implementation

composants.typ

@@ -1,6 +1,7 @@
 #import "@preview/polylux:0.4.0": *
 #import "@preview/cetz:0.5.0"
 #import "@preview/cetz-plot:0.1.3": plot
+#import "@preview/cetz:0.5.0": canvas
 
 #set math.mat(delim: "[")
 
@@ -26,10 +27,13 @@
   // Footer
   #v(1fr)
   #context {
-    // let cur = counter(page).get().first()
-    // let tot = counter(page).final().first()
     let cur = counter("logical-slide").get().first()
-    let tot = counter("logical-slide").final().first()
+    let fins = query(<fin>)
+    let tot = if fins.len() > 0 {
+      counter("logical-slide").at(fins.first().location()).first()
+    } else {
+      counter("logical-slide").final().first()
+    }
 
     if cur > 1 {
       block(width: 100%, fill: black, inset: (top: 0.2cm, bottom: 0.2cm, left: 1.5cm, right: 1.5cm))[
@@ -37,7 +41,7 @@
         #grid(
           columns: (1.5fr, 2fr, 1fr, auto),
           align: (left, center, center, right),
-          [#auteur n°#numero], [#titre], [#annee], [#(cur - 1) / #(tot - 1)],
+          [#auteur n°#numero], [#titre], [#annee], if cur <= tot [#(cur - 1) / #(tot - 1)] else [Annexe],
         )
       ]
     }
@@ -801,8 +805,8 @@
     let h_height = ny * cell_size
 
     // Palette unifiée
-    let color_blue = blue
+    let color_blue = orange
-    let color_orange = orange
+    let color_orange = blue
     let col_dot_base = gray.darken(30%)
 
     // Définition des couleurs de fond (lighten)
@@ -2825,15 +2829,15 @@
   let msgs = (2.8, 0.7, 4.2, 1.8)
   let sgns = (1, -1, 1, 1)
   let vals = ("+2.8", "-0.7", "+4.2", "+1.8")
-  
+
   let col_ms = blue.darken(15%)
   let col_min = red.darken(10%)
-  let col_vn_bg = blue.lighten(94%) 
+  let col_vn_bg = blue.lighten(94%)
 
   // --- 1. GRAPHE DE TANNER ---
   group(name: "tanner", {
     for i in (0, 1, 2, 3) {
-      let y_pos = 2.25 - i*1.5
+      let y_pos = 2.25 - i * 1.5
       line((-6.5, y_pos), (-2.0, 0), stroke: 1.2pt + gray.lighten(30%))
     }
 
@@ -2841,15 +2845,19 @@
     content((-2.0, 0), text(size: 1.2em, fill: orange, weight: "bold")[$c$])
 
     for i in (0, 1, 2, 3) {
-      let y_pos = 2.25 - i*1.5
+      let y_pos = 2.25 - i * 1.5
-      circle((-6.5, y_pos), radius: 0.4, name: "v"+str(i), fill: col_vn_bg, stroke: 1.5pt + blue)
+      circle((-6.5, y_pos), radius: 0.4, name: "v" + str(i), fill: col_vn_bg, stroke: 1.5pt + blue)
-      content("v"+str(i), text(size: 0.75em, fill: blue.darken(20%), weight: "bold")[$v_#i$])
+      content("v" + str(i), text(size: 0.75em, fill: blue.darken(20%), weight: "bold")[$v_#i$])
 
       let val = vals.at(i)
-      content(((-6.5, y_pos), 42%, (-2.0, 0)), 
+      content(((-6.5, y_pos), 42%, (-2.0, 0)), box(
-        box(fill: col_vn_bg, stroke: 0.5pt + blue.lighten(60%), radius: 2pt, inset: 4pt)[
+        fill: col_vn_bg,
-          #text(size: 0.65em, fill: black.lighten(10%), weight: "bold")[#val]
+        stroke: 0.5pt + blue.lighten(60%),
-        ])
+        radius: 2pt,
+        inset: 4pt,
+      )[
+        #text(size: 0.65em, fill: black.lighten(10%), weight: "bold")[#val]
+      ])
     }
   })
 
