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## Symbol Level Network Coding

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**Symbol Level Network Coding**By Sachin Katti, Dina Katabi, Hari Balakrishnan, Muriel Medard Sigcomm 2008**Mesh Networks Borrowed the Internet Contract**Conflicts with wireless mesh characteristics Current contract builds reliability on a link by link basis Spatial diversity more naturally provides reliability across multiple links**Wireless Naturally Provides Reliability Across Links**99% (10-3 BER) 0% R1 R2 D S 0% 99% (10-3 BER) Even 1 bit in 1000 incorrect Packet loss of 99%**Wireless Naturally Provides Reliability Across Links**99% (10-3 BER) Loss 0% R1 R2 D S Loss 0% 99% (10-3 BER) Current contract Link by link reliability 50 transmissions**Wireless Naturally Provides Reliability Across Links**99% (10-3 BER) 0% R1 R2 D S 0% 99% (10-3 BER) Spatial diversity: Even if no correct packets, every bit is likely received correctly at some node Current contract 50 tx Low throughput Exploit wireless characteristics 3 tx High throughput Exploit wireless characteristics 3 transmissions**Useful with High Quality Links?**R1 1% 0% Loss Sa Da Pa 0% Pa 2% R2 Loss Pa R3 1% Loss 0% Pb Db Sb 0% R4 3% Pb Loss Pb**Useful with High Quality Links?**R1 1% 0% Sa Da Pa 0% Pa 2% R2 Pa R3 1% 0% Pb Current contract Inhibits concurrency Exploit wireless characteristics Enables high concurrency Db Sb 0% R4 3% Pb Pb**Current Contract**• Limits throughput, inhibits concurrency New Contract Exploiting Wireless Characteristics • High throughput, high concurrency**MIXIT**• New contract between layers to harness wireless characteristics • Novel symbol-level network code that scalably routes correct symbols • High concurrency MAC**How does a Router Identify Correct Symbols?**• PHY already estimates a confidence for every decoded symbol [JB07] • PHY + LL delivers high confidence symbols to network layer PHY Confidence Packet**What Should Each Router Forward?**R1 R2 D S P1 P2 P1 P2 P1 P2**What Should Each Router Forward?**R1 R2 D S P1 P1 P2 P2 P1 P2 P1 P1 P2 P2 • But overlap in correctly received symbols • Potential solutions • Forward everything Inefficient • Coordinate Unscalable**MIXIT Prevents Duplicates using Symbol Level Network Coding**R1 R2 D S P1 P2 P1 P2 P1 P2 Forward random combinations of correct symbols**MIXIT Prevents Duplicates using Symbol Level Network Coding**D R2 R1 … … … … … … Routers create random combinations of correct symbols**MIXIT Prevents Duplicates using Symbol Level Network Coding**D … R2 R1 … Solve 2 equations Randomness prevents duplicates without co-ordination Destination decodes by solving linear equations**MIXIT Prevents Duplicates using Symbol Level Network Coding**D R2 R1 … … … … … … Routers create random combinations of correct symbols**MIXIT Prevents Duplicates using Symbol Level Network Coding**D … R2 R1 … Solve 2 equations • Symbol Level Network Coding • No duplicates Efficient • No coordination Scalable Destination decodes by solving linear equations**Destination needs to know which combinations it received**(if both symbols were correct) (if only s1 was correct) (if only s2 was correct) Nothing (if neither symbol was correct)**Destination needs to know which combinations it received**Use run length encoding Coded Packet Original Packets**Destination needs to know which combinations it received**Use run length encoding Coded Packet Original Packets**Destination needs to know which combinations it received**Use run length encoding Coded Packet Original Packets**Destination needs to know which combinations it received**Use run length encoding Coded Packet Original Packets**Destination needs to know which combinations it received**Use run length encoding Run length encoding efficiently expresses combinations**Routers May Forward Erroneous Bits Despite High Confidence**MIXIT has E2E error correction capability Decode ECC ECC Symbol-Level Network Coding Data Data Source Destination MIXIT’s Error Correcting Code (ECC) Routers are oblivious to ECC Optimal error correction capability Rateless**High Concurrency MAC**w& x NO! w& u YES! u w x • Each node maintains a map of conflicting transmissions • Map is based on empirical measurements and built in distributed, online manner**Evaluation**• Implementation on GNURadio SDR and USRP • Zigbee (IEEE 802.15.4) link layer • 25 node indoor testbed, random flows • Compared to: • Shortest path routing based on ETX • MORE: Packet-level opportunistic routing**Throughput Comparison**CDF 2.1x MIXIT 3x MORE Shortest Path Throughput (Kbps) Throughput increase: 3x over SPR, 2x over MORE**Where do the gains come from?**CDF MIXIT MORE Shortest Path Throughput (Kbps) Take concurrency away from MIXIT**Where do the gains come from?**CDF MIXIT without concurrency 1.5x MORE Shortest Path Throughput (Kbps) Without concurrency, 1.5x gain over MORE Take concurrency away from MIXIT**Where do the gains come from?**MIXIT CDF MIXIT without concurrency MORE Shortest Path Gains come from both moving to the symbol level and high concurrency Throughput (Kbps)**Where do the gains come from?Higher Concurrency?**CDF 1.4x Throughput (Kbps) MORE, enhanced with higher concurrency is only 1.4x better**Where do the gains come from?**CDF 1.5x 2.1x Higher concurrency MAC fully exploits symbol-level diversity Throughput (Kbps)**Conclusion**• MIXIT • New contract harnesses wireless characteristics • Symbol-level network coding to scalably route correct symbols • High concurrency • Implementation and evaluation demonstrating • 3-4x over shortest path,2-3xgains over MORE