Systems, methods, and instrumentalities are disclosed for interleaving coded bits. A wireless transmit/receive unit (WTRU) may generate a plurality of polar encoded bits using polar encoding. The WTRU may divide the plurality of polar encoded bits into sub-blocks of equal size in a sequential manner. The WTRU may apply sub-block wise interleaving to the sub-blocks using an interleaver pattern. The sub-blocks associated with a subset of the sub-blocks may be interleaved, and sub-blocks associated with another subset of the sub-blocks may not be interleaved. The sub-block wise interleaving may include applying interleaving across the sub-blocks without interleaving bits associated with each of the sub-blocks. The WTRU may concatenate bits from each of the interleaved sub-blocks to generate interleaved bits, and store the interleaved bits associated with the interleaved sub-blocks in a circular buffer. The WTRU may select a plurality of bits for transmission from the interleaved bits.

A node (110, 115) receives (804) transmissions associated with a given set of information bits, wherein each of the transmissions use a different polar code and share one or more information bits of the given set of information bits. The node determines (808), at each of a plurality of polar decoders (505, 605) of the node, soft information for each information bit included in an associated one of the transmissions, wherein each of the plurality of polar decoders is associated with a different transmission of the transmissions. The node provides (812), from each polar decoder of the plurality to one or more other polar decoders of the plurality, the determined soft information for any information bits shared by their respective associated transmissions, and uses (816) the provided soft information in an iterative decoding process to decode one or more of the received transmissions.

Apparatus and methods are provided for polar code sub-block interleaving and bit selection. In one novel aspect, middle-part interlaced sub-block interleaving is provided for polar code interleaving. In one embodiment, the middle part of the polar code is interlaced and generates the interleaved polar code. In another embodiment, the lower part and the upper part are also sub-block interleaved with the middle-part interlaced method. In another novel, rate-dependent unified bit selection is provided. The bit selection is categorized into three operation categories of repetition, puncturing and the shortening. Each category follows unified bit selection rule with different categories differ only in the access scheme. In one embodiment, the circular buffer is used for bit selection.

A method for constructing a low-density parity-check (LDPC) code using a structured base parity check matrix with permutation matrix, pseudo-permutation matrix, or zero matrix as constituent sub-matrices; and expanding the structured base parity check matrix into an expanded parity check matrix. A method for constructing a LDPC code using a structured base parity check matrix H=[H.sub.d|H.sub.p], H.sub.d is the data portion, and H.sub.p is the parity portion of the parity check matrix; the parity portion of the structured base parity check matrix is such so that when expanded, an inverse of the parity portion of the expanded parity check matrix is sparse; and expanding the structured base parity check matrix into an expanded parity check matrix. A method for encoding variable sized data by using the expanded LDPC code; and applying shortening, puncturing.

Methods, systems, and devices for wireless communications are described. A transmitting device may perform a lifting procedure on a base graph including multiple variable nodes and multiple check nodes to obtain a lifted graph. The lifting procedure may include replacing each edge between multiple variable nodes and multiple check nodes of the base graph with a respective identity matrices with respective circular shift values. The base graph may include a punctured variable node which corresponds to each of one or more check nodes of the plurality of check nodes via multiple edges. The transmitting device may encode multiple information nodes and multiple parity nodes according to the lifted graph. The transmitting device may transmit a signal including multiple information bits and multiple parity bits based on encoding the multiple information nodes and the multiple parity nodes.

Systems, methods, and instrumentalities are disclosed for interleaving coded bits. A wireless transmit/receive unit (WTRU) may generate a plurality of polar encoded bits using polar encoding. The WTRU may divide the plurality of polar encoded bits into sub-blocks of equal size in a sequential manner. The WTRU may apply sub-block wise interleaving to the sub-blocks using an interleaver pattern. The sub-blocks associated with a subset of the sub-blocks may be interleaved, and sub-blocks associated with another subset of the sub-blocks may not be interleaved. The sub-block wise interleaving may include applying interleaving across the sub-blocks without interleaving bits associated with each of the sub-blocks. The WTRU may concatenate bits from each of the interleaved sub-blocks to generate interleaved bits, and store the interleaved bits associated with the interleaved sub-blocks in a circular buffer. The WTRU may select a plurality of bits for transmission from the interleaved bits.

Systems and methods are disclosed herein relating to rate-compatible polar codes and the use thereof in a wireless communications system. In some embodiments, a transmit node operable for use in a wireless communications system comprises a rate-compatible polar encoder operable to encode information bits to provide coded bits utilizing parallel concatenated polar codes. The transmit node further comprises a transmitter operable to transmit the plurality of coded bits. In this manner, the transmit node may, in some embodiments, use polar codes having different coding rates to adapt to time-varying channel conditions.

Methods, systems, and devices for wireless communications are described. A transmitting device may perform a lifting procedure on a base graph including multiple variable nodes and multiple check nodes to obtain a lifted graph. The lifting procedure may include replacing each edge between multiple variable nodes and multiple check nodes of the base graph with a respective identity matrices with respective circular shift values. The base graph may include a punctured variable node which corresponds to each of one or more check nodes of the plurality of check nodes via multiple edges. The transmitting device may encode multiple information nodes and multiple parity nodes according to the lifted graph. The transmitting device may transmit a signal including multiple information bits and multiple parity bits based on encoding the multiple information nodes and the multiple parity nodes.

Systems, methods, and instrumentalities are disclosed for interleaving coded bits. A wireless transmit/receive unit (WTRU) may generate a plurality of polar encoded bits using polar encoding. The WTRU may divide the plurality of polar encoded bits into sub-blocks of equal size in a sequential manner. The WTRU may apply sub-block wise interleaving to the sub-blocks using an interleaver pattern. The sub-blocks associated with a subset of the sub-blocks may be interleaved, and sub-blocks associated with another subset of the sub-blocks may not be interleaved. The sub-block wise interleaving may include applying interleaving across the sub-blocks without interleaving bits associated with each of the sub-blocks. The WTRU may concatenate bits from each of the interleaved sub-blocks to generate interleaved bits, and store the interleaved bits associated with the interleaved sub-blocks in a circular buffer. The WTRU may select a plurality of bits for transmission from the interleaved bits.

Methods, systems, and devices for wireless communications are described. A transmitting device may perform a lifting procedure on a base graph including multiple variable nodes and multiple check nodes to obtain a lifted graph. The lifting procedure may include replacing each edge between multiple variable nodes and multiple check nodes of the base graph with a respective identity matrices with respective circular shift values. The base graph may include a punctured variable node which corresponds to each of one or more check nodes of the plurality of check nodes via multiple edges. The transmitting device may encode multiple information nodes and multiple parity nodes according to the lifted graph. The transmitting device may transmit a signal including multiple information bits and multiple parity bits based on encoding the multiple information nodes and the multiple parity nodes.