Abstract:
Provided is a base matrix of a rate-adaptive irregular QC-LDPC code, the base matrix being formed by columns and rows having entries representing circulant submatrices. The columns of the base matrix are divided into at least one or more higher weight first columns and lower weight second columns and the rows of the base matrix are divided into first high weight rows corresponding to the high rate mother code and second low weight rows corresponding to the extension part related to lower rate codes. A first submatrix formed by an intersection of entries of the second columns and entries of the first and the second rows is divided into first quadratic submatrices, wherein at most one entry in each column of each first submatrix and/or at most one entry in each row of each first submatrix is labelled thereby dividing the first submatrix into layers of groups of orthogonally labelled rows, wherein the number of orthogonally labelled rows corresponds to the size of the first quadratic submatrices. One or more check node unit processors perform flooding or a combination of flooding and layered (hence hybrid) decoding operations in view of the one or more higher weight first columns and one or more CNU processors perform layered decoding operations in view of the second columns.
Abstract:
The present invention in particular provides a variable-length rate-adaptive quasi cyclic (QC) low density parity check (LDPC) code with linear time encoding and low error floor. To this end, the present invention provides a data encoding method, the method comprising the steps of receiving a user bits vector u ; determining a parity bits vector p , wherein a vector с=(u,p) is a codeword satisfying a Type-I mZ x nZ parity-check matrix H=(H u ,H p ) with a quasi-cyclic mZ x mZ submatrix H p of circulant size Z , wherein the first left m - r circulant columns of H p have zero circulants above a main diagonal of H p , the remaining right r circulant columns have zero circulants in the first top m - r circulant rows of H p , and the remaining bottom r circulant rows of H p and the remaining right r circulant columns of H p form an rZ x rZ square quasi-cyclic submatrix A , wherein a polynomial representation of the submatrix A over the ring F 2 [x] has a determinant equal to a monomial x i , wherein 0 ≤ i , and 4 ≤ r ≤ m . The present invention also provides a data encoder, a communication device, a storage device and a computer program product comprising said method.
Abstract:
A decoding method, an encoding method, a decoder and an encoder are disclosed. In an embodiment the decoding method includes receiving, at a receiver of a receiving side, signals from a transmitting side, the signals including a code word and decoding, at a decoder of the receiving side, the code word using a low density parity check (LDPC) code in which each n adjacent rows, n>1, in an extension part of a base parity check matrix (PCM) are orthogonal except for punctured information columns.
Abstract:
A method for generating a code, a method for encoding and decoding data, and an encoder and a decoder performing the encoding and decoding are disclosed. In an embodiment, a method for lifting a child code from a base code for encoding and decoding data includes determining a single combination of a circulant size, a lifting function, and a labelled base matrix PCM according to an information length and a code rate using data stored in a lifting table. The lifting table was defined at a code generation stage. The method also includes calculating a plurality of shifts for the child code. Each shift is calculated by applying the lifting function to the labelled base matrix PCM with a defined index using the circulant size and using the derived child PCM to encode or decode data.
Abstract:
The present disclosure relates to processing input data by a neural network. Methods and apparatuses of some embodiments process the input data by at least one layer of the neural network and obtain thereby a feature tensor. Then, the distribution of the obtained feature tensors estimated. Another distribution is obtained. Such other distribution may be a distribution of another input data, or a distribution obtained by combining a plurality of distributions obtained for respective plurality of some input data. Then a distance value indicative of a distance between the two distributions is calculated and based thereon, a characteristic of the input data is determined. The characteristic may be pertinence to a certain class of data or a detection of out-of-distribution data or determination of reliability of a class determination or the like.
Abstract:
Provided is a base matrix of a rate-adaptive irregular QC-LDPC code, the base matrix being formed by columns and rows having entries representing circulant submatrices. The columns of the base matrix are divided into at least one or more higher weight first columns and lower weight second columns and the rows of the base matrix are divided into first high weight rows corresponding to the high rate mother code and second low weight rows corresponding to the extension part related to lower rate codes. A first submatrix formed by an intersection of entries of the second columns and entries of the first and the second rows is divided into first quadratic submatrices, wherein at most one entry in each column of each first submatrix and/or at most one entry in each row of each first submatrix is labelled thereby dividing the first submatrix into layers of groups of orthogonally labelled rows, wherein the number of orthogonally labelled rows corresponds to the size of the first quadratic submatrices. One or more check node unit processors perform flooding or a combination of flooding and layered (hence hybrid) decoding operations in view of the one or more higher weight first columns and one or more CNU processors perform layered decoding operations in view of the second columns.
Abstract:
Provided is an efficiently decodable QC-LDPC code which is based on a base matrix of an irregular QC-LDPC matrix, the base matrix being formed by columns and rows, the columns being dividable into one or more columns corresponding to punctured variable nodes (i.e. variable nodes corresponding to information bits which are used by the encoder but are not transmitted to or effectively treated as not received by the decoder) and columns corresponding to not-punctured variable nodes, and the rows being dividable into high-density rows (i.e. rows having a weight which is above a first weight) and low-density rows (i.e. rows having a weight which is below a second weight, wherein the second weight is equal to or smaller than the first weight), wherein a matrix defined by the overlap of the low-density rows and the columns corresponding to the not-punctured variable nodes is dividable into groups of orthogonal rows.
Abstract:
A method and system for offset lifting is provided. In an embodiment, a method for encoding data includes receiving a K-bit source word input. The method also includes encoding the K-bit source word input according to a LDPC code, a lifting function, and a circulant size offset to generate an N-bit code word output. The circulant size and lifting function are determined according to an information length, a code rate, and a decoder. The method also includes storing the N-bit code word output in input/output memory.
Abstract:
Provided is an efficiently decodable QC-LDPC code which is based on a base matrix of an irregular QC-LDPC matrix, the base matrix being formed by columns and rows, the columns being dividable into one or more columns corresponding to punctured variable nodes (i.e. variable nodes corresponding to information bits which are used by the encoder but are not transmitted to or effectively treated as not received by the decoder) and columns corresponding to not-punctured variable nodes, and the rows being dividable into high-density rows (i.e. rows having a weight which is above a first weight) and low-density rows (i.e. rows having a weight which is below a second weight, wherein the second weight is equal to or smaller than the first weight), wherein a matrix defined by the overlap of the low-density rows and the columns corresponding to the not-punctured variable nodes is dividable into groups of orthogonal rows. Combination of a flooding decoding process for punctured variable nodes and a layered decoding process for non-punctured variable nodes.