belief-prop + min-sum
This commit is contained in:
458
composants.typ
458
composants.typ
@ -2423,3 +2423,461 @@
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content((-7.3, (y_cn + y_check) / 2), angle: 90deg, text(size: 1.1em, style: "italic", weight: "bold")[iter $+1$])
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content((-7.3, (y_cn + y_check) / 2), angle: 90deg, text(size: 1.1em, style: "italic", weight: "bold")[iter $+1$])
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})
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})
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}
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}
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/////
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//
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//
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//
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#let schema_llr_droite() = {
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cetz.canvas(length: 1cm, {
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import cetz.draw: *
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let col_left = blue.darken(10%) // Bit 0 (Inversé)
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let col_right = red.darken(10%) // Bit 1 (Inversé)
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let col_ax = black
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let col_mid = gray.darken(30%)
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let L = 7.0 // demi-longueur de l'axe
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let y0 = 0.0
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let y_top = 1.8
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// ── 1. Zones colorées (Dessinées en PREMIER, en HAUT) ──
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// Zone gauche (négative) -> Bit 0
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rect((-L, y0 + 0.02), (-0.05, y0 + 0.32), fill: col_left.lighten(92%), stroke: none)
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content((-L / 2, y0 + 0.65), text(fill: col_left, weight: "bold", size: 0.9em)[Bit = 0])
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// Zone droite (positive) -> Bit 1
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rect((0.05, y0 + 0.02), (L, y0 + 0.32), fill: col_right.lighten(92%), stroke: none)
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content((L / 2, y0 + 0.65), text(fill: col_right, weight: "bold", size: 0.9em)[Bit = 1])
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// ── 2. Axe horizontal (Dessiné APRÈS pour passer AU-DESSUS) ──
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line((-L, y0), (L, y0), stroke: 1.8pt + col_ax, mark: (end: "stealth", fill: col_ax, size: 0.22))
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content((L + 0.5, y0), text(size: 0.85em)[$L(v_i)$], anchor: "west")
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// ── 3. Zéro ──
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line((0, -0.2), (0, 0.2), stroke: 1.5pt + col_mid)
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content((0, -0.5), text(size: 0.8em, fill: col_mid)[0])
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// ── 4. Points exemples (Sans les Volts) ──
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// -6 (Bit 0 à gauche)
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let px_left = -5.0
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circle((px_left, y0), radius: 0.15, fill: col_left, stroke: none)
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// La ligne pointillée part de l'axe vers le haut
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line((px_left, y0), (px_left, y_top), stroke: (paint: col_left, thickness: 1pt, dash: "dashed"))
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content(
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(px_left, y_top + 0.1),
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box(fill: col_left.lighten(92%), stroke: 0.5pt + col_left, radius: 3pt, inset: 4pt)[
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#text(fill: col_left, weight: "bold", size: 0.75em)[$-6$]
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],
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anchor: "south",
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)
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// +0.3 (Proche de zéro, Bit 1)
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let px_near = 0.6
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circle((px_near, y0), radius: 0.15, fill: col_right.lighten(40%), stroke: none)
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line((px_near, y0), (px_near, y_top - 0.7), stroke: (paint: col_right.lighten(20%), thickness: 1pt, dash: "dashed"))
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content(
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(px_near, y_top - 0.65),
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box(fill: white, stroke: 0.5pt + col_right.lighten(30%), radius: 3pt, inset: 3pt)[
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#text(fill: col_right.darken(20%), size: 0.7em)[$+0.3$]
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],
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anchor: "south-west",
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)
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// +10 (Bit 1 à droite)
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let px_right = 5.8
