diff --git a/packages/node/src/sync/decoder.ts b/packages/node/src/sync/decoder.ts
new file mode 100644
index 000000000..49599439a
--- /dev/null
+++ b/packages/node/src/sync/decoder.ts
@@ -0,0 +1,130 @@
+import type {Symbol} from "./symbol.js"
+import type { CodedSymbol, HashedSymbol } from "./symbol.js";
+
+
+export class Decoder<T extends Symbol<T>> {
+	// Coded symbols received so far
+	private cs: CodedSymbol<T>[] = [];
+	// Set of source symbols that are exclusive to the decoder
+	private local: CodingWindow<T>;
+	// Set of source symbols that the decoder initially has
+	private window: CodingWindow<T>;
+	// Set of source symbols that are exclusive to the encoder
+	private remote: CodingWindow<T>;
+	// Indices of coded symbols that can be decoded, i.e., degree equal to -1
+	// or 1 and sum of hash equal to hash of sum, or degree equal to 0 and sum
+	// of hash equal to 0
+	private decodable: number[] = [];
+	// Number of coded symbols that are decoded
+	private decoded: number = 0;
+
+	constructor() {
+		this.local = new CodingWindow<T>();
+		this.window = new CodingWindow<T>();
+		this.remote = new CodingWindow<T>();
+	}
+
+	// Decoded returns true if and only if every existing coded symbols d received
+	// so far have been decoded.
+	public decoded(): boolean {
+		return this.decoded === this.cs.length;
+	}
+
+	// Local returns the list of source symbols that are present in B but not in A.
+	public localSymbols(): HashedSymbol<T>[] {
+		return this.local.symbols;
+	}
+
+	// Remote returns the list of source symbols that are present in A but not in B.
+	public remoteSymbols(): HashedSymbol<T>[] {
+		return this.remote.symbols;
+	}
+
+	// AddSymbol adds a source symbol to B, the Decoder's local set.
+	public addSymbol(s: T): void {
+		const th = new HashedSymbol<T>(s, s.hash());
+		this.addHashedSymbol(th);
+	}
+
+	// AddHashedSymbol adds a source symbol to B, the Decoder's local set.
+	public addHashedSymbol(s: HashedSymbol<T>): void {
+		this.window.addHashedSymbol(s);
+	}
+
+	// AddCodedSymbol passes the next coded symbol in A's sequence to the Decoder.
+	public addCodedSymbol(c: CodedSymbol<T>): void {
+		// Scan through decoded symbols to peel off matching ones
+		c = this.window.applyWindow(c, "remove");
+		c = this.remote.applyWindow(c, "remove");
+		c = this.local.applyWindow(c, "add");
+		// Insert the new coded symbol
+		this.cs.push(c);
+		// Check if the coded symbol is decodable, and insert into decodable list if so
+		if ((c.count === 1 || c.count === -1) && c.hash === c.symbol.hash()) {
+			this.decodable.push(this.cs.length - 1);
+		} else if (c.count === 0 && c.hash === 0) {
+			this.decodable.push(this.cs.length - 1);
+		}
+	}
+
+	// Apply a new symbol and modify the corresponding coded symbols
+	private applyNewSymbol(t: HashedSymbol<T>, direction: number): RandomMapping {
+		let m = new RandomMapping(t.hash, 0);
+		while (m.lastIdx < this.cs.length) {
+			const cidx = m.lastIdx;
+			this.cs[cidx] = this.cs[cidx].apply(t, direction);
+			// Check if the coded symbol is now decodable
+			if (
+				(this.cs[cidx].count === -1 || this.cs[cidx].count === 1) &&
+				this.cs[cidx].hash === this.cs[cidx].symbol.hash()
+			) {
+				this.decodable.push(cidx);
+			}
+			m.nextIndex();
+		}
+		return m;
+	}
+
+	// TryDecode tries to decode all coded symbols received so far.
+	public tryDecode(): void {
+		for (const didx of this.decodable) {
+			const cidx = this.decodable[didx];
+			const c = this.cs[cidx];
+			switch (c.count) {
+				case 1:
+					// Allocate a symbol and then XOR with the sum
+					const ns1 = new HashedSymbol<T>();
+					ns1.symbol = ns1.symbol.xor(c.symbol);
+					ns1.hash = c.hash;
+					const m1 = this.applyNewSymbol(ns1, -1);
+					this.remote.addHashedSymbolWithMapping(ns1, m1);
+					this.decoded += 1;
+					break;
+				case -1:
+					const ns2 = new HashedSymbol<T>();
+					ns2.symbol = ns2.symbol.xor(c.symbol);
+					ns2.hash = c.hash;
+					const m2 = this.applyNewSymbol(ns2, 1);
+					this.local.addHashedSymbolWithMapping(ns2, m2);
+					this.decoded += 1;
+					break;
+				case 0:
+					this.decoded += 1;
+					break;
+				default:
+					throw new Error("Invalid degree for decodable coded symbol");
+			}
+		}
+		this.decodable = [];
+	}
+
+	// Reset clears the decoder.