@@ -2858,7 +2866,7 @@
 
   // --- 3. GRAPHIQUE DES BARRES ---
   group(name: "bars", {
-    let base_x = 1.4 
+    let base_x = 1.4
     for (i, m) in msgs.enumerate() {
       let x = base_x + i * 1.4
       let is_min = (m == 0.7)
@@ -2875,9 +2883,320 @@
 
   // --- 4. FLÈCHE ROUGE ---
   line((6.5, 0), (8.0, 0), mark: (end: "stealth", fill: col_min), stroke: 2pt + col_min)
-  
+
   // --- 5. RÉSULTAT FINAL (Décalé plus à droite à x = 11.5) ---
   content((10.5, 0), box(stroke: 1.5pt + col_min, fill: col_min.lighten(96%), radius: 5pt, inset: 10pt)[
     #text(size: 0.8em, weight: "bold")[$m_(c arrow v_"cible") = -0.7$]
   ])
 })
+
+
+#let waterfall_plot(pts_uncoded, pts_bf) = {
+  cetz.canvas({
+    import cetz.draw
+    plot.plot(
+      size: (23, 14.5),
+      x-label: pad(top: 5cm)[],
+      y-label: [BER],
+      x-min: 0,
+      x-max: 8,
+      y-min: -9,
+      y-max: 0.2,
+      x-tick-step: 1,
+      y-tick-step: 1,
+      x-grid: true,
+      y-grid: true,
+      y-format: y => $10^(#int(y))$,
+      x-format: x => pad(top: 1cm)[#x],
+      legend: (2, 6),
+      legend-style: (
+        padding: 0.3,
+        stroke: gray.lighten(50%),
+        fill: white,
+      ),
+      {
+        plot.annotate({
+          // for decade in range(-9, 0) {
+          //   for minor in (2, 3, 4, 5, 6, 7, 8, 9) {
+          //     let y_pos = decade + (calc.log(minor) / calc.log(10))
+          //     if y_pos >= -9 and y_pos <= 0 {
+          //       draw.line(
+          //         (0, y_pos),
+          //         (8, y_pos),
+          //         stroke: (paint: gray.lighten(70%), thickness: 0.3pt),
+          //       )
+          //     }
+          //   }
+          // }
+          draw.content((4, -10), text(size: 1.2em)[$E_b/N_0$ (dB)])
+        })
+        plot.add(
+          pts_uncoded,
+          label: [Signal non codé],
+          style: (stroke: (paint: orange, thickness: 2pt, dash: "dashed")),
+          mark: "+",
+          mark-style: (stroke: orange, size: 0.5),
+        )
+
+        plot.add(
+          pts_bf,
+          label: [Bit-Flipping],
+          style: (stroke: (paint: blue, thickness: 2.5pt)),
+          mark: "square",
+          mark-style: (stroke: blue, fill: white, size: 0.25),
+        )
+      },
+    )
+  })
+}
+
+#let convergence_plot(iters, syndrms) = {
+  let n = iters.len()
+  let max_s = 160.0
+  let W = 20.0
+  let H = 15.0
+  let bw = W / n
+
+  cetz.canvas({
+    import cetz.draw
+
+    for tick in (0, 50, 100, 150) {
+      let y = (tick / max_s) * H
+      draw.line((0, y), (W, y), stroke: 0.5pt + gray.lighten(60%))
+      draw.content((-0.8, y), text(size: 13pt)[#tick])
+    }
+
+    for i in range(n) {
+      let s = syndrms.at(i)
+      let bh = (s / max_s) * H
+      let x0 = i * bw
+      let col = if s == 0 { green.darken(20%) } else { blue }
+
+      draw.rect(
+        (x0, 0),
+        (x0 + bw * 0.8, bh),
+        fill: col.lighten(70%),
+        stroke: 1.2pt + col,
+      )
+
+      if calc.rem(i, 2) == 0 or i == n - 1 {
+        draw.content((x0 + bw * 0.4, -0.4), text(size: 13pt)[#i])
+      }
+    }
+
+    draw.line((0, 0), (W + 0.8, 0), stroke: 2pt, mark: (end: "stealth"))
+    draw.line((0, 0), (0, H + 0.8), stroke: 2pt, mark: (end: "stealth"))
+
+    draw.content((W / 2, -1), text(size: 19pt, weight: "bold")[Itérations])