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circle((px_right, y0), radius: 0.15, fill: col_right, stroke: none)
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line((px_right, y0), (px_right, y_top), stroke: (paint: col_right, thickness: 1pt, dash: "dashed"))
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content(
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(px_right, y_top + 0.1),
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box(fill: col_right.lighten(92%), stroke: 0.5pt + col_right, radius: 3pt, inset: 4pt)[
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#text(fill: col_right, weight: "bold", size: 0.75em)[$+10$]
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],
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anchor: "south",
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)
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})
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}
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///2
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#let schema_sum_product_dual() = {
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cetz.canvas(length: 1cm, {
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import cetz.draw: *
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let col_cn = orange.darken(0%)
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let col_vn = blue.darken(0%)
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let col_msg = gray.darken(35%)
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// --- PARTIE HAUTE : MISE À JOUR CN (PRODUIT DES TANH) ---
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group({
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let base_y = 4.0
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let cn_pos = (0.0, base_y)
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let vn_in_pos = ((-3.2, base_y + 1.3), (-3.2, base_y - 1.3))
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let vn_out_pos = (3.2, base_y)
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// 1. Check Node Central (cj)
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rect(
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(cn_pos.at(0) - 0.45, cn_pos.at(1) - 0.45),
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(cn_pos.at(0) + 0.45, cn_pos.at(1) + 0.45),
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fill: col_cn.lighten(90%),
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stroke: 2pt + col_cn,
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name: "cj_top",
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)
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content("cj_top", text(size: 0.75em, fill: col_cn, weight: "bold")[$c_j$])
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// 2. Variable Node de sortie (v0)
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circle(vn_out_pos, radius: 0.5, fill: white, stroke: 2pt + col_vn, name: "v0_top")
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content("v0_top", text(size: 0.7em, fill: col_vn, weight: "bold")[$v_0$])
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// 3. Arête de sortie : cj -> v0
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line("cj_top", "v0_top", stroke: 2.2pt + orange, mark: (end: "stealth", fill: orange, size: 0.25))
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content((1.8, base_y + 0.6), text(size: 0.8em, fill: orange.darken(0%), weight: "bold")[$m_(c_j arrow v_0)$])
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// 4. Voisins entrants (vi)
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for (i, p) in vn_in_pos.enumerate() {
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let n_name = "vin_" + str(i)
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circle(p, radius: 0.45, fill: col_vn.lighten(92%), stroke: 1.2pt + col_vn, name: n_name)
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content(n_name, text(size: 0.65em, fill: col_vn, weight: "bold")[$v_#(i + 1)$])
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line(n_name, "cj_top", stroke: 1.1pt + col_msg, mark: (end: "stealth", fill: col_msg, size: 0.2))
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content((p.at(0) + 1.4, p.at(1)), text(size: 0.75em, fill: col_msg)[$m_(v_#(i + 1) arrow c_j)$])
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}
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})
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// Séparateur discret
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line((-4.5, 1.8), (4.5, 1.8), stroke: (paint: gray.lighten(85%), dash: "dashed"))
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// --- PARTIE BASSE : MISE À JOUR VN (SOMME DES LLR) ---
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group({
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let base_y = -1.5
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let vn_pos = (0.0, base_y)
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let cn_in_pos = ((-3.2, base_y + 1.2), (-3.2, base_y - 1.2))
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let cn_out_pos = (3.2, base_y)
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// 1. Variable Node Central (vj)
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circle(vn_pos, radius: 0.55, fill: col_vn.lighten(90%), stroke: 2pt + col_vn, name: "vj_bot")
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content("vj_bot", text(weight: "bold", fill: col_vn)[$v_j$])
