Systems and methods for a soft-input decoder of linear network codes

1. A method for decoding linear network codes, comprising:

receiving, by a processor, a plurality of packets from an error detector;

generating, by the processor, a matrix wherein elements of each column of the matrix correspond to symbols of the plurality of packets; and

decoding, by the processor using both soft information and a plurality of results from said error detector, across each row of the matrix using only the symbols with highest associated reliability values to obtain a decoded matrix, wherein each column of the decoded matrix corresponds to a message packet.

2. The method of claim 1 further comprising:

receiving, by a processor, a plurality of packets from an error detector, wherein the plurality of packets comprises recovered packets and at least one erasure packet, wherein all symbols in recovered packets have high associated reliability values;

selecting, by the processor, a replacement packet from a physical layer that corresponds to the erasure packet, wherein each symbol in the replacement packet comprises a reliability value; and

replacing, by the processor, the at least one erasure packet with the replacement packet.

3. The method of claim 1 further comprising:

selecting, by the processor, a replacement packet from a physical layer that corresponds to each of the plurality of packets from the error detector, wherein each symbol in the replacement packet comprises a reliability value; and

replacing, by the processor, the plurality of packets with the replacement packets.

4. The method of claim 1 wherein the number of symbols selected from each row to perform the decoding is at least equal to a number of message packets originally encoded.

5. The method of claim 1 wherein the symbols selected from each row to perform the decoding are taken from a linearly independent set of columns, wherein the number of columns decoded is at least equal to the number of message packets originally encoded.

6. The method of claim 1 wherein the reliability values comprise a characterization made by the physical layer that represents a level of confidence in each symbol being received without error, and the associated reliability value is a continuum of values ranging from low to high.

7. The method of claim 1 further comprising:

decoding, by the processor using both soft information and a plurality of results from said error detector, across each row of the matrix using an inverted subs-matrix of a linear operator matrix;

wherein the inverted sub-matrix of the linear operator matrix is determined by the symbols having associated high reliability values; and

wherein the subset of the invertible linear operator matrix is only applied to the symbols of the matrix having associated high reliability values.

8. A system for decoding linear network codes, comprising:

a packet receiver configured to:

receive a plurality of packets from an error detector including soft information and a plurality of results from said error detector; and

receive a plurality of packets from a physical layer, wherein each packet from the physical layer corresponds to one of the packets from the error detector and each symbol in the packets from the physical layer comprises a reliability value;

a matrix generator configured to generate a decoding matrix, wherein elements of each column of the decoding matrix correspond to symbols of one of the plurality of packets; and

a decoder configured to decode across each row of the decoding matrix using only the symbols having a highest reliability value to obtain a decoded matrix, wherein all bits in recovered packets have high reliability values, wherein the columns of the decoded matrix correspond to a message packet.

9. The system of claim 8 further comprising:

a packet replacement unit configured to replace an erasure packet with its corresponding packet from the physical layer, wherein the plurality of packets received from the error detector comprise recovered packets and at least one erasure packet.

10. The system of claim 8 wherein the packet replacement unit is further configured to replace the plurality of packets with their corresponding packets from the physical layer.

11. The system of claim 8 wherein the reliability values comprise a characterization made by the physical layer that represents a level of confidence of the physical layer in each symbol being received without error, and the reliability value is a continuum of values ranging from low to high.

12. The system of claim 8 wherein the decoder is further configured to select for decoding a number of symbols from each row at least equal to a number of message packets originally encoded.

13. The system of claim 8 wherein the decoder is further configured to select for decoding symbols from each row from a linearly independent set of columns, wherein the number of columns selected is at least equal to the number of message packets originally encoded.

14. A method for decoding linear network codes, comprising:

receiving, by a processor, a plurality of output packets from an error detector, wherein each packet comprises symbols with associated reliability values;

generating, by the processor, a decoding matrix, wherein elements of each column of the decoding matrix correspond to symbols of one of the plurality of output packets; and

decoding, by the processor using both soft information and a plurality of results from said error detector, across each row of the decoding matrix, using only the symbols having a highest reliability value, wherein each column of the resulting decoded matrix represents a message packet.

15. The method of claim 14 further comprising:

wherein the plurality of output packets comprises of recovered packets and at least one erasure packet, wherein all symbols in the recovered packets have high reliability values;

selecting, by the processor, a packet from a physical layer that corresponds to the at least one erasure packet, wherein each symbol in the packet from the physical layer comprises an associated reliability value ranging from low to high; and

replacing, by the processor, the erasure packet with the packet from the physical layer.

16. The method of claim 15 further comprising:

replacing, by the processor, the plurality of output packets with their corresponding packets from the physical layer.

17. The method of claim 15 wherein at least one of the plurality of output packets is not recovered by the physical layer and the error checker replaces it with an erasure packet.

18. The method of claim 14 wherein the reliability values correspond to a characterization made by the physical layer that denotes the physical layer's level of confidence in each symbol being received without error, and the associated reliability value is a continuum of values ranging from low to high.

19. The method of claim 14 wherein the number of symbols selected to perform the decoding is at least equal to a number of message packets originally encoded.

20. The method of claim 14 wherein the symbols selected to perform the decoding are taken from a linearly independent set of columns, wherein the number of columns decoded is at least equal to the number of message packets originally encoded.