RU2014110139A

RU2014110139A - ARBITRARY LENGTH POLAR CODES

Info

Publication number: RU2014110139A
Application number: RU2014110139/08A
Authority: RU
Inventors: Эльяр Эльдарович Гасанов; Павел Анатольевич Пантелеев; Юрий Сергеевич Шуткин; Андрей Павлович Соколов; Дмитрий Владимирович Алексеев
Original assignee: ЭлЭсАй Корпорейшн
Priority date: 2014-03-17
Filing date: 2014-03-17
Publication date: 2015-09-27

Abstract

1. Способ кодирования данных с помощью полярного кода, содержащий этапы, на которых:- идентифицируют число позиций пропущенных битов, которые следует включать в информационные биты, которые должны быть кодированы так, что кодовое слово, полученное из полярного кодирования информационных битов и позиций пропущенных битов с помощью полярного кода, имеет длину со степенью двух; и- выполняют рекурсивную канальную поляризацию по меньшей мере одного выходного симметричного канала без памяти с двоичным вводом, связанного с позициями пропущенных битов и информационными битами, чтобы возвращать множество битовых каналов, при этом надежность каждого из множества битовых каналов не является одинаковой, при этом позиции пропущенных битов связаны с более надежными из множества битовых каналов, при этом информационные биты и биты четности связаны с менее надежными из множества битовых каналов, и при этом местоположения бита четности задают полярный код.2. Способ по п. 1, дополнительно содержащий этап, на котором кодируют информационные биты и значения в позициях пропущенных битов в схеме полярного кодера с помощью полярного кода с возвращением кодового слова.3. Способ по п. 2, дополнительно содержащий этап, на котором удаляют пропущенные биты из кодового слова, при этом кодовое слово после удаления может иметь длину, которая не является степенью двух.4. Способ по п. 3, дополнительно содержащий этап, на котором повторно добавляют удаленные пропущенные биты к кодовому слову и декодируют кодовое слово.5. Способ по п. 1, в котором упомянутый по меньшей мере один выходной симметричный канал без памяти с двоичным вводом содержит м1. A method of encoding data using a polar code, comprising the steps of: - identifying the number of positions of the skipped bits that should be included in the information bits that should be encoded so that the code word obtained from the polar coding of information bits and positions of the skipped bits using the polar code, has a length with a power of two; and - perform recursive channel polarization of at least one output memory-free symmetric channel with binary input associated with the positions of the skipped bits and information bits to return a plurality of bit channels, while the reliability of each of the many bit channels is not the same, while the positions of the skipped the bits are associated with the more reliable of the plurality of bit channels, wherein the information bits and parity bits are associated with the less reliable of the plurality of bit channels, and wherein parity bits define polar kod.2. The method of claim 1, further comprising encoding information bits and values at the positions of the skipped bits in the polar encoder circuit using a polar code with the return of the code word. The method according to claim 2, further comprising the step of removing the missing bits from the codeword, wherein the codeword after deletion may have a length that is not a power of two. The method of claim 3, further comprising the step of re-adding the deleted missing bits to the codeword and decode the codeword. The method of claim 1, wherein said at least one output memory balanced binary input channel comprises m

Claims

1. A method of encoding data using a polar code, comprising the steps of:

- identify the number of positions of the skipped bits, which should be included in the information bits that must be encoded so that the code word obtained from the polar coding of information bits and positions of the skipped bits using the polar code has a length of two degrees; and

- perform recursive channel polarization of at least one output symmetric channel without memory with binary input associated with the positions of the skipped bits and information bits in order to return a plurality of bit channels, while the reliability of each of the many bit channels is not the same, while the position of the skipped bits associated with the more reliable of the plurality of bit channels, wherein information bits and parity bits are associated with the less reliable of the plurality of bit channels, and wherein the locations parity bits specify the polar code.

2. The method according to claim 1, further comprising encoding information bits and values at the positions of the skipped bits in the polar encoder circuit using a polar code with the return of the code word.

3. The method according to claim 2, further comprising the step of removing the missing bits from the codeword, wherein the codeword after deletion may have a length that is not a power of two.

4. The method according to claim 3, further comprising the step of re-adding the deleted missing bits to the codeword and decode the codeword.

5. The method according to claim 1, in which said at least one output symmetric channel without memory with binary input contains many different channels with different probability vectors.

6. The method according to claim 1, wherein said at least one output symmetric channel without memory with binary input is specified by a probability vector associated with each possible combination of inputs and outputs for the channel.

7. The method according to claim 1, further comprising the step of identifying the position of the positions of the skipped bits so that the position vector of the skipped bits is monotonic.

8. The method according to p. 7, in which for the vector

skipped bit positions for at least one

, the fact that the binary representation B (i) is less than or equal to the binary representation B (j) implies that

less than or equal

.

9. The method according to claim 7, in which the locations of the positions of the skipped bits are located in the last channels from at least one output symmetric channel without memory with binary input.

10. The method according to claim 1, wherein at least one fatal error position is identified for the information bits, further comprising the step of moving said at least one fatal error position so that the vector of fatal error positions is monotonic.

11. The method according to p. 10, in which for the vector

fatal error positions for at least one

less than or equal

.

12. The method of claim 10, wherein said at least one fatal error position is moved by an interleaver so that it corresponds to the first channels of said at least one output balanced channel without binary input memory.

13. The method of claim 10, wherein said at least one fatal error position is moved by an interleaver circuit so that they communicate with less reliable of the plurality of bit channels.

14. The method of claim 1, wherein the fatal errors are located in the first of said at least one output symmetric channel without binary memory and the positions of the skipped bits are placed in the last of said at least one output symmetric channel without binary memory input, additionally containing a stage at which recursive channel polarization is performed starting with a triple containing a channel surrounded by zero values, while a recursive channel polarization returns ETS triplets, each of which has only one non-empty channel to be used as a channel bit.

15. A system for generating a polar code with a codeword of arbitrary length, comprising:

a material computer-readable medium, wherein the computer-readable medium includes instructions executed by a processor in order to:

- select the positions of the skipped bits, which should be added to the information bits and parity bits so that the position vector of the skipped bits is monotonic, and the length of the code word generated by the polar encoder has a length of two degrees;

- place fatal errors in the information bits in such a way that the position vector of fatal errors is monotonic;

- associate the positions of the skipped bits with channels that are more reliable than channels associated with fatal errors;

- perform recursive channel polarization of the input channels to return a plurality of bit channels; and

- select the weakest of the many bit channels for parity bits with the return of the polar code.

16. The system of claim 15, wherein the input channels contain many different probability vectors.

17. The system according to p. 15, in which the input channels contain output balanced channels without memory with binary input.

18. The system of claim 15, wherein each of the input channels is defined by probability vectors associated with each possible combination of inputs and outputs for the input channel.

19. The system of claim 15, wherein the computer-readable medium further includes instructions executed by the processor to place unrecoverable errors in the first of the input channels, and positions of the skipped bits in the last of the input channels.

20. A data storage system comprising:

- a polar code encoder, configured to fill in the positions of the skipped bits and encode information bits and values assigned to the positions of the skipped bits to return a codeword having an arbitrary length not limited to a power of two;

- data storage medium configured to store a codeword; and

a polar code decoder, configured to decode a codeword to return information bits.