Mud pulse telemetry using gray coding

1. A system comprising:

a well tool operable to transmit a fluid through an interior of the well tool; and

a transmitter coupled to the well tool and operable to:

determine a value to transmit;

determine a Gray code representing the value;

select a transmission waveform corresponding to the Gray code using a predefined lookup table, wherein the predefined lookup table includes relationships between (i) a plurality of Gray code values and (ii) a plurality of different transmission waveforms for pressure waves; and

generate a pressure wave having the transmission waveform in the fluid.

2. The system of claim 1 , wherein the pressure wave comprises modulated pulse positions, and wherein data is encoded in the modulated pulse positions.

3. The system of claim 2 , wherein the pressure wave comprises modulated pulse widths, and wherein data is encoded in the modulated pulse widths.

4. The system of claim 1 , wherein the Gray code comprises a binary value that differs by one binary digit from another binary value in an adjacent row of the predefined lookup table.

5. The system of claim 1 , wherein the pressure wave comprises a plurality of pressure pulses, and wherein data is encoded in a time difference between the plurality of pressure pulses.

6. The system of claim 1 , further comprising:

a sensor operable to transmit a sensor signal associated with a characteristic of the well tool or a wellbore to the transmitter, wherein the transmitter is operable to determine the value to transmit based on the sensor signal.

7. The system of claim 1 , wherein the well tool comprises a logging while drilling tool or a measuring while drilling tool.

8. A method comprising:

determining, by a transmitter, a value to transmit;

determining, by the transmitter, a Gray code representing the value;

selecting, by the transmitter, a transmission waveform corresponding to the Gray code using a predefined lookup table, wherein the predefined lookup table includes relationships between (i) a plurality of Gray code values and (ii) a plurality of different transmission waveforms for pressure waves; and

generating, by the transmitter, a pressure wave having the transmission waveform by modulating a pressure of a fluid in a well tool.

9. The method of claim 8 , wherein the pressure wave comprises modulated pulse positions, and wherein data is encoded in the modulated pulse positions.

10. The method of claim 9 , wherein the pressure wave comprises modulated pulse widths, and wherein data is encoded in the modulated pulse widths.

11. The method of claim 8 , wherein the pressure wave-comprises a plurality of pressure pulses, and wherein data is encoded in a time difference between the plurality of pressure pulses.

12. The method of claim 8 , further comprising:

receiving a sensor signal from a sensor, the sensor signal associated with a characteristic of the well tool or a wellbore; and

determining the value to transmit based on the sensor signal.

13. The method of claim 8 , wherein the well tool comprises a logging while drilling tool or a measuring while drilling tool.

14. The method of claim 8 , wherein the Gray code comprises a binary value that differs by one binary digit from another binary value in an adjacent row of the predefined lookup table.

15. A telemetry transmitter comprising:

a processor; and

a memory in which instructions executable by the processor are stored for causing the processor to:

determine a Gray code;

select a transmission waveform corresponding to the Gray code using a predefined lookup table, wherein the predefined lookup table includes relationships between (i) a plurality of Gray code values and (ii) a plurality of different transmission waveforms for pressure waves; and

operate a valve to generate a pressure wave having the transmission waveform in a fluid in a well tool.

16. The telemetry transmitter of claim 15 , wherein the pressure wave comprises modulated pulse positions, and wherein data is encoded in the modulated pulse positions.

17. The telemetry transmitter of claim 16 , wherein the pressure wave comprises modulated pulse widths, and wherein data is encoded in the modulated pulse widths.

18. The telemetry transmitter of claim 15 , wherein the Gray code comprises a binary value that differs by one binary digit from another binary value in an adjacent row of the predefined lookup table.

19. The telemetry transmitter of claim 15 , further comprising a sensor operable to transmit a sensor signal associated with a characteristic of the well tool or a wellbore to the processor, wherein the memory further comprises instructions executable by the processor for causing the processor to determine the Gray code based on the sensor signal.

20. The telemetry transmitter of claim 15 , wherein the well tool comprises a logging while drilling tool or a measuring while drilling tool.

21. The system of claim 1 , wherein the predefined lookup table further includes a relationship between the Gray code and the value.

22. The system of claim 21 , wherein the transmitter is operable to select the transmission waveform by:

determining that the value is to be expressed by the pressure wave;

determining the Gray code based on the relationship between the value and the Gray code in the predefined lookup table; and

determining the transmission waveform based on another relationship between the Gray code and the transmission waveform in the predefined lookup table.

23. The system of claim 1 , wherein the predefined lookup table includes a plurality of rows, each row of the plurality of rows including (i) a respective transmission waveform, (ii) a respective Gray code corresponding to the respective transmission waveform, and (iii) a respective value corresponding to the respective Gray code.

24. The system of claim 23 , wherein the plurality of rows are organized in the predefined lookup table such that each adjacent row has a respective Gray code with a single bit that is different from at least one of (i) a prior Gray code in a prior row, or (ii) a subsequent Gray code in a subsequent row.