+    draw.content((-2.2, H / 2), angle: 90deg, text(size: 19pt, weight: "bold")[Syndromes])
+  })
+}
+
+#let waterfall_plot(pts_uncoded, pts_bf) = {
+  cetz.canvas({
+    import cetz.draw: *
+    plot.plot(
+      size: (22, 15),
+      x-label: none,
+      y-label: none,
+      x-min: 0,
+      x-max: 10,
+      y-min: -9,
+      y-max: 0.2,
+      x-tick-step: 1,
+      y-tick-step: 1,
+      x-grid: true,
+      y-grid: true,
+      style: (
+        axes: (
+          bottom: (tick: (label: (offset: 0.2))), // Chiffres plus proches de l'axe
+          left: (tick: (label: (offset: 0.2))),
+        ),
+      ),
+      y-format: y => $10^(#int(y))$,
+      x-format: x => [#x],
+      legend: (14.4, 12.9),
+      legend-style: (padding: 0.3, stroke: gray.lighten(50%), fill: white),
+      {
+        plot.annotate({
+          // for decade in range(-9, 0) {
+          //   for minor in (2, 3, 4, 5, 6, 7, 8, 9) {
+          //     let y_pos = decade + (calc.log(minor) / calc.log(10))
+          //     if y_pos >= -9 and y_pos <= 0 {
+          //       line((0, y_pos), (8, y_pos), stroke: (paint: gray.lighten(60%), thickness: 0.3pt))
+          //     }
+          //   }
+          // }
+          content((4, -9.9), text(size: 1.3em)[$E_b/N_0$ (dB)])
+          content((-1, -4.5), angle: 90deg, text(size: 1.3em)[BER])
+        })
+        plot.add(
+          pts_uncoded,
+          label: [Signal non codé],
+          style: (stroke: (paint: orange, thickness: 2pt, dash: "dashed")),
+          mark: "+",
+          mark-style: (stroke: orange, size: 0.5),
+        )
+        plot.add(
+          pts_bf,
+          label: [Bit-Flipping LDPC],
+          style: (stroke: (paint: blue, thickness: 2.5pt)),
+          mark: "square",
+          mark-style: (stroke: blue, fill: white, size: 0.25),
+        )
+      },
+    )
+  })
+}
+
+#let simulation_image_flow(img_orig, img_noisy, img_r05, img_r66, img_r75, img_w: 150pt, gap_top: 3.0, gap_bot: 4.0) = {
+  cetz.canvas({
+    import cetz.draw: *
+
+    let w_unit = img_w / 1cm
+    let y_top = 5.0
+    let y_bot = -6.0
+
+    let x_side = (w_unit + gap_top) / 2
+    let x_res = w_unit + gap_bot
+
+    // --- LIGNE 1 : ÉMISSION ET BRUIT (Texte collé en haut) ---
+    content(
+      (-x_side, y_top),
+      [
+        #set align(center)
+        #set par(leading: 0pt)
+        #set text(bottom-edge: "baseline") // Supprime l'espace sous les lettres
+        #text(weight: "bold", size: 1.3em)[Originale]
+        #v(-0.6cm)
+        #box(width: img_w, stroke: 2pt + black, radius: 4pt, inset: 0pt, img_orig)
+      ],
+      name: "orig",
+    )
+
+    content(
+      (x_side, y_top),
+      [
+        #set align(center)
+        #set par(leading: 0pt)
+        #set text(bottom-edge: "baseline")
+        #text(weight: "bold", size: 1.3em, fill: red)[Reçue (Bruité)]
+        #v(-0.6cm)
+        #box(width: img_w, stroke: 2pt + red, radius: 4pt, inset: 0pt, img_noisy)
+      ],
+      name: "noisy",
+    )
+
+    // --- FLÈCHE CANAL (Ajustée pour le nouveau centre de gravité) ---
+    let y_img_center = y_top - 1.4
+
+    line(
+      (-x_side + w_unit / 2, y_img_center),
+      (x_side - w_unit / 2, y_img_center),
+      stroke: 4pt + gray,
+      mark: (end: "stealth", fill: gray, size: 0.5),
