Optimum

Optimum implements Random Linear Network Coding (RLNC) over the Ring0 gossip layer. Messages are fragmented into source symbols and encoded into coded shards using random linear combinations. Any k fragments out of n reconstruct the original message. This achieves provably optimal bandwidth under the max-flow min-cut theorem.

rlnc fundamentals

RLNC Fundamentals

Random Linear Network Coding works by fragmenting a message into k source symbols, then producing n coded shards where each shard is a random linear combination of source fragments. Decoding requires any k linearly independent shards — there is no distinction between "original" and "parity" pieces. This means the network can tolerate arbitrary loss patterns as long as enough total shards arrive.

rlnc properties

Three Key Properties

RLNC provides three properties that make it superior to traditional erasure codes for blockchain networking.

• Composability (recoding): Intermediate relay nodes can generate new coded shards from received shards without decoding — enabling efficient multi-hop relay
• Loss tolerance: Any k linearly independent shards suffice for recovery — provably optimal under arbitrary network conditions
• Bandwidth efficiency: Coefficient overhead is negligible relative to payload size, typically less than 0.5%

mump2p

The mump2p Protocol

Optimum implements RLNC over libp2p as the mump2p protocol. The workflow: fragment the block into source symbols, encode shards with random coefficients, distribute across the mesh network, validate incoming shards via source authentication, then store, decode (upon receiving enough independent shards), and forward. Control messages handle redundancy suppression, pull-based recovery, and mesh topology management.

deram

DeRAM: Decentralized RAM

DeRAM extends RLNC beyond gossip to persistent distributed storage. Coded fragments are stored across lightweight storage participants (flexnodes). Data is recoverable as long as any k of n flexnodes are reachable. The same algebraic property that enables relay without decoding also enables consistent distributed storage with linearizable reads and writes.

optimality

Provable Optimality

RLNC is provably optimal under the max-flow min-cut theorem for information dissemination in multicast networks. Traditional gossip protocols (used by Ethereum, Solana, etc.) waste bandwidth by redundantly forwarding identical data along multiple paths. RLNC achieves the theoretical capacity limit because coded shards are algebraically independent — every received shard contributes new information with high probability.

network security

Network Security

Optimum defends against pollution attacks (malicious nodes injecting invalid coded shards) through source authentication: each shard carries a hash of the original data and a signature from the block producer. Invalid shards are detected immediately upon receipt and the sender's reputation score is decremented. Persistent misbehavior triggers mesh pruning — the malicious peer is removed from the gossip topology.