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// 2. Check Node de sortie (c0) - Toujours ORANGE
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rect(
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(cn_out_pos.at(0) - 0.4, cn_out_pos.at(1) - 0.4),
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(cn_out_pos.at(0) + 0.4, cn_out_pos.at(1) + 0.4),
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fill: white,
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stroke: 1.8pt + orange,
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name: "c0_bot",
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)
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content("c0_bot", text(size: 0.65em, fill: orange.darken(0%), weight: "bold")[$c_0$])
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// 3. Arête de sortie : vj -> c0
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line("vj_bot", "c0_bot", stroke: 2.2pt + blue, mark: (end: "stealth", fill: blue, size: 0.25))
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content((1.8, base_y - 0.7), text(size: 0.8em, fill: blue.darken(0%), weight: "bold")[$m_(v_j arrow c_0)$])
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// 4. Entrée Canal LLR
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let canal_top = (0.0, base_y + 2.2)
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line(canal_top, "vj_bot", stroke: 1.8pt + blue, mark: (end: "stealth", fill: blue, size: 0.22))
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content((canal_top.at(0), canal_top.at(1) + 0.3), text(
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size: 0.85em,
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fill: blue,
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weight: "bold",
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)[$L_"canal" (y_j)$])
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// 5. Check Nodes entrants
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for (i, p) in cn_in_pos.enumerate() {
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let n_name = "cin_" + str(i)
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rect(
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(p.at(0) - 0.35, p.at(1) - 0.35),
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(p.at(0) + 0.35, p.at(1) + 0.35),
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fill: orange.lighten(95%),
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stroke: 1pt + orange,
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name: n_name,
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)
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content(n_name, text(size: 0.6em, fill: orange.darken(0%))[$c_#(i + 1)$])
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line(n_name, "vj_bot", stroke: 1.1pt + col_msg, mark: (end: "stealth", fill: col_msg, size: 0.2))
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content((p.at(0) + 1.4, p.at(1)), text(size: 0.75em, fill: col_msg)[$m_(c_#(i + 1) arrow v_j)$])
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}
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})
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})
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}
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#let col_cn = orange
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#let col_vn = blue
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#let col_msg = gray.darken(50%)
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#let s_len = 1.1cm
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// 1. INITIALISATION
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#let schema_detailed_init() = cetz.canvas(length: s_len, {
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import cetz.draw: *
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// Couleurs pures
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let col_vn_pure = blue
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let col_cn_pure = orange
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let col_msg_dark = gray.darken(50%)
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// Noeud Variable
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circle((0, 0), radius: 0.6, fill: col_vn_pure.lighten(90%), stroke: 2pt + col_vn_pure, name: "vj")
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content("vj", text(weight: "bold")[$v_j$])
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// Entrée canal
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line((0, 1.8), (0, 0.6), stroke: 2pt + blue, mark: (end: "stealth", fill: blue, size: 0.2))
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content((0, 2.1), text(fill: blue, size: 0.9em, weight: "bold")[$L_("canal")$])
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// Targets plus éloignées sur la droite (x: 4.0)
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let targets = ((4.0, 1.2), (4.0, -1.2))
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for (i, p) in targets.enumerate() {
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let name = "c" + str(i + 1)
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// Check Nodes
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rect(
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(p.at(0) - 0.4, p.at(1) - 0.4),
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(p.at(0) + 0.4, p.at(1) + 0.4),
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fill: col_cn_pure.lighten(95%),
