Patent Publication Number: US-11398837-B2

Title: Unified pattern for puncturing and shortening polar codes

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application for Patent is a national stage application under 35 U.S.C. 371 of PCT/CN2017/097290, filed Aug. 12, 2017, which is assigned to the assignee hereof and hereby expressly incorporated by reference herein as if fully set forth below and for all applicable purposes. 
     BACKGROUND 
     Field of the Disclosure 
     Certain aspects of the present disclosure generally relate to wireless communications and, more particularly, to methods and apparatus for rate-matching a stream of bits encoded using a polar code. 
     Description of Related Art 
     Wireless communication systems are widely deployed to provide various telecommunication services such as telephony, video, data, messaging, and broadcasts. Typical wireless communication systems may employ multiple-access technologies capable of supporting communication with multiple users by sharing available system resources (e.g., bandwidth, transmit power). Examples of such multiple-access technologies include Long Term Evolution (LTE) systems, code division multiple access (CDMA) systems, time division multiple access (TDMA) systems, frequency division multiple access (FDMA) systems, orthogonal frequency division multiple access (OFDMA) systems, single-carrier frequency division multiple access (SC-FDMA) systems, and time division synchronous code division multiple access (TD-SCDMA) systems. 
     In some examples, a wireless multiple-access communication system may include a number of base stations, each simultaneously supporting communication for multiple communication devices, otherwise known as user equipment (UEs). In LTE or LTE-A network, a set of one or more base stations may define an e NodeB (eNB). In other examples (e.g., in a next generation or 5G network), a wireless multiple access communication system may include a number of distributed units (DUs) (e.g., edge units (EUs), edge nodes (ENs), radio heads (RHs), smart radio heads (SRHs), transmission reception points (TRPs), etc.) in communication with a number of central units (CUs) (e.g., central nodes (CNs), access node controllers (ANCs), etc.), where a set of one or more distributed units, in communication with a central unit, may define an access node (e.g., a new radio base station (NR BS), a new radio node-B (NR NB), a network node, 5G NB, gNB, etc.). A base station or DU may communicate with a set of UEs on downlink channels (e.g., for transmissions from a base station or to a UE) and uplink channels (e.g., for transmissions from a UE to a base station or distributed unit). 
     These multiple access technologies have been adopted in various telecommunication standards to provide a common protocol that enables different wireless devices to communicate on a municipal, national, regional, and even global level. An example of an emerging telecommunication standard is new radio (NR), for example, 5G radio access. NR is a set of enhancements to the LTE mobile standard promulgated by Third Generation Partnership Project (3GPP). It is designed to better support mobile broadband Internet access by improving spectral efficiency, lowering costs, improving services, making use of new spectrum, and better integrating with other open standards using OFDMA with a cyclic prefix (CP) on the downlink (DL) and on the uplink (UL) as well as support beamforming, multiple-input multiple-output (MIMO) antenna technology, and carrier aggregation. 
     However, as the demand for mobile broadband access continues to increase, there exists a need for further improvements in NR technology. Preferably, these improvements should be applicable to other multi-access technologies and the telecommunication standards that employ these technologies. 
     SUMMARY 
     The systems, methods, and devices of the disclosure each have several aspects, no single one of which is solely responsible for its desirable attributes. Without limiting the scope of this disclosure as expressed by the claims which follow, some features will now be discussed briefly. After considering this discussion, and particularly after reading the section entitled “Detailed Description” one will understand how the features of this disclosure provide advantages that include improved communications in a wireless network. 
     Certain aspects of the present disclosure provide a method for wireless communications in a network. The method generally includes encoding K information bits using a polar code with a mother code length. N, to generate a stream of encoded bits; storing a portion of the encoded bits in a circular buffer of size N; reordering P blocks of the circular buffer according to row weights of a Hadamard matrix J; interlacing the encoded bits of the blocks having a same row weight; selecting, based on the row weights, a subset of the encoded bits in the blocks to modify; modifying the selected subset of the encoded bits; and transmitting the encoded bits in the P blocks, subsequent to modifying the selected subset of the encoded bits, via transmission resources. 
     Certain aspects of the present disclosure provide an apparatus for wireless communications in a network. The apparatus generally includes at least one processor configured to encode K information bits using a polar code with a mother code length, N, to generate a stream of encoded bits; to store a portion of the encoded bits in a circular buffer of size N; to reorder P blocks of the circular buffer according to row weights of a Hadamard matrix J; to interlace the encoded bits of the blocks having a same row weight; to select, based on the row weights, a subset of the encoded bits in the blocks to modify; to modify the selected subset of the encoded bits; and to transmit the encoded bits in the P blocks, subsequent to modifying the selected subset of the encoded bits, via transmission resources. The apparatus also generally includes a memory coupled with the at least one processor. 
