Apparatus and method for generating polar codes

    公开(公告)号:US10924137B2

    公开(公告)日:2021-02-16

    申请号:US16443105

    申请日:2019-06-17

    Abstract: A method for generating a polar code cN of length N and dimension K, on the basis of a generator matrix GN of size N×N, is provided. The method includes generating a distance spectrum vector dTp=(dTp(1), . . . , dTp(p)) of size p of the kernel Tp, wherein dTp(h), h=1, . . . , p, corresponds to a maximum value among all possible minimum distances of all possible polar codes of size p and dimension h generated on the basis of the kernel Tp. The method also includes generating a distance spectrum vector dGN of size N of the generator matrix GN on the basis of the distance spectrum vector dTp, determining the set of K information bit indices I on the basis of the distance spectrum vector dGN, and generating the polar code cN on the basis of the set of K information bit indices I.

    Method to generate ordered sequence for polar codes

    公开(公告)号:US10985871B2

    公开(公告)日:2021-04-20

    申请号:US15875766

    申请日:2018-01-19

    Abstract: A number K of N sub-channels that are defined by a code and that have associated reliabilities for input bits at N input bit positions, are to be selected to carry bits that are to be encoded. A localization area that includes multiple sub-channels and is located below fewer than K of the N sub-channels in a partial order of the N sub-channels is determined based on one or more coding parameters. The fewer than K sub-channels of the N sub-channels above the localization area in the partial order are selected, and a number of sub-channels from those in the localization area are also selected. The selected fewer than K sub-channels and the number of sub-channels selected from those in the localization area together include K sub-channels to carry the bits that are to be encoded.

    APPARATUS AND METHOD FOR RANDOM LINEAR CODE ENCODING AND GUESSING RANDOM ADDITIVE NOISE DECODING (GRAND)

    公开(公告)号:US20250007650A1

    公开(公告)日:2025-01-02

    申请号:US18884753

    申请日:2024-09-13

    Abstract: An apparatus for encoding an information word of size N into a codeword includes a processing unit to initialize a current vector as being the information word and run T times, T being a predetermined integer greater or equal to 1, a loop. The loop includes generating a scrambled vector by interleaving values of the current vector, grouping values of the scrambled vector into N/m input vectors of size m, and multiplying each of the input vectors by an encoding matrix of size m×m to obtain output vectors. The loop further includes setting the current vector with a concatenation of the output vectors. Moreover, the apparatus includes a transmitting unit configured to transmit the codeword through a communication channel, the codeword being the last current vector in the loop.

    Device and method for generating a multi-kernel polar code

    公开(公告)号:US11245424B2

    公开(公告)日:2022-02-08

    申请号:US16797214

    申请日:2020-02-21

    Abstract: A device for generating a multi-kernel polar code xN of length N and dimension K on the basis of a first transformation matrix GN of size N×N that defines a first multi-kernel polar code includes a processor configured to generate a second transformation matrix G′N of size N×N by permuting the order of at least two columns of a sub-matrix of the first transformation matrix GN, and generate the multi-kernel polar code xN an the basis of xN=uN·G′N, wherein uN=(u0, . . . , uN−1) is a vector of size N, with the elements ui, i=0, . . . N−1, corresponding to an information bit if i∈I, I being a set of K information bit indices, and ui=0, if i∈F, F being a set of N−K frozen bit indices.

    Automorphism-based polar encoding and decoding

    公开(公告)号:US12199635B2

    公开(公告)日:2025-01-14

    申请号:US18450203

    申请日:2023-08-15

    Abstract: The present disclosure relates generally to the field of data encoding and decoding, and particularly to automorphism-based polar encoding and decoding apparatuses and methods, as well as computer program products embodying the method steps in the form of computer codes. More specifically, polar codes are designed such that their frozen bits support automorphisms described by a binary upper triangular matrix having a diagonal including at least one of zeros and units. Codewords generated using these polar codes may be subsequently subjected to automorphism-based polar decoding in an efficient manner and with a lower decoding latency compared to the conventional Successive Cancellation List decoding algorithms. Furthermore, the efficiency of the automorphism-based polar decoding may be increased even more if the automorphisms are based on matrix elements arranged above the diagonal in a vicinity of a bottom right corner of the binary upper triangular matrix.

    Apparatuses and methods for mapping frozen sets between polar codes and product codes

    公开(公告)号:US11323139B2

    公开(公告)日:2022-05-03

    申请号:US17201891

    申请日:2021-03-15

    Abstract: A method generates a frozen vector associated with a polar code codeword on the basis of a frozen matrix associated with a product code codeword, the frozen matrix being of size Nc×Nr. The method includes replicating a first matrix row of the frozen matrix Nc times to generate an expanded matrix row; replicating a first matrix column of the frozen matrix Nr times to generate an expanded matrix column; generating the frozen vector on the basis of the expanded matrix row and the expanded matrix column. The disclosure further provides a method for generating a frozen matrix associated with a product code codeword on the basis of a frozen vector associated with a polar code codeword, wherein the product code codeword comprises a matrix of size Nc×Nr, and the frozen vector comprises a vector of size N with a plurality of bits.

    Channel code construction for decoder reuse

    公开(公告)号:US11316614B2

    公开(公告)日:2022-04-26

    申请号:US16934180

    申请日:2020-07-21

    Abstract: The present disclosure provides a code generator for generating an {N′, K′} code for encoding and/or decoding data transmitted in a communication channel from an {N, K} code, wherein N and N′ are code lengths, K and K′ are code dimensions. The code generator is configured to shorten the {N, K} code to obtain an intermediate code, and to extend the intermediate code to obtain the {N′, K′} code. The present disclosure also provides a corresponding code construction method. Further, the present disclosure provides a device for encoding and/or decoding data transmitted in a communication channel, the device being configured to encode and/or decode the data based on an {N′, K′} code generated from the {N, K} code.

    Devices and methods implementing polar codes

    公开(公告)号:US10541710B2

    公开(公告)日:2020-01-21

    申请号:US16188717

    申请日:2018-11-13

    Abstract: An encoder for encoding K information bits into a code word of length N′ on the basis of a polar code of length N is provided, wherein N is a power of 2 and greater than or equal to N′. The encoder comprises a memory storing a plurality of bit indices, which comprise a set of N frozen bit indices associated with the polar code of length N, a set of N/2 puncturing bit indices and/or a set of N/2 shortening bit indices and a processor configured to retrieve at least a subset of the plurality of bit indices from the memory, to encode the K information bits using the polar code of length N for obtaining encoded data of length N and to reduce the number of bits of the encoded data to the length N′ for obtaining the code word of length N′.

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