+    )
+
+    content((0, y_img_center + 0.8), text(size: 1.1em, fill: gray.darken(40%), style: "italic")[AWGN (2.3 dB)])
+
+    // --- LIGNE 2 : COMPARAISON DES RENDEMENTS (Texte collé en bas) ---
+    let targets = (
+      (pos: (-x_res, y_bot), img: img_r05, rate: [$R = 1/2$], col: green.darken(20%), name: "r1"),
+      (pos: (0, y_bot), img: img_r66, rate: [$R = 2/3$], col: orange, name: "r2"),
+      (pos: (x_res, y_bot), img: img_r75, rate: [$R = 3/4$], col: red, name: "r3"),
+    )
+
+    for t in targets {
+      content(
+        t.pos,
+        [
+          #set align(center)
+          #set par(leading: 0pt)
+          #set text(top-edge: "baseline") // Supprime l'espace au-dessus des lettres
+          #box(width: img_w, stroke: 2.5pt + t.col, radius: 4pt, inset: 0pt, t.img)
+          #v(-0.6cm)
+          #text(weight: "bold", size: 1.5em, fill: t.col)[#t.rate]
+        ],
+        name: t.name,
+      )
+    }
+  })
+}
+
+#let comparison_waterfall_plot(pts_unc, pts_bf, pts_sp, pts_ms) = {
+  cetz.canvas({
+    import cetz.draw: *
+    plot.plot(
+      size: (21, 15),
+      x-label: none,
+      y-label: none,
+      x-min: 0,
+      x-max: 11,
+      y-min: -8,
+      y-max: 0.2,
+      x-tick-step: 1,
+      y-tick-step: 1,
+      x-grid: true,
+      y-grid: true,
+      style: (
+        axes: (
+          bottom: (tick: (label: (offset: 0.2))),
+          left: (tick: (label: (offset: 0.2))),
+        ),
+      ),
+      y-format: y => $10^(#int(y))$,
+      x-format: x => [#x],
+      legend: (13.2, 11.4),
+      legend-style: (padding: 0.3, stroke: gray.lighten(50%), fill: white),
+      {
+        plot.annotate({
+          // Grille logarithmique étendue jusqu'à x=11
+          // for decade in range(-8, 0) {
+          //   for minor in (2, 3, 4, 5, 6, 7, 8, 9) {
+          //     let y_pos = decade + (calc.log(minor) / calc.log(10))
+          //     if y_pos >= -8 and y_pos <= 0 {
+          //       line((0, y_pos), (11, y_pos), stroke: (paint: gray.lighten(75%), thickness: 0.3pt))
+          //     }
+          //   }
+          // }
+          // Label X centré sur 11 unités (environ 5.5)
+          content((5.5, -8.7), text(size: 1.3em)[$E_b/N_0$ (dB)])
+          // Label Y
+          content((-1.2, -4.0), angle: 90deg, text(size: 1.3em)[BER])
+        })
+
+        plot.add(
+          pts_unc,
+          label: [Signal non codé],
+          style: (stroke: (paint: orange, thickness: 2pt, dash: "dashed")),
+          mark: "+",
+          mark-style: (stroke: orange, size: 1),
+        )
+
+        plot.add(
+          pts_bf,
+          label: [Bit-Flipping (Hard)],
+          style: (stroke: (paint: red, thickness: 2pt)),
+          mark: "x",
+          mark-style: (stroke: red, size: 1),
+        )
+
+        plot.add(
+          pts_ms,
+          label: [Min-Sum (Soft)],
+          style: (stroke: (paint: green.darken(20%), thickness: 2pt)),
+          mark: "triangle",
+          mark-style: (stroke: green.darken(20%), fill: white, size: 0.3),
+        )
+
+        plot.add(
+          pts_sp,
+          label: [Sum-Product (Soft)],
+          style: (stroke: (paint: blue, thickness: 2pt)),
+          mark: "square",
+          mark-style: (stroke: blue, fill: white, size: 1),
+        )
+      },
+    )
+  })
+}