     Certain aspects of the present disclosure provide an apparatus for wireless communications in a network. The apparatus generally includes means for encoding K information bits using a polar code with a mother code length, N, to generate a stream of encoded bits; means for storing a portion of the encoded bits in a circular buffer of size N; means for reordering P blocks of the circular buffer according to row weights of a Hadamard matrix J; means for interlacing the encoded bits of the blocks having a same row weight; means for selecting, based on the row weights, a subset of the encoded bits in the blocks to modify; means for modifying the selected subset of the encoded bits; and means for transmitting the encoded bits in the P blocks, subsequent to modifying the selected subset of the encoded bits, via transmission resources. 
     Certain aspects of the present disclosure provide a non-transitory computer-readable medium for wireless communications in a network. The non-transitory computer-readable medium generally includes instructions that, when executed by at least one processor, cause the at least one processor to encode K information bits using a polar code with a mother code length. N, to generate a stream of encoded bits; storing a portion of the encoded bits in a circular buffer of size N; to reorder P blocks of the circular buffer according to row weights of a Hadamard matrix J; to interlace the encoded bits of the blocks having a same row weight; to select, based on the row weights, a subset of the encoded bits in the blocks to modify; to modify the selected subset of the encoded bits; and to transmit the encoded bits in the P blocks, subsequent to modifying the selected subset of the encoded bits, via transmission resources. 
     Numerous other aspects are provided including methods, apparatus, systems, computer program products, and processing systems. 
     To the accomplishment of the foregoing and related ends, the one or more aspects comprise the features hereinafter fully described and particularly pointed out in the claims. The following description and the annexed drawings set forth in detail certain illustrative features of the one or more aspects. These features are indicative, however, of but a few of the various ways in which the principles of various aspects may be employed, and this description is intended to include all such aspects and their equivalents. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above-recited features of the present disclosure can be understood in detail, a more particular description, briefly summarized above, may be had by reference to aspects, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only certain typical aspects of this disclosure and are therefore not to be considered limiting of its scope, for the description may admit to other equally effective aspects. 
         FIG. 1  is a block diagram conceptually illustrating an example telecommunications system, in accordance with certain aspects of the present disclosure. 
         FIG. 2  is a block diagram illustrating an example logical architecture of a distributed RAN, in accordance with certain aspects of the present disclosure. 
         FIG. 3  is a diagram illustrating an example physical architecture of a distributed RAN, in accordance with certain aspects of the present disclosure. 
         FIG. 4  is a block diagram conceptually illustrating a design of an example BS and user equipment (UE), in accordance with certain aspects of the present disclosure. 
         FIG. 5  is a diagram showing examples for implementing a communication protocol stack, in accordance with certain aspects of the present disclosure. 
         FIG. 6  illustrates a block diagram of an example wireless device in accordance with certain aspects of the present disclosure. 
         FIG. 7  is a simplified block diagram illustrating a encoder, in accordance with certain aspects of the present disclosure. 
         FIG. 8  is a simplified block diagram illustrating a decoder, in accordance with certain aspects of the present disclosure. 
         FIG. 9  illustrates an example of a DL-centric subframe, in accordance with certain aspects of the present disclosure. 
         FIG. 10  illustrates an example of an UL-centric subframe, in accordance with certain aspects of the present disclosure. 
         FIG. 11  illustrates an example process for polar encoding and rate matching information, according to aspects of the present disclosure. 
         FIG. 12  illustrates an example circular buffer, in accordance with certain aspects of the present disclosure. 
         FIG. 13  illustrates rate-matching in a circular buffer, in accordance with certain aspects of the present disclosure. 
         FIG. 14  is a diagram illustrating a block-level interlacing technique for rate matching, according to previously known techniques. 
         FIG. 15  is a diagram illustrating a bit-level interlacing technique for rate matching, according to previously known techniques. 
         FIG. 16  is a flow diagram illustrating example operations for wireless communications, in accordance with certain aspects of the present disclosure. 
         FIG. 17  is a diagram of an exemplary algorithm for determining bits to be punctured and/or shortened for rate-matching, in accordance with certain aspects of the present disclosure. 
     
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements disclosed in one embodiment may be beneficially utilized on other embodiments without specific recitation. 
     DETAILED DESCRIPTION 
     Aspects of the present disclosure provide apparatus, methods, processing systems, and computer readable mediums for multi-slice networks, such as new radio (NR) (new radio access technology or 5G technology). 
     New radio (NR) may refer to radios configured to operate according to a new air interface (e.g., other than Orthogonal Frequency Divisional Multiple Access (OFDMA)-based air interfaces) or fixed transport layer (e.g., other than Internet Protocol (IP)). NR may include Enhanced mobile broadband (eMBB) techniques targeting wide bandwidth (e.g. 80 MHz and larger) communications, millimeter wave (mmW) techniques targeting high carrier frequency (e.g. 60 GHz) communications, massive MTC (mMTC) techniques targeting non-backward compatible MTC techniques, and mission critical targeting ultra reliable low latency communications (URLLC). These services may include latency and reliability requirements. These services may also have different transmission time intervals (TTI) to meet respective quality of service (QoS) requirements. In addition, these services may co-exist in the same subframe. 
