EP-4740304-A1 - NESTED SEQUENCES FOR POLAR CODES

EP4740304A1EP 4740304 A1EP4740304 A1EP 4740304A1EP-4740304-A1

Abstract

According to an example aspect of the present invention, there is provided encode or decode data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix formula (I), where B N ; is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where formula (II) is an n- fold Kronecker product of formula (III), a set of indices of rows of the polar transform matrix which form the generator matrix being set A.

Inventors

Coskun, Mustafa Cemil
DU, Jinfeng

Assignees

Nokia Technologies Oy

Dates

Publication Date: 20260513
Application Date: 20240703

Claims (15)

CLAIMS: 1. An apparatus comprising at least one processing core and at least one memory storing instructions that, when executed by the at least one processing core, cause the apparatus at least to: − encode or decode data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^ ^ = ^ ^ ^ ⊗ ^ ^ , where ^ ^ ;is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where ^⊗ ^ ^ is an n-fold Kronecker product of ^ ^ ≜ ^ 1 0 1 1 ^; − a set of indices of rows of the polar transform matrix which form the generator matrix being set A, − wherein at least one of the following applies: o A) for encoded length N = 64 with 44 payload bits the set A is {4, 6, 8, 12, 14, 15, 16, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64}, o B) for encoded length N = 64 with 20 payload bits the set A is {16, 24, 28, 30, 31, 32, 40, 44, 46, 47, 48, 52, 54, 55, 56, 58, 60, 62, 63, 64}, and o C) for encoded length N = 32 with 20 payload bits the set A is {8, 12, 14, 15, 16, 24, 28, 30, 31, 32}.
2. The apparatus according to claim 1, wherein the apparatus is configured to perform the encoding, and an encoder of the apparatus is configured to use an upper-unitriangular NxN pre-transformation matrix before the polar transformation and to place the data to be encoded in subvector u_A defined by the indices of the set A and elements of subvector u_F are set to zeroes.
3. The apparatus according to claim 1 or 2, wherein the apparatus comprises, or is comprised in, a user equipment, the data is uplink data and the apparatus is configured to encode the data for transmission.
4. The apparatus according to claim 1, wherein the apparatus comprises, or is comprised in, a base station, the data is downlink data and the apparatus is configured to encode the data for transmission.
5. The apparatus according to any of claims 1 – 4, wherein the apparatus is configured to store plural of the sets A in a nested manner.
6. The apparatus according to claim 5, wherein the storing in the nested manner comprises use of an integer vector.
7. The apparatus according to any of claims 1 – 6, wherein the apparatus is configured to perform the encoding such that the encoding comprises a pre-transformation using an upper- triangular pre-transformaton matrix T.
8. The apparatus according to any of claims 1 – 7, wherein each one of A), B) and C) applies.
9. The apparatus according to any of claims 1 – 7, wherein exactly one of A), B) and C) does not apply and exactly two of A), B) and C) do apply.
10. The apparatus according to any of claims, wherein configured to employ, in the encoding, precoding defined by a KxN binary matrix P before the NxN polar transformation, where P satisfies the following: A) the collection of column indices of the first “1” in each row constitutes set A, B) if the column index of the first “1” in row i is larger than that of the first “1” in row j, then i>j, and C) the apparatus is configured to perform the encoding by multiplying a K-bit message with matrix P followed by a length-N polar transform. 11. An apparatus comprising at least one processing core and at least one memory storing instructions that, when executed by the at least one processing core, cause the apparatus at least to: − encode or decode data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^ ^ = ^ ^ ^ ⊗ ^ ^ , where ^ ^ ;is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where ^⊗ ^ ^ is an n-fold Kronecker product of ^ ^ ≜ ^ 1 0 1 1 ^; − a set of indices of rows of the polar matrix which form the generator matrix being set A, wherein the apparatus to generate set A for the polar code with N encoded bits, N not greater than 128, and K payload bits as follows: o select from vector ^ ^^^^ = [1, 65, 33, 17, 9, 5, 3, 2, 97, 81, 73, 69, 67, 66, 49, 41, 37, 35, 34, 25, 21, 19, 18, 13,
