Systems and methods for networking coding using Reed-Solomon codes

A non-transitory computer-readable medium containing instructions that, when executed by a processor, cause the processor to:

• encode a plurality of message packets to produce a plurality of encoded packets;
• wherein each message packet and each encoded packet comprises a plurality of symbols having an index;
• wherein each symbol of the encoded packets is generated by applying a Reed-Solomon code to the symbols of the message packets having the same index as the symbol of the encoded packets;
• wherein a length of the encoded packets is the same as a length of the message packets;
• wherein the encoded packets comprise the message packets and one or more parity packets;
• wherein each symbol of the parity packets is generated by applying a Reed-Solomon code to the symbols of the message packets having the same index as the symbol of the parity packets and
• wherein executing the instructions further causes the processor to send the encoded packets to a physical layer of a wireless transmitter for wireless transmission.

A wireless communication device, comprising:

• a network encoder to:
• encode a plurality of message packets to produce a plurality of encoded packets;
• wherein each message packet and each encoded packet comprises a plurality of symbols having an index;
• wherein each symbol of the encoded packets is generated by applying a Reed-Solomon code to the symbols of the message packets having the same index as the symbol of the encoded packets;
• wherein a length of the encoded packets is the same as a length of the message packets;
• wherein the encoded packets comprise the message packets and one or more parity packets;
• wherein each symbol of the parity packets is generated by applying a Reed-Solomon code to the symbols of the message packets having the same index as the symbol of the parity packets and
• a physical layer to transmit the encoded packets via a wireless antenna and sending by the network encoder the resulting encoded packets to a physical layer of a wireless transmitter for wireless transmission using an existing underlying wireless communication protocol without modification.

A wireless communication device, comprising:

• a physical layer to receive a plurality of encoded packets via a wireless antenna, the encoded packets resulting from encoding a number of message packets by applying a network code matrix to the message packets;
• and
• a network decoder to:
• receive a number of received packets at least equal to the number of message packets, each of the received packets comprising a sequence index that correlates the received packet to one of the encoded packets;
• and
• generate a received packet matrix by selecting a number of the received packets equal to the number of message packets, wherein each column of the received packet matrix corresponds to one of the selected received packets;
• generate a decoding matrix by forming a sub-matrix by selecting columns of the network code matrix that have indices that are the same as the sequence indices of the selected received packets and inverting the sub-matrix;
• multiply the received packet matrix by the decoding matrix to generate a recovered matrix, wherein each column of the recovered matrix corresponds to a decoded packet and
• sending the resulting decoded packets to a higher-layer application of a wireless receiver without the need for retransmission using an existing underlying wireless communication protocol without modification.