     Aspects of the present disclosure relate to a rate-matching scheme for control channels using polar codes. Rate matching is a process whereby the number of bits to be transmitted is matched to the available bandwidth of the number of bits allowed to be transmitted. In certain instances the amount of data to be transmitted is less than the available bandwidth, in which case all the data to be transmitted (and one or more copies of the data) will be transmitted (a technique called repetition). In other instances the amount of data to be transmitted exceeds the available bandwidth, in which case a certain portion of the data to be transmitted will be omitted from the transmission (a technique called puncturing). 
     In NR, polar codes may be used to encode a stream of bits for transmission. However, in some cases, using a traditional rate matching scheme (e.g., for TBCC codes) may lead to performance loss when used with polar codes. Thus, aspects of the present disclosure propose an efficient rate-matching scheme to be used to rate-match a stream of bits encoded using a polar code. 
     Various aspects of the disclosure are described more fully hereinafter with reference to the accompanying drawings. This disclosure may, however, be embodied in many different forms and should not be construed as limited to any specific structure or function presented throughout this disclosure. Rather, these aspects are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Based on the teachings herein one skilled in the art should appreciate that the scope of the disclosure is intended to cover any aspect of the disclosure disclosed herein, whether implemented independently of or combined with any other aspect of the disclosure. For example, an apparatus may be implemented or a method may be practiced using any number of the aspects set forth herein. In addition, the scope of the disclosure is intended to cover such an apparatus or method which is practiced using other structure, functionality, or structure and functionality in addition to or other than the various aspects of the disclosure set forth herein. It should be understood that any aspect of the disclosure disclosed herein may be embodied by one or more elements of a claim. 
     The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any aspect described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects. 
     Although particular aspects are described herein, many variations and permutations of these aspects fall within the scope of the disclosure. Although some benefits and advantages of the preferred aspects are mentioned, the scope of the disclosure is not intended to be limited to particular benefits, uses, or objectives. Rather, aspects of the disclosure are intended to be broadly applicable to different wireless technologies, system configurations, networks, and transmission protocols, some of which are illustrated by way of example in the figures and in the following description of the preferred aspects. The detailed description and drawings are merely illustrative of the disclosure rather than limiting, the scope of the disclosure being defined by the appended claims and equivalents thereof. 
     The techniques described herein may be used for various wireless communication networks such as CDMA, TDMA, FDMA, OFDMA, SC-FDMA and other networks. The terms “network” and “system” are often used interchangeably. A CDMA network may implement a radio technology such as universal terrestrial radio access (UTRA), cdma2000, etc. UTRA includes wideband CDMA (WCDMA), time division synchronous CDMA (TD-SCDMA), and other variants of CDMA. cdma2000 covers IS-2000, IS-95 and IS-856 standards. A TDMA network may implement a radio technology such as global system for mobile communications (GSM). An OFDMA network may implement a radio technology such as evolved UTRA (E-UTRA), ultra mobile broadband (UMB), IEEE 802.11 (Wi-Fi). IEEE 802.16 (WiMAX), IEEE 802.20, Flash-OFDM®, etc. UTRA and E-UTRA are part of universal mobile telecommunication system (UMTS). 3GPP Long Term Evolution (LTE) and LTE-Advanced (LTE-A), in both frequency division duplex (FDD) and time division duplex (TDD), are new releases of UMTS that use E-UTRA, which employs OFDMA on the downlink and SC-FDMA on the uplink. UTRA, E-UTRA, UMTS, LTE, LTE-A and GSM are described in documents from an organization named “3rd Generation Partnership Project” (3GPP). cdma2000 and UMB are described in documents from an organization named “3rd Generation Partnership Project 2” (3GPP2). The techniques described herein may be used for the wireless networks and radio technologies mentioned above as well as other wireless networks and radio technologies, such as a 5G nextgen/NR network. 
     Example Wireless Communications System 
       FIG. 1  illustrates an example wireless network  100 , such as a new radio (NR) or 5G network, in which aspects of the present disclosure may be performed, for example, for improving device discovery in a multi-slice network. In some cases, the network  100  may be a multi-slice network, each slice defines as a composition of adequately configured network functions, network applications, and underlying cloud infrastructures that are bundled together to meet the requirement of a specific use case or business model. 
     As illustrated in  FIG. 1 , the wireless network  100  may include a number of BSs  110  and other network entities. A BS may be a station that communicates with UEs. Each BS  110  may provide communication coverage for a particular geographic area. In 3GPP, the term “cell” can refer to a coverage area of a Node B and/or a Node B subsystem serving this coverage area, depending on the context in which the term is used. In NR systems, the term “cell” and eNB, Node B, 5G NB, AP, NR BS, NR BS, BS, or TRP may be interchangeable. In some examples, a cell may not necessarily be stationary, and the geographic area of the cell may move according to the location of a mobile base station. In some examples, the base stations may be interconnected to one another and/or to one or more other base stations or network nodes (not shown) in the wireless network  100  through various types of backhaul interfaces such as a direct physical connection, a virtual network, or the like using any suitable transport network. 