11, 10, 7, 6, 4, 113, 105, 101, 99, 98, 89, 85, 83, 82, 77, 75, 71, 70, 68, 57, 53, 51, 50, 45, 43, 42, 39, 38, 36, 29, 27, 26, 23, 22, 20, 15, 14, 12, 8, 121, 117, 115, 114, 109, 107, 106, 103, 102, 100, 93, 91, 90, 87, 86, 84, 79, 78, 76, 72, 61, 59, 58, 55, 54, 52, 47, 46, 44, 40, 31, 30, 28, 24, 16, 125, 123, 122, 119, 118, 116, 111, 110, 108, 104, 95, 94, 92, 88, 80, 63, 62, 60, 56, 48, 32, 127, 126, 124, 120, 112, 96, 64, 128] each element not greater than N to thereby obtain, while maintaining the order of the selected elements, vector r; o obtain set A by selecting the K last elements from vector r. 12. A method comprising: − encoding or decoding data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^ ^ = ^ ^ ^ ⊗ ^ ^ , where ^ ^ ;is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where ^ ⊗ ^ ^ is an n-fold Kronecker product of ^ ^ ≜ ^ 1 0 1 1 ^; − a set of indices of rows of the polar matrix which form the generator matrix being set A, − wherein at least one of the following applies: o A) for encoded length N = 64 with 44 payload bits the set A is {4, 6, 8, 12, 14, 15, 16, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64}, o B) for encoded length N = 64 with 20 payload bits the set A is {16, 24, 28, 30, 31, 32, 40, 44, 46, 47, 48, 52, 54, 55, 56, 58, 60, 62, 63, 64}, and o C) for encoded length N = 32 with 20 payload bits the set A is {8,
12, 14, 15, 16, 24, 28, 30, 31, 32}.
13. A method, comprising: − encoding or decoding data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^ ^ = ^ ^ ^ ⊗ ^ ^ , where ^ ^ ;is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where ^ ⊗ ^ ^ is an n-fold Kronecker product of ^ ^ ≜ ^ 1 0 1 1^ ; − a set of indices of rows of the polar matrix which form the generator matrix being set A, wherein the apparatus to generate set A for the polar code with N encoded bits, N not greater than 128, and K payload bits as follows: o select from vector ^ ^^^^ = [1, 65, 33, 17, 9, 5, 3, 2, 97, 81, 73, 69, 67, 66, 49, 41, 37, 35, 34, 25, 21, 19, 18, 13, 11, 10, 7, 6, 4, 113, 105, 101, 99, 98, 89, 85, 83, 82, 77, 75, 74, 71, 70, 68, 57, 53, 51, 50, 45, 43, 42, 39, 38, 36, 29, 27, 26, 23, 22, 20, 15, 14, 12, 8, 121, 117, 115, 114, 109, 107, 106, 103, 102, 100, 93, 91, 90, 87, 86, 84, 79, 78, 76, 72, 61, 59, 58, 55, 54, 52, 47, 46, 44, 40, 31, 30, 28, 24, 16, 125, 123, 122, 119, 118, 116, 111, 110, 108, 104, 95, 94, 92, 88, 80, 63, 62, 60, 56, 48, 32, 127, 126, 124, 120, 112, 96, 64, 128] each element not greater than N to thereby obtain, while maintaining the order of the selected elements, vector r; o obtain set A by selecting the K last elements from vector r.
14. An apparatus comprising means for: − encoding or decoding data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^ ^ = ^ ^ ^ ⊗ ^ ^ , where ^ ^ ;is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where ^ ⊗ ^ ^ is an n-fold Kronecker product of ^ ^ ≜ ^ 1 0 − a set of indices of rows of the polar matrix which form the generator matrix being set A, − wherein at least one of the following applies: o A) for encoded length N = 64 with 44 payload bits the set A is {4, 6, 8, 12, 14, 15, 16, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64}, o B) for encoded length N = 64 with 20 payload bits the set A is {16, 24, 28, 30, 31, 32, 40, 44, 46, 47, 48, 52, 54, 55, 56, 58, 60, 62, 63, 64}, and o C) for encoded length N = 32 with 20 payload bits the set A is {8, 12, 14, 15, 16, 24, 28, 30, 31, 32}.
15. A non-transitory computer readable medium having stored thereon a set of computer readable instructions that, when executed by at least one processor, cause an apparatus to at least: − encode or decode data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^ ^ = ^ ^ ^ ⊗ ^ ^ , where ^ ^ ;is an N × N bit-reversal matrix, where N = 2 n is a non-negative integer and where ^ ⊗ ^ ^ is an n-fold Kronecker product of ^ ^ ≜ ^ 1 0 1 1 ^; − a set of indices of rows of the polar matrix which form the generator matrix being set A, − wherein at least one of the following applies: o A) for encoded length N = 64 with 44 payload bits the set A is {4, 6, 8, 12, 14, 15, 16, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64}, o B) for encoded length N = 64 with 20 payload bits the set A is {16, 24, 28, 30, 31, 32, 40, 44, 46, 47, 48, 52, 54, 55, 56, 58, 60, 62, 63, 64}, and o C) for encoded length N = 32 with 20 payload bits the set A is {8, 12, 14, 15, 16, 24, 28, 30, 31, 32}.