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stroke: 1.5pt + col_cn_pure,
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name: name,
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)
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content(name, text(size: 0.7em, fill: col_cn_pure, weight: "bold")[$c_#(i + 1)$])
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// Arête
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line("vj.east", name, stroke: 1.2pt + col_msg_dark, mark: (end: "stealth", fill: col_msg_dark))
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// Position du message calculée pour être "collée" à l'arête
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// On place le texte à mi-chemin (x=2.0) avec un léger offset y
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let y_offset = if p.at(1) > 0 { 0.4 } else { -0.25 }
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content((2.0, p.at(1) * 0.5 + y_offset), text(size: 0.75em, fill: col_msg_dark)[$m_(v_j arrow c_#(i + 1))$])
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}
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})
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// 2. CN UPDATE
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#let schema_detailed_cn() = cetz.canvas(length: s_len, {
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import cetz.draw: *
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rect((-0.5, -0.5), (0.5, 0.5), fill: col_cn.lighten(90%), stroke: 2.2pt + col_cn, name: "cj")
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content("cj", text(weight: "bold", fill: col_cn)[$c_j$])
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let ins = ((-3.0, 1.3), (-3.0, -1.3))
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for (i, p) in ins.enumerate() {
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let v_name = "vi" + str(i + 1)
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circle(p, radius: 0.45, fill: col_vn.lighten(92%), stroke: 1.2pt + col_vn, name: v_name)
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line(v_name, "cj", stroke: 1.1pt + col_msg, mark: (end: "stealth", fill: col_msg))
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content(v_name, text(size: 0.65em, fill: col_vn, weight: "bold")[$v_#(i + 1)$])
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content((p.at(0) + 1.5, p.at(1)), text(size: 0.75em, fill: col_msg)[$m_(v_#(i + 1) arrow c_j)$])
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}
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circle((3.0, 0), radius: 0.6, fill: white, stroke: 2pt + col_vn, name: "v0")
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content("v0", text(size: 0.75em, fill: col_vn, weight: "bold")[$v_0$])
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line("cj", "v0", stroke: 2.3pt + orange, mark: (end: "stealth", fill: orange, size: 0.25))
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content((1.8, 0.6), text(size: 0.85em, fill: orange, weight: "bold")[$m_(c_j arrow v_0)$])
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})
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// 3. VN UPDATE
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#let schema_detailed_vn() = cetz.canvas(length: s_len, {
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import cetz.draw: *
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circle((0, 0), radius: 0.7, fill: col_vn.lighten(90%), stroke: 2.5pt + col_vn, name: "vj")
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content("vj", text(weight: "bold", fill: col_vn)[$v_j$])
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line((0, 2.0), (0, 0.7), stroke: 2pt + blue, mark: (end: "stealth", fill: blue, size: 0.2))
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content((0, 2.3), text(size: 0.85em, fill: blue, weight: "bold")[$L_("canal")$])
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let ins = ((-3.0, 1.2), (-3.0, -1.2))
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for (i, p) in ins.enumerate() {
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let c_name = "ci" + str(i + 1)
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rect(
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(p.at(0) - 0.4, p.at(1) - 0.4),
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(p.at(0) + 0.4, p.at(1) + 0.4),
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fill: col_cn.lighten(95%),
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stroke: 1.2pt + col_cn,
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name: c_name,
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)
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line(c_name, "vj", stroke: 1.1pt + col_msg, mark: (end: "stealth", fill: col_msg))
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content(c_name, text(size: 0.65em, fill: col_cn, weight: "bold")[$c_#(i + 1)$])
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content((p.at(0) + 1.5, p.at(1)), text(size: 0.75em, fill: col_msg)[$m_(c_#(i + 1) arrow v_j)$])
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}
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rect((2.6, -0.45), (3.4, 0.45), fill: white, stroke: 2pt + orange, name: "c0")
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content("c0", text(size: 0.7em, fill: col_cn, weight: "bold")[$c_0$])
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line("vj", "c0", stroke: 2.3pt + blue, mark: (end: "stealth", fill: blue, size: 0.25))