     In general, any number of wireless networks may be deployed in a given geographic area. Each wireless network may support a particular radio access technology (RAT) and may operate on one or more frequencies. A RAT may also be referred to as a radio technology, an air interface, etc. A frequency may also be referred to as a carrier, a frequency channel, etc. Each frequency may support a single RAT in a given geographic area in order to avoid interference between wireless networks of different RATs. In some cases, NR or 5G RAT networks may be deployed, employing a multi-slice network architecture. 
     A BS may provide communication coverage for a macro cell, a pico cell, a femto cell, and/or other types of cell. A macro cell may cover a relatively large geographic area (e.g., several kilometers in radius) and may allow unrestricted access by UEs with service subscription. A pico cell may cover a relatively small geographic area and may allow unrestricted access by UEs with service subscription. A femto cell may cover a relatively small geographic area (e.g., a home) and may allow restricted access by UEs having association with the femto cell (e.g., UEs in a Closed Subscriber Group (CSG), UEs for users in the home, etc.). A BS for a macro cell may be referred to as a macro BS. A BS for a pico cell may be referred to as a pico BS. A BS for a femto cell may be referred to as a femto BS or a home BS. In the example shown in  FIG. 1 , the BSs  110   a ,  110   b  and  110   c  may be macro BSs for the macro cells  102   a ,  102   b  and  102   c , respectively. The BS  110   x  may be a pico BS for a pico cell  102   x . The BSs  110   y  and  110   z  may be femto BS for the femto cells  102   y  and  102   z , respectively. A BS may support one or multiple (e.g., three) cells. 
     The wireless network  100  may also include relay stations. A relay station is a station that receives a transmission of data and/or other information from an upstream station (e.g., a BS or a UE) and sends a transmission of the data and/or other information to a downstream station (e.g., a UE or a BS). A relay station may also be a UE that relays transmissions for other UEs. In the example shown in  FIG. 1 , a relay station  110   r  may communicate with the BS  110   a  and a UE  120   r  in order to facilitate communication between the BS  110   a  and the UE  120   r . A relay station may also be referred to as a relay BS, a relay, etc. 
     The wireless network  100  may be a heterogeneous network that includes BSs of different types, e.g., macro BS, pico BS, femto BS, relays, etc. These different types of BSs may have different transmit power levels, different coverage areas, and different impact on interference in the wireless network  100 . For example, macro BS may have a high transmit power level (e.g., 20 Watts) whereas pico BS, femto BS, and relays may have a lower transmit power level (e.g., 1 Watt). 
     The wireless network  100  may support synchronous or asynchronous operation. For synchronous operation, the BSs may have similar frame timing, and transmissions from different BSs may be approximately aligned in time. For asynchronous operation, the BSs may have different frame timing, and transmissions from different BSs may not be aligned in time. The techniques described herein may be used for both synchronous and asynchronous operation. 
     A network controller  130  may couple to a set of BSs and provide coordination and control for these BSs. The network controller  130  may communicate with the BSs  110  via a backhaul. The BSs  110  may also communicate with one another, e.g., directly or indirectly via wireless or wireline backhaul. 
     The UEs  120  (e.g.,  120   x ,  120   y , etc.) may be dispersed throughout the wireless network  100 , and each UE may be stationary or mobile. A UE may also be referred to as a mobile station, a terminal, an access terminal, a subscriber unit, a station, a Customer Premises Equipment (CPE), a cellular phone, a smart phone, a personal digital assistant (PDA), a wireless modem, a wireless communication device, a handheld device, a laptop computer, a cordless phone, a wireless local loop (WLL) station, a tablet, a camera, a gaming device, a netbook, a smartbook, an ultrabook, a medical device or medical equipment, a biometric sensor/device, a wearable device such as a smart watch, smart clothing, smart glasses, a smart wrist band, smart jewelry (e.g., a smart ring, a smart bracelet, etc.), an entertainment device (e.g., a music device, a video device, a satellite radio, etc.), a vehicular component or sensor, a smart meter/sensor, industrial manufacturing equipment, a global positioning system device, or any other suitable device that is configured to communicate via a wireless or wired medium. Some UEs may be considered evolved or machine-type communication (MTC) devices or evolved MTC (eMTC) devices. MTC and eMTC UEs include, for example, robots, drones, remote devices, sensors, meters, monitors, location tags, etc., that may communicate with a BS, another device (e.g., remote device), or some other entity. A wireless node may provide, for example, connectivity for or to a network (e.g., a wide area network such as Internet or a cellular network) via a wired or wireless communication link. Some UEs may be considered Internet-of-Things (IoT) devices. 