Description

CHANNEL CODING FIELD [0001] The present disclosure relates to the field of channel coding, such as channel coding for wireless communication systems, such as cellular wireless communication systems, for example. BACKGROUND [0002] Information to be transmitted, known as payload, may be encoded prior to transmission over a transmission channel. This encoding, which may be referred to as error correction coding or channel coding, may facilitate use of a noisy communication channel to convey payload which tolerates no errors, or fewer errors than would occur over the communication channel without the use of encoding. [0003] Typically, when the payload bit sequence is encoded, the result is an encoded bit sequence which is longer than the original payload bit sequence, as redundancy information is provided in the encoded bit sequence in addition to payload. An extent of redundancy information may be associated with an extent of error detection or error correction that is possible. In case errors are merely detected with channel coding, an information block with a detected error may be requested to be re-transmitted, to overcome the detected error. SUMMARY [0004] According to some aspects, there is provided the subject-matter of the independent claims. Some embodiments are defined in the dependent claims. The scope of protection sought for various embodiments of the invention is set out by the independent claims. The embodiments, examples and features, if any, described in this specification that do not fall under the scope of the independent claims are to be interpreted as examples useful for understanding various embodiments of the invention. [0005] According to a first aspect of the present disclosure, there is provided an apparatus comprising at least one processing core and at least one memory storing instructions that, when executed by the at least one processing core, cause the apparatus at least to encode or decode data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^^ = ^^^⊗ ^ ^, where ^^ ;is an N × N bit-reversal matrix, where N = 2n is a non-negative integer and where ^⊗ ^ ^ is an n-fold Kronecker product of ^^ ≜ ^1 0 1 1^, a set of indices of rows of the polar transform matrix which form the generator matrix set A, wherein at least one of the following applies: A) for encoded length N = 64 with payload bits the set A is {4, 6, 8, 12, 14, 15, 16, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64}, B) for encoded length N = 64 with 20 payload bits the set A is {16, 24, 28, 30, 31, 32, 40, 44, 46, 47, 48, 52, 54, 55, 56, 58, 60, 62, 63, 64}, and C) for encoded length N = 32 with 20 payload bits the set A is {8, 12, 14, 15, 16, 24, 28, 30, 31, 32}. [0006] According to a second aspect of the present disclosure, there is provided an apparatus comprising at least one processing core and at least one memory storing instructions that, when executed by the at least one processing core, cause the apparatus at least to encode or decode data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^^ = ^^^⊗ ^ ^, where ^^ ;is an N × N bit-reversal matrix, where N = 2n is a non-negative integer and where ^⊗ ^ ^ is an n-fold Kronecker product of ^^ ≜ ^1 0 1 1^, a set of indices of rows of the polar transform matrix which form the generator matrix set A, wherein the apparatus is configured to generate set A for the polar code with N encoded bits, N not greater than 128, and K payload bits as follows: select from vector ^^^^^ = [1, 65, 33, 17, 9, 5, 3, 2, 97, 81, 73, 69, 67, 66, 49, 41, 37, 35, 34, 25, 21, 19, 18, 13, 11, 10, 7, 6, 4, 113, 105, 101, 99, 98, 89, 85, 83, 82, 77, 75, 74, 71, 70, 68, 57, 53, 51, 50, 45, 43, 42, 39, 38, 36, 29, 27, 26, 23, 22, 20, 15, 14, 12, 8, 121, 117, 115, 114, 109, 107, 106, 103, 102, 100, 93, 91, 90, 87, 86, 84, 79, 78, 76, 72, 61, 59, 58, 55, 54, 52, 47, 46, 44, 40, 31, 30, 28, 24, 16, 125, 123, 122, 119, 118, 116, 111, 110, 108, 104, 95, 94, 92, 88, 80, 63, 62, 60, 56, 48, 32, 127, 126, 124, 120, 112, 96, 64, 128] each element not greater than N to thereby obtain, while maintaining the order of the selected elements, vector r, and obtain set A by selecting the K last elements from vector r. [0007] According to a third aspect of the present disclosure, there is provided a method comprising encoding or decoding data using a polar code, wherein a generator matrix of the polar code is comprised of rows of a polar transform matrix ^^ = ^^^⊗ ^ ^, where ^^ ;is an N × N bit-reversal matrix, where N = 2n is a non-negative integer and where ^⊗ ^ ^ is an n-fold Kronecker product of ^^ ≜ ^1 0 1 1^, a set of indices of rows of the polar transform matrix which form the generator matrix set A, wherein at least one of the following applies: A) for encoded length N = 64 bits