Huawei Technologies Co., Limited

Ingmar Land

Valerio Bioglio

Jean-Claude Belfiore

Frederic Gabry

Gaoning He

Wen Tong

Yiqun Ge

Wuxian Shi

Wai Kong Raymond Leung

Ran Zhang

Huijian Zhang

Zhipeng Zhao

Carlo Condo

Beatrice Tomasi

Charles Pillet

Marc Fossorier

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.

Automorphism-based polar encoding and decoding

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 N&#xd7;N. The method includes replicating a first matrix row of the frozen matrix Ntimes to generate an expanded matrix row; replicating a first matrix column of the frozen matrix Ntimes 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 N&#xd7;N, and the frozen vector comprises a vector of size N with a plurality of bits.

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

The present disclosure provides a code generator for generating an {N', K&#x2032;} code for encoding and/or decoding data transmitted in a communication channel from an {N, K} code, wherein N and N&#x2032; are code lengths, K and K&#x2032; 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&#x2032;, K&#x2032;} 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&#x2032;, K&#x2032;} code generated from the {N, K} code.

Channel code construction for decoder reuse

A device for generating a multi-kernel polar code xof length N and dimension K on the basis of a first transformation matrix Gof size N&#xd7;N that defines a first multi-kernel polar code includes a processor configured to generate a second transformation matrix G'of size N&#xd7;N by permuting the order of at least two columns of a sub-matrix of the first transformation matrix G, and generate the multi-kernel polar code xan the basis of x=u&#xb7;G&#x2032;, wherein u=(u, . . . , u) is a vector of size N, with the elements u, i=0, . . . N&#x2212;1, corresponding to an information bit if i&#x2208;I, I being a set of K information bit indices, and u=0, if i&#x2208;F, F being a set of N&#x2212;K frozen bit indices.

Device and method for generating a multi-kernel polar code

The present disclosure relates to a device for generating a polar code xof length N and dimension K on the basis of a transformation matrix Gof size N&#xd7;N, wherein the transformation matrix Gis based on a first matrix G, of size N&#xd7;N, and on a second matrix Gof size N&#xd7;N, wherein N=N&#xb7;N, and wherein the polar code xis given by x=u&#xb7;G, wherein u=(u, . . . u) is a vector of size N, an element u, i=0, . . . N&#x2212;1, of the vector corresponding to an information bit if i&#x2208;I, I being a set of K information bit indices, and u=0, if i&#x2208;F, F being a set of N&#x2212;K frozen bit indices.

Construction of a polar code based on a distance criterion and a reliability criterion, in particular of a multi-kernel polar code

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.

Method to generate ordered sequence for polar codes

A method for generating a polar code cof length N and dimension K, on the basis of a generator matrix Gof size N&#xd7;N, is provided. The method includes generating a distance spectrum vector d=(d(1), . . . , d(p)) of size p of the kernel T, wherein d(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 T. The method also includes generating a distance spectrum vector dof size N of the generator matrix Gon the basis of the distance spectrum vector d, determining the set of K information bit indices I on the basis of the distance spectrum vector d, and generating the polar code con the basis of the set of K information bit indices I.

Apparatus and method for generating polar codes

Encoding of information bit sequences by use of an encoding device having more than two encoding entities is provided. Decoding of output codewords by a decoding device having more than two decoding entities is further provided. The encoding and the decoding are implemented through transmitting output codewords, generated by the encoding device, to the decoding device via a channel, wherein two or more user devices transmit the respective output codewords concurrently via the channel.

Encoding device and method and corresponding decoding device and method

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&#x2032;. 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&#x2032; for obtaining the code word of length N&#x2032;.

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Boulogne Billancourt, France

Ingmar Land