     In  FIG. 1 , a solid line with double arrows indicates desired transmissions between a UE and a serving BS, which is a BS designated to serve the UE on the downlink and/or uplink. A dashed line with double arrows indicates interfering transmissions between a UE and a BS. 
     Certain wireless networks (e.g., LTE) utilize orthogonal frequency division multiplexing (OFDM) on the downlink and single-carrier frequency division multiplexing (SC-FDM) on the uplink. OFDM and SC-FDM partition the system bandwidth into multiple (K) orthogonal subcarriers, which are also commonly referred to as tones, bins, etc. Each subcarrier may be modulated with data. In general, modulation symbols are sent in the frequency domain with OFDM and in the time domain with SC-FDM. The spacing between adjacent subcarriers may be fixed, and the total number of subcarriers (K) may be dependent on the system bandwidth. For example, the spacing of the subcarriers may be 15 kHz and the minimum resource allocation (called a ‘resource block’) may be 12 subcarriers (or 180 kHz). Consequently, the nominal FFT size may be equal to 128, 256, 512, 1024 or 2048 for system bandwidth of 1.25, 2.5, 5, 10 or 20 megahertz (MHz), respectively. The system bandwidth may also be partitioned into subbands. For example, a subband may cover 1.08 MHz (i.e.,  6  resource blocks), and there may be 1, 2, 4, 8 or 16 subbands for system bandwidth of 1.25, 2.5, 5, 10 or 20 MHz, respectively. 
     While aspects of the examples described herein may be associated with LTE technologies, aspects of the present disclosure may be applicable with other wireless communications systems, such as NR/5G. 
     NR may utilize OFDM with a CP on the uplink and downlink and include support for half-duplex operation using TDD. A single component carrier bandwidth of 100 MHz may be supported. NR resource blocks may span  12  sub-carriers with a subcarrier bandwidth of 75 kHz over a 0.1 ms duration. Each radio frame may consist of 50 subframes with a length of 10 ms. Consequently, each subframe may have a length of 0.2 ms. Each subframe may indicate a link direction (i.e., DL or UL) for data transmission and the link direction for each subframe may be dynamically switched. Each subframe may include DL/UL data as well as DL/UL control data. UL and DL subframes for NR may be as described in more detail below with reference to  FIGS. 9 and 10 . Beamforming may be supported and beam direction may be dynamically configured. MIMO transmissions with precoding may also be supported. MIMO configurations in the DL may support up to 8 transmit antennas with multi-layer DL transmissions up to 8 streams and up to 2 streams per UE. Multi-layer transmissions with up to 2 streams per UE may be supported. Aggregation of multiple cells may be supported with up to 8 serving cells. Alternatively, NR may support a different air interface, other than an OFDM-based. NR networks may include entities such CUs and/or DUs. 
     In some examples, access to the air interface may be scheduled, wherein a scheduling entity (e.g., a base station) allocates resources for communication among some or all devices and equipment within its service area or cell. Within the present disclosure, as discussed further below, the scheduling entity may be responsible for scheduling, assigning, reconfiguring, and releasing resources for one or more subordinate entities. That is, for scheduled communication, subordinate entities utilize resources allocated by the scheduling entity. Base stations are not the only entities that may function as a scheduling entity. That is, in some examples, a UE may function as a scheduling entity, scheduling resources for one or more subordinate entities (e.g., one or more other UEs). In this example, the UE is functioning as a scheduling entity, and other UEs utilize resources scheduled by the UE for wireless communication. A UE may function as a scheduling entity in a peer-to-peer (P2P) network, and/or in a mesh network. In a mesh network example, UEs may optionally communicate directly with one another in addition to communicating with the scheduling entity. 
     Thus, in a wireless communication network with a scheduled access to time-frequency resources and having a cellular configuration, a P2P configuration, and a mesh configuration, a scheduling entity and one or more subordinate entities may communicate utilizing the scheduled resources. 
     As noted above, a RAN may include a CU and DUs. A NR BS (e.g., gNB, 5G Node B, Node B, transmission reception point (TRP), access point (AP)) may correspond to one or multiple BSs. NR cells can be configured as access cell (ACells) or data only cells (DCells). For example, the RAN (e.g., a central unit or distributed unit) can configure the cells. DCells may be cells used for carrier aggregation or dual connectivity, but not used for initial access, cell selection/reselection, or handover. In some cases DCells may not transmit synchronization signals—in some case cases DCells may transmit SS. NR BSs may transmit downlink signals to UEs indicating the cell type. Based on the cell type indication, the UE may communicate with the NR BS. For example, the UE may determine NR BSs to consider for cell selection, access, handover, and/or measurement based on the indicated cell type. 
