Markov encoder-decoder optimized for cyclo-stationary communications channel or storage media

1. A method, comprising:

determining a cyclo-stationary signal and noise statistic of a communications channel, the cyclo-stationary signal and noise statistic having K-cycles, K>1;

defining Markov transition probabilities that depend on a discrete phase ϕ=t mod K, wherein t is a discrete time value;

training an encoder to optimize the Markov transition probabilities for encoding data sent through the communications channel; and

using the optimized Markov transition probabilities to decode the data from the communications channel.

2. The method of claim 1 , wherein in a soft output Viterbi algorithm (SOVA) decoder is used to decode the data from the communications channel, and wherein branch metrics of the SOVA decoder utilize the optimized Markov transition probabilities.

3. The method of claim 1 , wherein the communications channel is a data storage channel, and the data is stored on a grain-patterned media.

4. The method of claim 3 , wherein the cyclo-stationary signal and noise statistic is due to bit transitions recorded in K-grain rows of the grain-patterned media separated by pattern transition boundaries.

5. The method of claim 4 , wherein each data segment of the grain-patterned media starts with a bit having a bit transition characteristic corresponding to a predetermined one of the K-cycles.

6. The method of claim 1 , wherein training the encoder to optimize the Markov transition probabilities comprises:

generating a training sequence as a Markov code;

propagating the training sequence through the communications channel;

estimating, with a SOVA detector with branch metrics that utilize the Markov code, data values of the training sequence after propagation through the communications channel;

comparing the estimated data values to the generated training sequence to determine an error rate; and

changing the training sequence as a different Markov code to lower the error rate of the data through the communications channel.

7. The method of claim 6 , wherein generating the training sequence as the Markov code comprises mapping random data to sequences having the transition probabilities of the Markov code.

8. The method of claim 1 , wherein the data is encoded and decoded in a block size of B-bits, where B is an integer multiple of K, such that a number of the optimized Markov transition probabilities is the same as with a stationary Markov model that encodes and decodes B-bit data blocks.

9. The method of claim 1 , wherein the data is encoded and decoded in a block size of B-bits, where d is a greatest common denominator of B and K, such that a number of the optimized Markov transition probabilities correspond to K/d discrete phase values.

10. A data storage device comprising a controller configured to perform the method of claim 1 , wherein the communications channel is used to perform one or both of storing and retrieving data to a storage media of the data storage device.

11. The data storage device of claim 10 , wherein the storage media comprises a grain-patterned media.

12. A method, comprising:

determining a cyclo-stationary signal and noise statistic of a storage media, the cyclo-stationary signal and noise statistic having K-cycles, K>1;

defining Markov transition probabilities that depend on a discrete phase ϕ=t mod K, wherein t is a discrete time value;

training an encoder to optimize the Markov transition probabilities for encoding data sent for storage on the storage media; and

using the optimized Markov transition probabilities to decode the data retrieved from the storage media.

13. The method of claim 12 , wherein in a soft output Viterbi algorithm (SOVA) decoder is used to decode the data from the storage media, and wherein branch metrics of the SOVA decoder utilize the optimized Markov transition probabilities.

14. The method of claim 12 , wherein the storage media comprises a grain-patterned media.

15. The method of claim 14 , wherein the cyclo-stationary signal and noise statistic is due to bit transitions recorded in K-grain rows of the grain-patterned media separated by pattern transition boundaries.

16. The method of claim 15 , wherein each data segment of the grain-patterned media starts with a bit having a bit transition characteristic corresponding to a predetermined one of the K-cycles.

17. The method of claim 12 , wherein training the encoder to optimize the Markov transition probabilities comprises:

mapping random data to sequences having the transition probabilities of a Markov code to generating a training sequence;

propagate the training sequence through a communication channel coupled to the storage media;

estimate, with a SOVA detector, data values of the training sequence after propagation through the communication channel;

compare the estimated data values to the generated training sequence to determine an error rate; and

change the training sequence as a different Markov code to lower the error rate of the data through the communication channel.

18. The method of claim 12 , wherein the data is encoded and decoded in a block size of B-bits, where B is an integer multiple of K, such that a number of the optimized Markov transition probabilities is the same as with a stationary Markov model that encodes and decodes B-bit data blocks.

19. The method of claim 12 , wherein the data is encoded and decoded in a block size of B-bits, where d is a greatest common denominator of B and K, such that a number of the optimized Markov transition probabilities correspond to Kid discrete phase values.

20. A data storage device comprising the storage media of claim 12 and a controller configured to perform the method of claim 12 , wherein the storage media comprises a grain-patterned media.