main.typ

@@ -789,6 +789,11 @@
   ]
 ]
 
+#myslide("Méthode de génération de H")[
+  - Gallager
+  - Mackay
+  - Progressive Edge-growth
+]
 
 #myslide("Encodage LDPC : Calcul de G")[
   #set text(size: 18pt)
@@ -932,17 +937,62 @@
   ]
 ]
 
-#myslide("Exemple implementation Bit-Flipping rust")[
+#let log10(x) = if x < 1e-9 { -9.0 } else { calc.log(x) / calc.log(10) }
-  ex + canal d'etude bruit AWGN avec ce qu'il se passe dans les radio / cable etc + tension
+
+#let raw_waterfall = (
+  (0.0, 0.158461, 0.281269),
+  (1.0, 0.130748, 0.247257),
+  (2.0, 0.104310, 0.205882),
+  (3.0, 0.079301, 0.151808),
+  (4.0, 0.056395, 0.063852),
+  (4.5, 0.046493, 0.023414),
+  (5.0, 0.037572, 0.004078),
+  (5.5, 0.029673, 0.000470),
+  (6.0, 0.022973, 0.000045),
+  (7.0, 0.012519, 0.000002),
+  (8.0, 0.006030, 0.000000001),
+  // On lisse la fin pour éviter l'effet "escalier"
+  (8.5, 0.004200, 0.0), 
+  (9.0, 0.002800, 0.0), 
+  (9.5, 0.001800, 0.0),
+  (10.0, 0.001100, 0.0),
+)
+
+#let pts_unc = raw_waterfall.map(r => (r.at(0), log10(r.at(1))))
+#let pts_bf = raw_waterfall.map(r => (r.at(0), log10(r.at(2))))
+
+// Données Convergence
+#let iters = range(25)
+#let syndrms = (135, 66, 60, 61, 31, 24, 21, 19, 19, 16, 15, 155, 45, 35, 31, 19, 16, 13, 10, 9, 6, 5, 4, 3, 0)
+
+#myslide([Waterfall : LDPC (3, 6) $n = 1296, space k = 648, space R = 1/2$])[
+  #align(center)[#waterfall_plot(pts_unc, pts_bf)]
+  // #place(dx: 140pt, dy: -140pt)[
+  //   #align(center)[
+  //     // Affichage des paramètres du code
+  //     #scale(110%)[
+  //     #rect(fill: blue.lighten(95%), stroke: 0.5pt + blue.lighten(80%), radius: 4pt, inset: 10pt)[
+  //       #set text(size: 18pt)
+  //       *LDPC $(3, 6)$* #h(1cm)
+  //       $n = 1296$, $k = 648$ #h(1cm)
+  //       Rendement $R = 1/2$
+  //     ]]
+  //   ]
+  // ]
+]
+
+#myslide([Résultats : Convergence syndrome])[
+  #align(center)[#convergence_plot(iters, syndrms)]
 ]
 
 #myslide("Bit-Flipping : Analyse")[
   // TODO  PARLER DU GIRTH 4 => MAUVAIS
   #set text(size: 17pt)
 
+  #place(dy: 4.5cm)[
   #definition(titre: "Avantages", accent: green.darken(10%))[
     #set text(size: 0.88em)
-    - *Complexité* : simples XOR et compteurs — $cal(O)(n)$ par itération
+    - *Complexité* : simples XOR et compteurs -- $cal(O)(n)$ par itération
     // - *Matériel* : idéal FPGA/ASIC, massivement parallélisable
     // - *Simplicité* : inventé par Gallager (1962)
   ]
@@ -961,13 +1011,14 @@
     // ]
     // ]
   ]
+  ]
 ]
 
 #myslide("Décodage Soft : Le LLR")[
   #set text(size: 17pt)
 
   #definition(titre: "Signal", accent: blue.darken(10%))[
-    On reçoit une valeur $y_i$ (ex: $+4.5$V ou $-0.2$V). Le LLR transforme cette mesure physique en une valeur statistique sans unité.
+    On reçoit une valeur $y_i$ (ex: $+4.5$V ou $-0.2$V).
   ]
 
   #v(0.6em)
@@ -978,7 +1029,7 @@
     $
   ]
 
-  #v(0.6em)
+  #v(1.3em)
 
   #align(center)[
     #scale(125%)[#schema_llr_droite()]
@@ -1121,8 +1172,21 @@
   ]
 ]
 