+	public reset(): void {
+		this.cs = [];
+		this.decodable = [];
+		this.local.reset();
+		this.remote.reset();
+		this.window.reset();
+		this.decoded = 0;
+	}
+}
diff --git a/packages/node/src/sync/encoder.ts b/packages/node/src/sync/encoder.ts
new file mode 100644
index 000000000..41415b594
--- /dev/null
+++ b/packages/node/src/sync/encoder.ts
@@ -0,0 +1,156 @@
+class SymbolMapping {
+	sourceIdx: number;
+	codedIdx: number;
+
+	constructor(sourceIdx: number, codedIdx: number) {
+		this.sourceIdx = sourceIdx;
+		this.codedIdx = codedIdx;
+	}
+}
+
+class MappingHeap {
+	private heap: SymbolMapping[];
+
+	constructor() {
+		this.heap = [];
+	}
+
+	private fixHead(): void {
+		let curr = 0;
+		while (true) {
+			let child = curr * 2 + 1;
+			if (child >= this.heap.length) {
+				break; // No left child
+			}
+			if (
+				child + 1 < this.heap.length &&
+				this.heap[child + 1].codedIdx < this.heap[child].codedIdx
+			) {
+				child = child + 1; // Right child has higher priority
+			}
+			if (this.heap[curr].codedIdx <= this.heap[child].codedIdx) {
+				break; // Invariant is satisfied
+			}
+			// Swap current and child
+			[this.heap[curr], this.heap[child]] = [this.heap[child], this.heap[curr]];
+			curr = child;
+		}
+	}
+
+	private fixTail(): void {
+		let curr = this.heap.length - 1;
+		while (curr > 0) {
+			const parent = Math.floor((curr - 1) / 2);
+			if (this.heap[parent].codedIdx <= this.heap[curr].codedIdx) {
+				break;
+			}
+			// Swap parent and current
+			[this.heap[parent], this.heap[curr]] = [
+				this.heap[curr],
+				this.heap[parent],
+			];
+			curr = parent;
+		}
+	}
+
+	push(mapping: SymbolMapping): void {
+		this.heap.push(mapping);
+		this.fixTail();
+	}
+
+	pop(): SymbolMapping | undefined {
+		if (this.heap.length === 0) return undefined;
+		const root = this.heap[0];
+		this.heap[0] = this.heap[this.heap.length - 1];
+		this.heap.pop();
+		this.fixHead();
+		return root;
+	}
+
+	get size(): number {
+		return this.heap.length;
+	}
+
+	get top(): SymbolMapping | undefined {
+		return this.heap[0];
+	}
+}
+
+class CodingWindow<T extends Symbol<T>> {
+	private symbols: HashedSymbol<T>[];
+	private mappings: RandomMapping[];
+	private queue: MappingHeap;
+	private nextIdx: number;
+
+	constructor() {
+		this.symbols = [];
+		this.mappings = [];
+		this.queue = new MappingHeap();
+		this.nextIdx = 0;
+	}
+
+	addSymbol(symbol: T): void {
+		const hashedSymbol = new HashedSymbol(symbol, symbol.hash());
+		this.addHashedSymbol(hashedSymbol);
+	}
+
+	addHashedSymbol(hashedSymbol: HashedSymbol<T>): void {
+		const mapping = new RandomMapping(hashedSymbol.hash, 0);
+		this.addHashedSymbolWithMapping(hashedSymbol, mapping);
+	}
+
+	addHashedSymbolWithMapping(
+		hashedSymbol: HashedSymbol<T>,
+		mapping: RandomMapping,
+	): void {
+		this.symbols.push(hashedSymbol);
+		this.mappings.push(mapping);
+		this.queue.push(
+			new SymbolMapping(this.symbols.length - 1, mapping.lastIdx),
+		);
+	}
+
+	applyWindow(cw: CodedSymbol<T>, direction: number): CodedSymbol<T> {
+		if (this.queue.size === 0) {
+			this.nextIdx += 1;
+			return cw;
+		}
+
+		while (this.queue.top?.codedIdx === this.nextIdx) {
+			const mapping = this.queue.pop();
+			if (mapping) {
+				cw = cw.apply(this.symbols[mapping.sourceIdx], direction);
+				const nextMap = this.mappings[mapping.sourceIdx].nextIndex();
+				mapping.codedIdx = nextMap;
+				this.queue.push(mapping);
+			}
+		}
+		this.nextIdx += 1;
+		return cw;
+	}
+
+	reset(): void {
+		this.symbols = [];
+		this.mappings = [];
+		this.queue = new MappingHeap();
+		this.nextIdx = 0;
+	}
+}
+
+class Encoder<T extends Symbol<T>> extends CodingWindow<T> {
+	addSymbol(s: T): void {
+		super.addSymbol(s);
+	}
+
+	addHashedSymbol(s: HashedSymbol<T>): void {
+		super.addHashedSymbol(s);
+	}
+
+	produceNextCodedSymbol(): CodedSymbol<T> {
+		return super.applyWindow(new CodedSymbol<T>(), 1);
+	}
+
+	reset(): void {
+		super.reset();
+	}
+}