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content((1.7, -0.8), text(size: 0.85em, fill: blue, weight: "bold")[$m_(v_j arrow c_0)$])
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})
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// 4. DÉCISION FINALE
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#let schema_detailed_decision() = cetz.canvas(length: s_len, {
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import cetz.draw: *
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let col_vn_dec = green
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// 1. Variable Node Central (Le bit j)
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circle((0, 0), radius: 0.75, fill: green.lighten(92%), stroke: 2.5pt + col_vn_dec, name: "vn")
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content("vn", text(weight: "bold", size: 1.1em)[$Lambda_j$])
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// 2. Entrée LLR Canal
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||||||
|
line((0, 1.7), (0, 0.75), stroke: 1.8pt + blue, mark: (end: "stealth", fill: blue, size: 0.15))
|
||||||
|
content((0, 2.0), text(fill: blue, size: 0.8em, weight: "bold")[$L_"canal"$])
|
||||||
|
|
||||||
|
// 3. Arrivées des Check Nodes (i)
|
||||||
|
let ins = ((-2.3, 1.0), (-2.3, -1.0), (2.3, 1.0), (2.3, -1.0))
|
||||||
|
for (i, p) in ins.enumerate() {
|
||||||
|
let name = "call" + str(i)
|
||||||
|
rect(
|
||||||
|
(p.at(0) - 0.3, p.at(1) - 0.3),
|
||||||
|
(p.at(0) + 0.3, p.at(1) + 0.3),
|
||||||
|
fill: orange.lighten(95%),
|
||||||
|
stroke: 1.1pt + orange,
|
||||||
|
name: name,
|
||||||
|
)
|
||||||
|
line(name, "vn", stroke: 1.1pt + orange, mark: (end: "stealth", fill: orange, size: 0.12))
|
||||||
|
content(name, text(size: 0.5em, fill: orange, weight: "bold")[$c_#i$])
|
||||||
|
}
|
||||||
|
|
||||||
|
// 4. ÉQUATION LAMBDA : On somme sur les voisins du bit j -> N(v_j)
|
||||||
|
content((0, -2), text(size: 0.8em, fill: col_vn_dec)[
|
||||||
|
$display(Lambda_j = L_("canal") + sum_(i in cal(N)(v_j)) m_(c_i arrow v_j))$
|
||||||
|
])
|
||||||
|
|
||||||
|
// 5. Bloc Hard Decision
|
||||||
|
content((3.5, 0), name: "verdict", box(fill: white, stroke: 1.5pt + black, inset: 6pt, radius: 2pt)[
|
||||||
|
#set text(size: 0.6em)
|
||||||
|
#set math.cases(gap: 0.3em)
|
||||||
|
$hat(v)_j = cases(0 "si" Lambda_j > 0, 1 "si" Lambda_j < 0)$
|
||||||
|
])
|
||||||
|
|
||||||
|
// 6. Liaison pointillés
|
||||||
|
line((0.8, 0), "verdict.west", stroke: (paint: black, thickness: 1.3pt, dash: "dotted"))
|
||||||
|
})
|
||||||
|
|
||||||
|
// ③ Schéma Min-Sum : comparaison SP vs MS + highlight du terme minimum
|
||||||
|
// #let schema_min_sum_vis() = {
|
||||||
|
// cetz.canvas(length: 1cm, {
|
||||||
|
// import cetz.draw: *
|
||||||
|
//
|
||||||
|
// let col_ms = blue.darken(15%)
|
||||||
|
// let col_min = red.darken(5%)
|
||||||
|
// let col_sgn = orange.darken(5%)
|
||||||
|
//
|
||||||
|
// // Messages entrants (4 voisins u ≠ v)
|
||||||
|
// let msgs = (2.1, 0.4, 3.7, 1.2)
|
||||||
|
// let sgns = (1, -1, 1, 1) // signes
|
||||||
|
//
|
||||||
|
// let y_base = 0.0
|
||||||
|
// let xs = (-4.5, -1.5, 1.5, 4.5)
|
||||||
|
//
|
||||||
|
// // Titre colonnes
|
||||||
|
// content((-3.0, 4.8), text(size: 0.82em, fill: col_sgn, weight: "bold")[Signes])
|
||||||
|
// content((3.0, 4.8), text(size: 0.82em, fill: col_ms, weight: "bold")[|Amplitudes|])
|
||||||
|
//
|
||||||
|
// for (i, x) in xs.enumerate() {
|
||||||
|
// let m = msgs.at(i)
|
||||||
|
// let s = sgns.at(i)
|
||||||
|
// let is_min = (m == 0.4)
|
||||||
|
// let col_box = if is_min { col_min } else { col_ms }
|
||||||
|
//
|
||||||
|
// // Barre amplitude
|
||||||
|
// let bar_h = m * 0.55
|
||||||
|
// rect((x - 0.5, y_base), (x + 0.5, y_base + bar_h),
|
||||||
|
// fill: col_box.lighten(if is_min { 70% } else { 85% }),
|
||||||
|
// stroke: 1.5pt + col_box)
|
||||||
|
//
|
||||||
|
// // Valeur amplitude
|
||||||
|
// content((x, y_base + bar_h + 0.35),
|
||||||
|
// text(size: 0.82em, fill: col_box, weight: "bold")[#m])
|
||||||
|
//
|
||||||
|
// // Signe (XOR logic)
|
||||||
|
// let s_txt = if s > 0 { [+] } else { [−] }
|
||||||
|
// let s_col = col_sgn
|
||||||
|
// content((x, -0.65),
|
||||||
|
// box(fill: s_col.lighten(88%), stroke: 0.5pt + s_col,
|
||||||
|
// radius: 2pt, inset: (x:6pt, y:3pt))[
|
||||||
|
// #text(size: 0.88em, fill: s_col, weight: "bold")[#s_txt]
|
||||||
|
// ])
|
||||||
|
//
|
||||||
|
// // Label u_i
|
||||||
|
// content((x, -1.3), text(size: 0.74em, fill: gray.darken(30%))[
|
||||||
|
// $m_(#(i+1)→c)$
|
||||||
|
// ])
|
||||||
|
// }
|
||||||
|
//
|
||||||
|
// // Flèche vers résultat
|
||||||
|
// let y_res = -2.4
|
||||||
|
// line((0, -1.6), (0, y_res + 0.3),
|
||||||
|
// mark: (end: "stealth", fill: black, size: 0.2),
|
||||||
|
// stroke: 1.4pt + black)
|
||||||
|
//
|
||||||
|
// // Encadré résultat
|
||||||
|
// content((0, y_res - 0.1),
|
||||||
|
// box(fill: col_min.lighten(88%), stroke: 1.5pt + col_min,
|
||||||
|
// radius: 5pt, inset: (x: 14pt, y: 8pt))[
|
||||||
|
// #set text(size: 0.82em)
|
||||||
|
// Signe produit : #text(fill: col_sgn, weight: "bold")[$(-1)^1 = -$]
|
||||||
|
// #h(8pt)
|
||||||
|
// Min : #text(fill: col_min, weight: "bold")[$0.4$]
|
||||||
|
// #h(8pt)
|
||||||
|
// $=>$ #text(fill: col_min, weight: "bold")[$m_(c→v) = -0.4$]
|
||||||
|
// ])
|
||||||
|
//
|
||||||
|
// // Étiquette "minimum"
|
||||||
|
// content((-1.5, y_base + 0.4 * 0.55 + 0.95),
|
||||||
|
// text(size: 0.72em, fill: col_min, style: "italic",
|
||||||
|
// weight: "bold")[← minimum !])