       FIG. 2  illustrates an example logical architecture of a distributed radio access network (RAN)  200 , which may be implemented in the wireless communication system illustrated in  FIG. 1 . A 5G access node  206  may include an access node controller (ANC)  202 . The ANC may be a central unit (CU) of the distributed RAN  200 . The backhaul interface to the next generation core network (NG-CN)  204  (e.g., associated with 5G control plane (5G C-plane) 212 and 5G gateway (5G-GW)  214 ) may terminate at the ANC. The backhaul interface to neighboring next generation access nodes (NG-ANs) may terminate at the ANC. The ANC may include one or more TRPs  208   a ,  808   b ,  208   c  (which may also be referred to as BSs, NR BSs, Node Bs, 5G NBs, APs, or some other term). As described above, a TRP may be used interchangeably with “cell.” 
     The TRPs  208   a ,  808   b ,  208   c  may be a DU. The TRPs  208   a ,  808   b ,  208   c  may be connected to one ANC (ANC  202 ) or more than one ANC (not illustrated). For example, for RAN sharing, radio as a service (RaaS), and service specific AND deployments, the TRP may be connected to more than one ANC. A TRP may include one or more antenna ports. The TRPs  208   a ,  808   b ,  208   c  may be configured to individually (e.g., dynamic selection) or jointly (e.g., joint transmission) serve traffic to a UE. 
     The local architecture  200  may be used to illustrate fronthaul definition. The architecture may be defined that support fronthauling solutions across different deployment types. For example, the architecture may be based on transmit network capabilities (e.g., bandwidth, latency, and/or jitter). 
     The architecture may share features and/or components with LTE. According to aspects, the next generation AN (NG-AN)  210  may support dual connectivity with NR. The NG-AN may share a common fronthaul for LTE and NR. 
     The architecture may enable cooperation between and among TRPs  208 . For example, cooperation may be preset within a TRP and/or across TRPs via the ANC  202 . According to aspects, no inter-TRP interface may be needed/present. 
     According to aspects, a dynamic configuration of split logical functions may be present within the architecture  200 . As will be described in more detail with reference to  FIG. 5 , the Radio Resource Control (RRC) layer, Packet Data Convergence Protocol (PDCP) layer, Radio Link Control (RLC) layer. Medium Access Control (MAC) layer, and a Physical (PHY) layers may be adaptably placed at the DU or CU (e.g., TRP or ANC, respectively). According to certain aspects, a BS may include a central unit (CU) (e.g., ANC  202 ) and/or one or more distributed units (e.g., one or more TRPs  208 ). 
       FIG. 3  illustrates an example physical architecture of a distributed RAN  300 , according to aspects of the present disclosure. A centralized core network unit (C-CU)  302  (e.g., associated with 5G C-plane  308  and 5G-GW  310  associated with mobile radio (MR) communication network (CN)  312 ) may host core network functions. The C-CU  302  may be centrally deployed. C-CU  302  functionality may be offloaded (e.g., to advanced wireless services (AWS)), in an effort to handle peak capacity. 
     A centralized RAN unit (C-RU)  304  (e.g., associated with MR access network (AN)  314  and 5G AN  316 ) may host one or more ANC functions. Optionally, the C-RU  304  may host core network functions locally. The C-RU  304  may have distributed deployment. The C-RU  304  may be closer to the network edge. 
     A DU  306  (e.g.,  306   a ,  306   b , or  306   c ) may host one or more TRPs (edge node (EN), an edge unit (EU), a radio head (RH), a smart radio head (SRH), or the like). The DU  306  may be located at edges of the network with radio frequency (RF) functionality. 
       FIG. 4  illustrates example components of the BS  110  and UE  120  illustrated in  FIG. 1 , which may be used to implement aspects of the present disclosure. As described above, the BS may include a TRP. One or more components of the BS  110  and UE  120  may be used to practice aspects of the present disclosure. For example, antennas  452 . Tx/Rx  222 , processors  466 ,  458 ,  464 , and/or controller/processor  480  of the UE  120  and/or antennas  434 , processors  460 ,  420 ,  438 , and/or controller/processor  440  of the BS  110  may be used to perform the operations described herein and illustrated with reference to  FIG. 16 . 
     According to aspects, for a restricted association scenario, the base station  110  may be the macro BS  110   c  in  FIG. 1 , and the UE  120  may be the UE  120   y . The base station  110  may also be a base station of some other type. The base station  110  may be equipped with antennas  434   a  through  434   t , and the UE  120  may be equipped with antennas  452   a  through  452   r.    