diff --git a/packages/node/src/sync/index.ts b/packages/node/src/sync/index.ts
new file mode 100644
index 000000000..e69de29bb
diff --git a/packages/node/src/sync/mapping.ts b/packages/node/src/sync/mapping.ts
new file mode 100644
index 000000000..756fae9a2
--- /dev/null
+++ b/packages/node/src/sync/mapping.ts
@@ -0,0 +1,17 @@
+export class RandomMapping {
+    private prng: bigint;
+    lastIdx: number;
+  
+    constructor(prng: number, lastIdx = 0) {
+        this.prng = BigInt(prng);
+        this.lastIdx = lastIdx;
+    }
+
+    nextIndex(): number {
+        const multiplier = 0xda942042e4dd58b5n;
+        this.prng = (this.prng * multiplier) & 0xffffffffffffffffn;
+
+        this.lastIdx += Math.ceil((this.lastIdx + 1.5) * ((2 ** 32) / Math.sqrt(Number(this.prng) + 1) - 1));
+        return this.lastIdx;
+    }
+}
diff --git a/packages/node/src/sync/sketch.ts b/packages/node/src/sync/sketch.ts
new file mode 100644
index 000000000..2c5f4e802
--- /dev/null
+++ b/packages/node/src/sync/sketch.ts
@@ -0,0 +1,67 @@
+import { Symbol } from "./symbol.js"
+import {HashedSymbol, CodedSymbol} from "./symbol.js"
+import {RandomMapping} from "./mapping.js"
+import {Decoder} from "./decoder.js"
+
+
+
+class Sketch<T extends Symbol<T>> {
+    s: CodedSymbol<T>[] = []
+
+    addHashedSymbol(t: HashedSymbol<T>) {
+        const m = new RandomMapping(t.Hash, 0);
+        while (m.lastIdx < this.s.length) {
+            const idx = m.lastIdx;
+            this.s[idx].Symbol = this.s[idx].Symbol.XOR(t.Symbol);
+            this.s[idx].Count += 1;
+            this.s[idx].Hash ^= t.Hash;
+            m.nextIndex();
+        }
+    }
+
+    removeHashedSymbol(t: HashedSymbol<T>) {
+        const m = new RandomMapping(t.Hash, 0);
+        while (m.lastIdx < this.s.length) {
+            const idx = m.lastIdx;
+            this.s[idx].Symbol = this.s[idx].Symbol.XOR(t.Symbol);
+            this.s[idx].Count -= 1;
+            this.s[idx].Hash ^= t.Hash;
+            m.nextIndex();
+        }
+    }
+
+    addSymbol(t: T) {
+        const hs = new HashedSymbol(t, t.Hash());
+        this.addHashedSymbol(hs);
+    }
+
+    removeSymbol(t: T) {
+        const hs = new HashedSymbol(t, t.Hash());
+        this.removeHashedSymbol(hs);
+    }
+
+    subtract(s2: Sketch<T>) {
+        if (this.s.length !== s2.s.length) {
+            throw Error("subtracting sketches of different sizes");
+        }
+
+        for (let i = 0; i < this.s.length; i++) {
+            this.s[i].Symbol = this.s[i].Symbol.XOR(s2.s[i].Symbol);
+            this.s[i].Count -= s2.s[i].Count;
+            this.s[i].Hash ^= s2.s[i].Hash;
+        }
+    }
+
+    decode(): { fwd: HashedSymbol<T>[]; rev: HashedSymbol<T>[]; succ: boolean } {
+        const dec = new Decoder<T>();
+        for (const c of this.s) {
+            dec.addCodedSymbol(c);
+        }
+        dec.tryDecode();
+        return {
+            fwd: dec.remote(),
+            rev: dec.local(),
+            succ: dec.decoded(),
+        };
+    }
+}
diff --git a/packages/node/src/sync/symbol.ts b/packages/node/src/sync/symbol.ts
new file mode 100644
index 000000000..44e2216c6
--- /dev/null
+++ b/packages/node/src/sync/symbol.ts
@@ -0,0 +1,33 @@
+export interface Symbol<T> {
+    XOR(t2: T): T;
+    Hash(): number;
+}
+
+export class HashedSymbol<T extends Symbol<T>> {
+    Symbol: T;
+    Hash: number;
+  
+    constructor(symbol: T, hash: number) {
+      this.Symbol = symbol;
+      this.Hash = hash;
+    }
+}
+
+export class CodedSymbol<T extends Symbol<T>> extends HashedSymbol<T> {
+    Count: number;
+  
+    constructor(symbol: T, hash: number, count = 0) {
+      super(symbol, hash);
+      this.Count = count;
+    }
+  
+    static readonly ADD = 1;
+    static readonly REMOVE = -1;
+
+    apply(s: HashedSymbol<T>, direction: number): CodedSymbol<T> {
+      this.Symbol = this.Symbol.XOR(s.Symbol);
+      this.Hash ^= s.Hash;
+      this.Count += direction;
+      return this;
+    }
+}