 'False'
+ entags: 'True'
+ grid: 'False'
+ gui_hint: ''
+ label1: Signal 1
+ label10: Signal 10
+ label2: Signal 2
+ label3: Signal 3
+ label4: Signal 4
+ label5: Signal 5
+ label6: Signal 6
+ label7: Signal 7
+ label8: Signal 8
+ label9: Signal 9
+ legend: 'True'
+ marker1: '-1'
+ marker10: '-1'
+ marker2: '-1'
+ marker3: '-1'
+ marker4: '-1'
+ marker5: '-1'
+ marker6: '-1'
+ marker7: '-1'
+ marker8: '-1'
+ marker9: '-1'
+ name: '""'
+ nconnections: '1'
+ samp_per_symbol: sps
+ size: '1024'
+ srate: samp_rate
+ style1: '1'
+ style10: '1'
+ style2: '1'
+ style3: '1'
+ style4: '1'
+ style5: '1'
+ style6: '1'
+ style7: '1'
+ style8: '1'
+ style9: '1'
+ tr_chan: '0'
+ tr_delay: '0'
+ tr_level: '0.0'
+ tr_mode: qtgui.TRIG_MODE_FREE
+ tr_slope: qtgui.TRIG_SLOPE_POS
+ tr_tag: '""'
+ type: complex
+ update_time: '0.10'
+ width1: '1'
+ width10: '1'
+ width2: '1'
+ width3: '1'
+ width4: '1'
+ width5: '1'
+ width6: '1'
+ width7: '1'
+ width8: '1'
+ width9: '1'
+ ylabel: Amplitude
+ ymax: '1'
+ ymin: '-1'
+ yunit: '""'
+ states:
+ bus_sink: false
+ bus_source: false
+ bus_structure: null
+ coordinate: [1360, 84.0]
+ rotation: 0
+ state: true
+- name: qtgui_eye_sink_x_1
+ id: qtgui_eye_sink_x
+ parameters:
+ affinity: ''
+ alias: ''
+ alpha1: '1.0'
+ alpha10: '1.0'
+ alpha2: '1.0'
+ alpha3: '1.0'
+ alpha4: '1.0'
+ alpha5: '1.0'
+ alpha6: '1.0'
+ alpha7: '1.0'
+ alpha8: '1.0'
+ alpha9: '1.0'
+ autoscale: 'False'
+ axislabels: 'True'
+ color1: blue
+ color10: blue
+ color2: blue
+ color3: blue
+ color4: blue
+ color5: blue
+ color6: blue
+ color7: blue
+ color8: blue
+ color9: blue
+ comment: ''
+ ctrlpanel: 'False'
+ entags: 'True'
+ grid: 'False'
+ gui_hint: 'plots@3: 1,0,1,1'
+ label1: Signal 1
+ label10: Signal 10
+ label2: Signal 2
+ label3: Signal 3
+ label4: Signal 4
+ label5: Signal 5
+ label6: Signal 6
+ label7: Signal 7
+ label8: Signal 8
+ label9: Signal 9
+ legend: 'True'
+ marker1: '-1'
+ marker10: '-1'
+ marker2: '-1'
+ marker3: '-1'
+ marker4: '-1'
+ marker5: '-1'
+ marker6: '-1'
+ marker7: '-1'
+ marker8: '-1'
+ marker9: '-1'
+ name: '""'
+ nconnections: '1'
+ samp_per_symbol: sps
+ size: '1024'
+ srate: samp_rate
+ style1: '1'
+ style10: '1'
+ style2: '1'
+ style3: '1'
+ style4: '1'
+ style5: '1'
+ style6: '1'
+ style7: '1'
+ style8: '1'
+ style9: '1'
+ tr_chan: '0'
+ tr_delay: '0'
+ tr_level: '0.0'
+ tr_mode: qtgui.TRIG_MODE_FREE
+ tr_slope: qtgui.TRIG_SLOPE_POS
+ tr_tag: '""'
+ type: complex
+ update_time: '0.10'
+ width1: '1'
+ width10: '1'
+ width2: '1'
+ width3: '1'
+ width4: '1'
+ width5: '1'
+ width6: '1'
+ width7: '1'
+ width8: '1'
+ width9: '1'
+ ylabel: Amplitude
+ ymax: '1'
+ ymin: '-1'
+ yunit: '""'
+ states:
+ bus_sink: false
+ bus_source: false
+ bus_structure: null
+ coordinate: [1840, 1028.0]
+ rotation: 0
+ state: true
- name: qtgui_freq_sink_x_1
id: qtgui_freq_sink_x
parameters:
@@ -1425,7 +1619,7 @@ blocks:
bus_structure: null
coordinate: [912, 60.0]
rotation: 0
- state: true
+ state: disabled
- name: qtgui_time_raster_sink_x_0
id: qtgui_time_raster_sink_x
parameters:
@@ -1482,7 +1676,7 @@ blocks:
bus_structure: null
coordinate: [1832, 852.0]
rotation: 0
- state: true
+ state: disabled
- name: qtgui_time_sink_x_2
id: qtgui_time_sink_x
parameters:
@@ -1790,7 +1984,7 @@ blocks:
comment: ''
dev_addr: '"serial=309AF59 "'
dev_args: '""'
- gain0: '0.3'
+ gain0: '0.35'
gain1: '0'
gain10: '0'
gain11: '0'
@@ -2343,6 +2537,7 @@ connections:
- [digital_constellation_modulator_0, '0', uhd_usrp_sink_0, '0']
- [digital_costas_loop_cc_0, '0', digital_constellation_decoder_cb_0, '0']
- [digital_costas_loop_cc_0, '0', qtgui_const_sink_x_2, '0']
+- [digital_costas_loop_cc_0, '0', qtgui_eye_sink_x_1, '0']
- [digital_costas_loop_cc_0, '0', qtgui_freq_sink_x_1_0_1_0, '0']
- [digital_costas_loop_cc_0, '0', qtgui_time_sink_x_2_0_0, '0']
- [digital_diff_decoder_bb_0, '0', digital_map_bb_0, '0']