     At the base station  110 , a transmit processor  420  may receive data from a data source  412  and control information from a controller/processor  440 . The control information may be for the Physical Broadcast Channel (PBCH), Physical Control Format Indicator Channel (PCFICH), Physical Hybrid ARQ Indicator Channel (PHICH), Physical Downlink Control Channel (PDCCH), etc. The data may be for the Physical Downlink Shared Channel (PDSCH), etc. The processor  420  may process (e.g., encode and symbol map) the data and control information to obtain data symbols and control symbols, respectively. The processor  420  may also generate reference symbols, e.g., for the PSS, SSS, and cell-specific reference signal. A transmit (TX) multiple-input multiple-output (MIMO) processor  430  may perform spatial processing (e.g., precoding) on the data symbols, the control symbols, and/or the reference symbols, if applicable, and may provide output symbol streams to the modulators (MODs)  432   a  through  432   t . Each modulator  432  may process a respective output symbol stream (e.g., for OFDM, etc.) to obtain an output sample stream. Each modulator  432  may further process (e.g., convert to analog, amplify, filter, and upconvert) the output sample stream to obtain a downlink signal. Downlink signals from modulators  432   a  through  432   t  may be transmitted via the antennas  434   a  through  434   t , respectively. 
     At the UE  120 , the antennas  452   a  through  452   r  may receive the downlink signals from the base station  110  and may provide received signals to the demodulators (DEMODs)  454   a  through  454   r , respectively. Each demodulator  454  may condition (e.g., filter, amplify, downconvert, and digitize) a respective received signal to obtain input samples. Each demodulator  454  may further process the input samples (e.g., for OFDM, etc.) to obtain received symbols. A MIMO detector  456  may obtain received symbols from all the demodulators  454   a  through  454   r , perform MIMO detection on the received symbols if applicable, and provide detected symbols. A receive processor  458  may process (e.g., demodulate, deinterleave, and decode) the detected symbols, provide decoded data for the UE  120  to a data sink  460 , and provide decoded control information to a controller/processor  480 . 
     On the uplink, at the UE  120 , a transmit processor  464  may receive and process data (e.g., for the Physical Uplink Shared Channel (PUSCH)) from a data source  462  and control information (e.g., for the Physical Uplink Control Channel (PUCCH) from the controller/processor  480 . The transmit processor  464  may also generate reference symbols for a reference signal. The symbols from the transmit processor  464  may be precoded by a TX MIMO processor  466  if applicable, further processed by the demodulators  454   a  through  454   r  (e.g., for SC-FDM, etc.), and transmitted to the base station  110 . At the BS  110 , the uplink signals from the UE  120  may be received by the antennas  434 , processed by the modulators  432 , detected by a MIMO detector  436  if applicable, and further processed by a receive processor  438  to obtain decoded data and control information sent by the UE  120 . The receive processor  438  may provide the decoded data to a data sink  439  and the decoded control information to the controller/processor  440 . 
     The controllers/processors  440  and  480  may direct the operation at the base station  110  and the UE  120 , respectively. The processor  440  and/or other processors and modules at the base station  110  may perform or direct, e.g., the execution of the functional blocks illustrated in  FIG. 6 , and/or other processes for the techniques described herein. The processor  480  and/or other processors and modules at the UE  120  may also perform or direct, e.g., the execution of the functional blocks illustrated in  FIG. 7 , and/or other processes for the techniques described herein. The memories  442  and  482  may store data and program codes for the BS  110  and the UE  120 , respectively. A scheduler  444  may schedule UEs for data transmission on the downlink and/or uplink. 
       FIG. 5  illustrates a diagram  500  showing examples for implementing a communications protocol stack, according to aspects of the present disclosure. The illustrated communications protocol stacks may be implemented by devices operating in a 5G system (e.g., a system that supports uplink-based mobility). Diagram  500  illustrates a communications protocol stack including a Radio Resource Control (RRC) layer  510 , a Packet Data Convergence Protocol (PDCP) layer  515 , a Radio Link Control (RLC) layer  520 , a Medium Access Control (MAC) layer  525 , and a Physical (PHY) layer  530 . In various examples the layers of a protocol stack may be implemented as separate modules of software, portions of a processor or ASIC, portions of non-collocated devices connected by a communications link, or various combinations thereof. Collocated and non-collocated implementations may be used, for example, in a protocol stack for a network access device (e.g., ANs, CUs, and/or DUs) or a UE. 
     A first option  505 - a  shows a split implementation of a protocol stack, in which implementation of the protocol stack is split between a centralized network access device (e.g., an ANC  202  in  FIG. 2 ) and distributed network access device (e.g., DU  208  in  FIG. 2 ). In the first option  505 - a , an RRC layer  510  and a PDCP layer  515  may be implemented by the central unit, and an RLC layer  520 , a MAC layer  525 , and a PHY layer  530  may be implemented by the DU. In various examples the CU and the DU may be collocated or non-collocated. The first option  505 - a  may be useful in a macro cell, micro cell, or pico cell deployment. 
     A second option  505 - b  shows a unified implementation of a protocol stack, in which the protocol stack is implemented in a single network access device (e.g., access node (AN), new radio base station (NR BS), a new radio Node-B (NR NB), a network node (NN), or the like.). In the second option, the RRC layer  510 , the PDCP layer  515 , the RLC layer  520 , the MAC layer  525 , and the PHY layer  530  may each be implemented by the AN. The second option  505 - b  may be useful in a femto cell deployment. 
