Reduced polar codes

1. A method for encoding a reduced polar code, comprising the steps of:

modifying an input codeword comprising polar code encoded input data by removing one or more bits from one of (i) a first part of the input codeword and (ii) a second part of the input codeword; and

generating an output codeword by concatenating the first and the second parts of the modified input codeword.

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

generating the input codeword by concatenating predetermined data to the input data prior to polar code encoding.

3. The method according to claim 1 , wherein the one or more bits are removed only from the first part of the input codeword.

4. The method according to claim 1 , wherein the one or more bits are removed by puncturing the second part of the input codeword at one or more locations.

5. The method according to claim 1 , wherein a plurality of bits are removed by:

discarding a first portion of the bits from the first part of the input codeword; and

puncturing a second portion of the bits from the second part of the input codeword.

6. The method according to claim 1 , further comprising the steps of:

modifying the output codeword by adding one or more bits to one of (i) a first part of the output codeword and (ii) a second part of the output codeword;

generating an internal codeword by concatenating the first and the second parts of the modified output codeword; and

generating output data by polar code decoding the internal codeword.

7. The method according to claim 1 , further comprising the step of:

writing the output codeword into a nonvolatile memory.

8. The method according to claim 1 , wherein the method is implemented in one or more integrated circuits.

9. A method for decoding a reduced polar code, comprising the steps of:

modifying an input codeword by adding one or more bits to one of (i) a first part of the input codeword and (ii) a second part of the input codeword, and concatenating the first and the second parts of the modified input codeword; and

generating output data by polar code decoding the modified input codeword.

10. The method according to claim 9 , further comprising the step of:

removing predetermined data from the output data.

11. The method according to claim 9 , wherein the input codeword is modified by concatenating the one or more bits to the first part of the input codeword.

12. The method according to claim 9 , wherein the input codeword is modified by inserting the one or more bits into the second part of the input codeword in one or more punctured locations.

13. The method according to claim 9 , wherein the input codeword is modified by (i) concatenating a first portion of a plurality of bits to the first part of the input codeword and (ii) inserting a second portion of the plurality of bits into the second portion of the input codeword in one or more punctured locations.

14. The method according to claim 9 , further comprising the step of:

reading the input codeword from a nonvolatile memory.

15. The method according to claim 9 , wherein the method is implemented in one or more integrated circuits.

16. An apparatus comprising:

a memory comprising one or more non-volatile memory devices; and

a controller, wherein the controller is configured to

modify an input codeword comprising polar code encoded input data by removing one or more bits from one of (i) a first part of the input codeword and (ii) a second part of the input codeword,

generate an output codeword by concatenating the first and the second parts of the modified input codeword, and

write the output codeword into the memory.

17. The apparatus according to claim 16 , wherein the memory and the controller are part of a solid-state drive or disk (SSD).

18. The apparatus according to claim 16 , wherein the controller is further configured to generate the input codeword by concatenating predetermined data to the input data prior to polar code encoding.

19. The apparatus according to claim 16 , wherein the controller is further configured to remove a plurality of bits by:

discarding a first portion of the bits from the first part of the input codeword; and

puncturing a second portion of the bits from the second part of the input codeword.

20. The apparatus according to claim 16 , wherein the controller is further configured to:

modify the output codeword by adding one or more bits to one of (i) a first part of the output codeword and (ii) a second part of the output codeword;

generate an internal codeword by concatenating the first and the second parts of the modified output codeword; and

generate output data by polar code decoding the internal codeword.