|
||||||
|
// })
|
||||||
|
// }
|
||||||
|
|
||||||
|
#let schema_min_sum_complet() = cetz.canvas(length: 1cm, {
|
||||||
|
import cetz.draw: *
|
||||||
|
|
||||||
|
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%)
|
||||||
|
|
||||||
|
// --- 1. GRAPHE DE TANNER ---
|
||||||
|
group(name: "tanner", {
|
||||||
|
for i in (0, 1, 2, 3) {
|
||||||
|
let y_pos = 2.25 - i*1.5
|
||||||
|
line((-6.5, y_pos), (-2.0, 0), stroke: 1.2pt + gray.lighten(30%))
|
||||||
|
}
|
||||||
|
|
||||||
|
rect((-2.5, -0.5), (-1.5, 0.5), name: "cn", stroke: 2pt + orange, fill: orange.lighten(92%))
|
||||||
|
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
|
||||||
|
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")[$v_#i$])
|
||||||
|
|
||||||
|
let val = vals.at(i)
|
||||||
|
content(((-6.5, y_pos), 42%, (-2.0, 0)),
|
||||||
|
box(fill: col_vn_bg, stroke: 0.5pt + blue.lighten(60%), radius: 2pt, inset: 4pt)[
|
||||||
|
#text(size: 0.65em, fill: black.lighten(10%), weight: "bold")[#val]
|
||||||
|
])
|
||||||
|
}
|
||||||
|
})
|
||||||
|
|
||||||
|
// --- 2. FLÈCHE GRISE ---
|
||||||
|
line((-1.0, 0), (0.5, 0), mark: (end: "stealth", fill: gray), stroke: 1.5pt + gray)
|
||||||
|
|
||||||
|
// --- 3. GRAPHIQUE DES BARRES ---
|
||||||
|
group(name: "bars", {
|
||||||
|
let base_x = 1.4
|
||||||
|
for (i, m) in msgs.enumerate() {
|
||||||
|
let x = base_x + i * 1.4
|
||||||
|
let is_min = (m == 0.7)
|
||||||
|
let col = if is_min { col_min } else { col_ms }
|
||||||
|
|
||||||
|
rect((x - 0.4, 0), (x + 0.4, m * 0.45), fill: col.lighten(if is_min { 75% } else { 88% }), stroke: 1.5pt + col)
|
||||||
|
content((x, m * 0.45 + 0.35), text(size: 0.7em, fill: col, weight: "bold")[#m])
|
||||||
|
content((x, -0.7), box(fill: orange.lighten(92%), stroke: 0.5pt + orange, inset: 5pt, radius: 2pt)[
|
||||||
|
#text(size: 0.8em, fill: orange, weight: "bold")[#(if sgns.at(i) > 0 [+] else [−])]
|
||||||
|
])
|
||||||
|
if is_min { content((x, m * 0.45 + 0.8), text(size: 0.55em, fill: col, weight: "bold")[MIN]) }
|
||||||
|
}
|
||||||
|
})
|
||||||
|
|
||||||
|
// --- 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")[$m_(c arrow v_"cible") = -0.7$]
|
||||||
|
])
|
||||||
|
})
|
||||||
|
|||||||
195
main.typ
195
main.typ
@ -937,6 +937,7 @@
|
|||||||
]
|
]
|
||||||
|
|
||||||
#myslide("Bit-Flipping : Analyse")[
|
#myslide("Bit-Flipping : Analyse")[
|
||||||
|
// TODO PARLER DU GIRTH 4 => MAUVAIS
|
||||||
#set text(size: 17pt)
|
#set text(size: 17pt)
|
||||||
|
|
||||||
#definition(titre: "Avantages", accent: green.darken(10%))[
|
#definition(titre: "Avantages", accent: green.darken(10%))[
|
||||||
@ -962,15 +963,199 @@
|
|||||||
]
|
]
|
||||||
]
|
]
|
||||||
|
|
||||||
#myslide("Soft decoding")[
|
#myslide("Décodage Soft : Le LLR")[
|
||||||
belief propagation, log ou virgule fixe, explication resultat meilleur
|
#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.