-#myslide("Implementation rust")[
+#myslide([Transmission d'image])[
-
+  #place(center, dy: -2cm)[
+    #scale(85%)[
+      #simulation_image_flow(
+        image("src/origine.png", width: 100%),
+        image("src/noisy.png", width: 100%),
+        image("src/decoded_R05_1-2.png", width: 100%),
+        image("src/decoded_R66_2-3.png", width: 100%),
+        image("src/decoded_R75_3-4.png", width: 100%),
+        img_w: 230pt,
+        gap_top: 7.0,
+        gap_bot: 2.0,
+      )
+    ]
+  ]
 ]
 
 #myslide("Min-Sum")[
@@ -1155,14 +1219,53 @@
   ]
 ]
 
-#myslide("Test réel")[
+#let log10(x) = if x <= 1e-9 { -8.0 } else { calc.log(x) / calc.log(10) }
-  Irl hackrf, test de diff de debit avec des paquets
+
+#let raw_data = (
+  (0.00, 1.2397e-1, 4.9986e-1, 1.1404e-1, 1.2470e-1),
+  (0.50, 1.1057e-1, 4.9993e-1, 9.5550e-2, 1.0485e-1),
+  (1.00, 9.7682e-2, 4.9978e-1, 7.5017e-2, 8.2555e-2),
+  (1.50, 8.4916e-2, 4.9993e-1, 4.6412e-2, 5.1824e-2),
+  (2.00, 7.3000e-2, 5.0008e-1, 1.1640e-2, 1.3790e-2),
+  (2.50, 6.1705e-2, 4.9987e-1, 4.0818e-4, 5.3380e-4),
+  (3.00, 5.1501e-2, 5.0020e-1, 4.8765e-5, 8.0247e-6),
+  (3.50, 4.1921e-2, 5.0005e-1, 0, 0),
+  (4.00, 3.3645e-2, 4.9959e-1, 0, 0),
+  (5.00, 1.9973e-2, 4.9890e-1, 0, 0),
+  (6.00, 1.0584e-2, 3.8048e-1, 0, 0),
+  (7.00, 4.8994e-3, 4.0660e-2, 0, 0),
+  (8.00, 1.8194e-3, 3.8519e-4, 0, 0),
+  (9.00, 5.6235e-4, 8.1790e-6, 0, 0),
+  (10.00, 1.3133e-4, 6.1728e-7, 0, 0),
+  (11.00, 2.5154e-5, 0, 0, 0),
+)
+
+#let pts_unc = raw_data.map(d => (d.at(0), log10(d.at(1))))
+#let pts_bf = raw_data.map(d => (d.at(0), log10(d.at(2))))
+#let pts_sp = raw_data.map(d => (d.at(0), log10(d.at(3))))
+#let pts_ms = raw_data.map(d => (d.at(0), log10(d.at(4))))
+
+#myslide([Waterfall : LDPC (3, 9) $n = 1296, space k = 864, space R = 2/3$])[
+  #align(center)[
+    // #rect(fill: gray.lighten(95%), radius: 4pt, inset: 8pt)[
+    //   #set text(size: 16pt)
+    //   Comparaison BER : *Bit-Flipping* (Décision dure) vs *Soft-Decisions* (SP & MS)
+    // ]
+    #comparison_waterfall_plot(pts_unc, pts_bf, pts_sp, pts_ms)
+  ]
 ]
 
-#myslide("Image")[
+#myslide("QC-LDPC")[
-  Test de transmission d'image avec différent ldpc non opti et opti (le H)
+
 ]
 
+#myslide("Test réel")[
+  Transmission hackrf, test de diff de debit avec paquets
+  Test de transmission d'image avec différent ldpc non opti et opti (H diff etc)
+]
+
+#[]<fin>
+
 #myslide("Annexe")[
   #align(center + horizon)[
     Annexe
@@ -1176,6 +1279,10 @@
   Poser les notations algebriques etc...
 ]
 
+#myslide("Définition du BER et SFR")[
+
+]
+
 #myslide("Decodage par maximum de vraisemblance")[
   Expliquer, quelle distance ? etc
 ]
@@ -1187,3 +1294,11 @@
 #myslide("Maths deriere Belief Propagation")[
 
 ]
+
+#myslide("AWGN")[
+
+]
+
+#myslide("PEG")[
+
+]