Indexing-based feedback codes and methods of use

1. A method comprising:

determining, at an encoder, error correction using a feedback packet for a received packet having errors, the received packet having been decoded at a decoder from an original packet which has been transmitted from the encoder to the decoder over a first communications channel, the feedback packet comprising the received decoded packet, which has been transmitted as the feedback packet from the decoder to the encoder over a second communications channel;

generating, at the encoder, an index of the error correction using the feedback packet, the index comprising error positions for the errors in the feedback packet; and

transmitting the index from the encoder to the decoder over the first communications channel as feedback to the decoder, the index transmitted instead of retransmitting the original packet to reduce transmission bandwidth requirement.

2. The method according to claim 1 , further comprising:

deindexing the index to identify the error positions; and

correcting the errors in the received packet using the error positions to generate a corrected packet.

3. The method according to claim 2 , further comprising performing one or more additional rounds of error correction by:

comparing the corrected packet to the original packet; and

generating another error correction and another index when errors are identified in the comparison.

4. The method according to claim 3 , wherein the one or more additional rounds of error correction terminate when a retransmission threshold is reached.

5. The method according to claim 4 , further comprising transmitting a new packet when the retransmission threshold is reached.

6. A method comprising:

transmitting an original packet from a transmitter to a receiver over a communications channel having noise that causes the original packet to be received with errors;

providing a first round of error correction in response to the errors in the received packet, the error correction comprising:

receiving at the transmitter a feedback packet from the receiver, the feedback packet comprising the received packet with the errors as received at the receiver;

determining error correction for the received packet with the errors using a comparison of the original packet and the feedback packet;

generating an index of the error correction, the index comprising error positions for the errors in the feedback packet, reflecting the errors in the received packet; and

transmitting the index, instead of retransmitting the original packet, from the transmitter to the receiver over the communications channel as feedback to the receiver, to reduce transmission bandwidth requirement.

7. The method according to claim 6 , further comprising reconstructing an error vector using source encoding and channel encoding.

8. The method according to claim 7 , wherein reconstructing the error vector comprises:

deindexing the index to identify error positions; and

correcting the errors in the received packet using the error positions to generate a corrected packet.

9. The method according to claim 8 , further comprising performing one or more additional rounds of error correction by:

comparing the corrected packet to the original packet; and

generating additional error vectors and additional indexes when errors are identified in the one or more additional rounds of error correction.

10. The method according to claim 9 , wherein the one or more additional rounds of error correction terminate when a retransmission threshold is reached.

11. A method comprising:

transmitting an original packet from an encoder to a decoder on an asymmetric link, the asymmetric link being a communication channel where available transmission power is not equal for both the encoder and the decoder, the asymmetric link including a forward link from the encoder to the decoder and a reverse link from the decoder to the encoder, a received packet at the decoder including errors introduced in the original packet as received at the decoder;

receiving a feedback packet at the encoder comprising the received packet from the decoder;

conducting a first round of error correction that comprises:

generating a first index of the error correction, the first index comprising error positions for the errors in the feedback packet;

transmitting the first index, instead of the original packet, from the encoder to the decoder via the forward link, the first index transmitted instead of the original packet to reduce transmission bandwidth requirement of the forward link;

deindexing the first index at the decoder to identify the error positions in the feedback packet; and

updating the received packet at the decoder using the first index; and

conducting one or more additional rounds of error correction using telescopic indexing, each of the one or more additional rounds of telescopic indexing comprising:

transmitting a feedback index via the reverse link from the decoder to the encoder, the feedback index transmitted instead of the updated packet, the feedback index resulting from errors introduced in the first index as received at the decoder;

determining an error correction for the errors in the feedback index from a comparison of the feedback index and the first index;

generating a second index of the error correction, the second index comprising error positions for the errors in the feedback index;

transmitting the second index from the encoder to the decoder via the forward link;

deindexing the second index at the decoder to identify the error positions in the first index; and

correcting the errors in the feedback index at the decoder using the error positions in the second index to generate an additional updated packet, wherein each round of the one or more additional rounds of error correction generates a new updated packet.

12. The method according to claim 11 , wherein the one or more additional rounds of error correction are conducted until a retransmission threshold is reached or the packet is received without error by a receiver decoder.

13. The method according to claim 11 , further comprising compressing the first index and the second index into coded indexes.

14. A system comprising:

a transmitter encoder comprising a processor, the processor executing instructions to:

determine error correction for a received packet having errors using a feedback packet;

generate an index of the error correction using the feedback packet, the index comprising error positions for the errors in the received packet; and

transmit the index, instead of a packet, from the transmitter encoder to a receiver decoder over a forward communications channel, to reduce transmission bandwidth requirement; and

the receiver decoder comprising a processor, the processor executing instructions to:

receive the packet transmitted from the transmitter encoder via the forward communications channel to the receiver decoder;

determine that the received packet has the errors;

transmit the received packet having the errors from the receiver decoder via a reverse communications channel to the transmitter encoder as a feedback packet;

receive the index transmitted from the transmitter encoder via the forward communications channel;

deindex the index to identify the error positions; and

correct the errors in the received packet using the error positions to generate a corrected packet.

15. The system according to claim 14 , wherein the transmitter encoder is configured to transmit the packet on a forward link of an asymmetric channel, the forward link having noise that creates the errors.

16. The system according to claim 15 , wherein the transmitter encoder is configured to transmit the received packet on a reverse link of the asymmetric channel, the asymmetric channel being created due to a disparity in available transmitting power between the transmitter encoder and the receiver decoder.

17. The system according to claim 14 , wherein the transmitter encoder is configured to:

determine the errors by comparing the received packet to an original packet; and

determine an error vector from the errors.

18. The system according to claim 17 , wherein the transmitter encoder is configured to generate the index from the error vector.

19. The system according to claim 18 , wherein the receiver decoder is configured to reconstruct the error vector using a source encoding and a channel encoding.

20. The system according to claim 14 , wherein the transmitter encoder and the receiver decoder are configured to perform one or more additional rounds of error correction that include the transmitter encoder being configured to:

compare the corrected packet to an original packet; and

generate additional error vectors and additional indexes when errors are identified in the one or more additional rounds of error correction.

21. The system according to claim 20 , wherein the transmitter encoder is configured to terminate the one or more additional rounds of error correction when a retransmission threshold is reached.

22. The system according to claim 14 , wherein the transmitter encoder is configured to compress the index.

23. The system according to claim 14 , wherein the transmitter encoder receives the corrected packet and compares the corrected packet to an original packet to determine if the corrected packet is correct or has additional errors.