|
||||||
|
]
|
||||||
|
|
||||||
|
#v(0.6em)
|
||||||
|
|
||||||
|
#definition(titre: "Log-Likelihood Ratio (LLR)", accent: black)[
|
||||||
|
$
|
||||||
|
L(v_i) = ln(display(frac(P(v_i = 0 | y_i), P(v_i = 1 | y_i))))
|
||||||
|
$
|
||||||
|
]
|
||||||
|
|
||||||
|
#v(0.6em)
|
||||||
|
|
||||||
|
#align(center)[
|
||||||
|
#scale(125%)[#schema_llr_droite()]
|
||||||
|
]
|
||||||
|
|
||||||
|
#v(1em)
|
||||||
|
|
||||||
|
// Blocs de légende centrés
|
||||||
|
#align(center)[
|
||||||
|
#grid(
|
||||||
|
columns: (220pt, 220pt),
|
||||||
|
gutter: 1cm,
|
||||||
|
block(fill: blue.lighten(92%), stroke: 1pt + blue, radius: 6pt, inset: 12pt)[
|
||||||
|
#align(center)[
|
||||||
|
#text(fill: blue.darken(20%), weight: "bold")[Signe] \
|
||||||
|
#text(size: 0.85em)[Définit la valeur du bit]
|
||||||
|
]
|
||||||
|
],
|
||||||
|
block(fill: orange.lighten(90%), stroke: 1pt + orange, radius: 6pt, inset: 12pt)[
|
||||||
|
#align(center)[
|
||||||
|
#text(fill: orange.darken(20%), weight: "bold")[|Valeur|] \
|
||||||
|
#text(size: 0.85em)[Confiance dans la décision]
|
||||||
|
]
|
||||||
|
],
|
||||||
|
)
|
||||||
|
]
|
||||||
]
|
]
|
||||||
|
|
||||||
#myslide("Implementation")[
|
#myslide("Sum-Product : Belief Propagation")[
|
||||||
|
#set text(size: 17pt)
|
||||||
|
#v(-0.4em)
|
||||||
|
|
||||||
|
#definition(titre: "Décodage Optimal")[
|
||||||
|
Échange itératif de croyances (LLR) entre les nœuds du graphe
|
||||||
|
]
|
||||||
|
|
||||||
|
#definition(titre: "Information Extrinsèque")[
|
||||||
|
Exclure l'avis du destinataire pour éviter l'auto-influence
|
||||||
|
]
|
||||||
|
#block(
|
||||||
|
fill: orange.lighten(92%),
|
||||||
|
stroke: (left: 4pt + orange),
|
||||||
|
radius: 4pt,
|
||||||
|
inset: 18pt,
|
||||||
|
width: 100%,
|
||||||
|
)[
|
||||||
|
#set text(size: 1.2em)
|
||||||
|
*Mise à jour CN* \
|
||||||
|
#set text(size: 1.1em)
|
||||||
|
$ tanh(m_(c arrow v) / 2) = product_(u != v) tanh(m_(u arrow c) / 2) $
|
||||||
|
]
|
||||||
|
|
||||||
|
#block(
|
||||||
|
fill: blue.lighten(92%),
|
||||||
|
stroke: (left: 4pt + blue),
|
||||||
|
radius: 4pt,
|
||||||
|
inset: 18pt,
|
||||||
|
width: 100%,
|
||||||
|
)[
|
||||||
|
#set text(size: 1.2em)
|
||||||
|
*Mise à jour VN* \
|
||||||
|
#set text(size: 1.1em)
|
||||||
|
$ m_(v arrow c) = L_"canal" + sum_(c' != c) m_(c' arrow v) $
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#myslide("Sum-Product")[
|
||||||
|
#set text(size: 16pt)
|
||||||
|
|
||||||
|
#place(left, dx: 1.5cm, dy: 0cm)[
|
||||||
|
#text(weight: "bold", size: 1.1em * 1.3)[Initialisation]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(left, dx: 1.5cm, dy: 2cm)[
|
||||||
|
#scale(130%)[
|
||||||
|
#grid(
|
||||||
|
columns: 1,
|
||||||
|
gutter: 0.2cm,
|
||||||
|
align: horizon,
|
||||||
|
schema_detailed_init(),
|
||||||
|
text(size: 0.9em)[$m_(v_j arrow c_i) = L_"canal"$],
|
||||||
|
)
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(right, dx: -4.5cm, dy: 0cm)[
|
||||||
|
#text(weight: "bold", fill: orange, size: 1.1em * 1.3)[Échange CN]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(right, dx: -1cm, dy: 2.7cm)[
|
||||||
|
#scale(130%)[
|
||||||
|
#schema_detailed_cn()
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(left, dx: 1.5cm, dy: 9cm)[
|
||||||
|
#text(weight: "bold", fill: blue, size: 1.1em * 1.3)[Échange VN]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(left, dx: 1.5cm, dy: 11cm)[
|
||||||
|
#scale(130%)[
|
||||||
|
#schema_detailed_vn()
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(right, dx: -3.5cm, dy: 9cm)[
|
||||||
|
#text(weight: "bold", fill: green, size: 1.1em * 1.3)[Décision Finale]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(right, dx: -1cm, dy: 11cm)[
|
||||||
|
#scale(145%)[
|
||||||
|
#schema_detailed_decision()
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#place(center + horizon, dx: -0.9cm, dy: 8.2cm)[
|
||||||
|
#scale(115%)[
|
||||||
|
#cetz.canvas(length: 1cm, {
|
||||||
|
import cetz.draw: *
|
||||||
|
|
||||||
|
let col_iter = gray.darken(50%)
|
||||||
|
|
||||||
|
arc(
|
||||||
|
(0, 0),
|
||||||
|
radius: 1.8,
|
||||||
|
start: 150deg,
|
||||||
|
delta: -300deg,
|
||||||
|
stroke: (paint: col_iter, thickness: 2pt, cap: "round"),
|
||||||
|
mark: (end: "stealth", fill: col_iter, size: 0.3),
|
||||||
|
)
|
||||||
|
|
||||||
|
content((1.6, -1), [
|
||||||
|
#set text(fill: col_iter, weight: "bold", size: 0.8em)
|
||||||
|
#set align(center)
|
||||||
|
Itérations\
|
||||||
|
$i = 1, dots, I_(max)$
|
||||||
|
])
|
||||||
|
})
|
||||||
|
]
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#myslide("Implementation rust")[
|
||||||
|
|
||||||
]
|
]
|
||||||
|
|
||||||
#myslide("Test")[
|
#myslide("Min-Sum")[
|
||||||
|
#set text(size: 15pt)
|
||||||
|
|
||||||
|
#grid(
|
||||||
|
columns: (1fr, 1fr),
|
||||||
|
gutter: 0.5cm,
|
||||||
|
definition(titre: "Avantage Matériel", accent: black)[
|
||||||
|
- *Comparateurs* pour le minimum
|
||||||
|
- *XOR* pour le produit des signes
|
||||||
|
#v(0.21cm)
|
||||||
|
],
|
||||||
|
definition(titre: "Mise à jour du CN", accent: orange)[
|
||||||
|
#set text(size: 19pt)
|
||||||
|
$
|
||||||
|
m_(c arrow v_i) = product_(j != i) "sgn"(m_(v_j arrow c)) times min_(j != i) |m_(v_j arrow c)|
|
||||||
|
$
|
||||||
|
],
|
||||||
|
)
|
||||||
|
|
||||||
|
#v(4.5em)
|
||||||
|
#align(center)[#scale(130%)[#schema_min_sum_complet()]]
|
||||||
|
|
||||||
|
#v(0.5em)
|
||||||
|
#align(center)[
|
||||||
|
#text(size: 1.1em, fill: gray.darken(40%), style: "italic")[
|
||||||
|
Pour les VN : $m_(v arrow c) = L_"canal" + sum_(c' != c) m_(c' arrow v)$
|
||||||
|
]
|
||||||
|
]
|
||||||
|
]
|
||||||
|
|
||||||
|
#myslide("Test réel")[
|
||||||
Irl hackrf, test de diff de debit avec des paquets
|
Irl hackrf, test de diff de debit avec des paquets
|
||||||
]
|
]
|
||||||
|
|
||||||
@ -999,4 +1184,6 @@
|
|||||||
|
|
||||||
]
|
]
|
||||||
|
|
||||||
|
#myslide("Maths deriere Belief Propagation")[
|
||||||
|
|
||||||
|
]
|
||||||
|
|||||||
Reference in New Issue
Block a user