     Regardless of whether a network access device implements part or all of a protocol stack, at  505 - c , a UE may implement an entire protocol stack (e.g., the RRC layer  510 , the PDCP layer  515 , the RLC layer  520 , the MAC layer  525 , and the PHY layer  530 ). 
       FIG. 6  illustrates various components that may be utilized in a wireless communications device  602  that may be employed within the wireless communication system from  FIG. 1 . The wireless communications device  602  is an example of a device that may be configured to implement the various methods described herein. The wireless communications device  602  may be an BS  110  from  FIG. 1  or any of user equipments  120 . 
     The wireless communications device  602  may include a processor  604  which controls operation of the wireless communications device  602 . The processor  604  may also be referred to as a central processing unit (CPU). Memory  606 , which may include both read-only memory (ROM) and random access memory (RAM), provides instructions and data to the processor  604 . A portion of the memory  606  may also include non-volatile random access memory (NVRAM). The processor  604  typically performs logical and arithmetic operations based on program instructions stored within the memory  606 . The instructions in the memory  606  may be executable to implement the methods described herein. 
     The wireless communications device  602  may also include a housing  608  that may include a transmitter  610  and a receiver  612  to allow transmission and reception of data between the wireless device  602  and a remote location. The transmitter  610  and receiver  612  may be combined into a transceiver  614 . A single or a plurality of transmit antennas  616  may be attached to the housing  608  and electrically coupled to the transceiver  614 . The wireless communications device  602  may also include (not shown) multiple transmitters, multiple receivers, and multiple transceivers. 
     The wireless communications device  602  may also include a signal detector  618  that may be used in an effort to detect and quantify the level of signals received by the transceiver  614 . The signal detector  618  may detect such signals as total energy, energy per subcarrier per symbol, power spectral density and other signals. The wireless communications device  602  may also include a digital signal processor (DSP)  620  for use in processing signals. 
     Additionally, the wireless communications device  602  may also include an encoder  622  for use in encoding signals for transmission. The encoder may also store the encoded signals in a circular buffer (not shown) and perform rate matching on the encoded signals (e.g., by implementing operations  1600 , shown in  FIG. 16 ). Further, the wireless communication device  602  may include a decoder  624  for use in decoding received signals. 
     The various components of the wireless communications device  602  may be coupled together by a bus system  626 , which may include a power bus, a control signal bus, and a status signal bus in addition to a data bus. The processor  604  may be configured to access instructions stored in the memory  606  to perform connectionless access, in accordance with aspects of the present disclosure discussed below. 
       FIG. 7  is a simplified block diagram illustrating an encoder, in accordance with certain aspects of the present disclosure.  FIG. 7  illustrates a portion of a radio frequency (RF) modem  704  that may be configured to provide an encoded message for wireless transmission (e.g., using polar codes described below). In one example, an encoder  706  in a wireless device (e.g., BS  110  or a UE  120 ) receives a message  702  for transmission. The message  702  may contain data and/or encoded voice or other content directed to the receiving device. The encoder  706  encodes the message using a suitable modulation and coding scheme (MCS), typically selected based on a configuration defined by the BS  110  or another network entity. The encoded bitstream  708  may then be stored in circular buffer and rate-matching may be performed on the stored encoded bitstream, for example, according to aspects of the present disclosure described in more detail below. After the encoded bitstream  708  is rate-matched, the encoded bitstream  708  may then be provided to a mapper  710  that generates a sequence of TX symbols  712  that are modulated, amplified and otherwise processed by TX chain  714  to produce an RF signal  716  for transmission through antenna  718 . 
       FIG. 8  is a simplified block diagram illustrating a decoder, in accordance with certain aspects of the present disclosure.  FIG. 8  illustrates a portion of a RF modem  810  that may be configured to receive and decode a wirelessly transmitted signal including an encoded message (e.g., a message encoded using a polar code as described below). In various examples, the modem  810  receiving the signal may reside at a user equipment, at a base station, or at any other suitable apparatus or means for carrying out the described functions. An antenna  802  provides an RF signal  716  (i.e., the RF signal produced in  FIG. 7 ) to an access terminal (e.g., UE  120 ). An RX chain  806  processes and demodulates the RF signal  716  and may provide a sequence of symbols  808  to a demapper  812 , which produces a bitstream  814  representative of the encoded message. 
     A decoder  816  may then be used to decode m-bit information strings from a bitstream that has been encoded using a coding scheme (e.g., a Polar code). The decoder  816  may comprise a Viterbi decoder, an algebraic decoder, a butterfly decoder, or another suitable decoder. In one example, a Viterbi decoder employs the well-known Viterbi algorithm to find the most likely sequence of signaling states (the Viterbi path) that corresponds to a received bitstream  814 . The bitstream  814  may be decoded based on a statistical analysis of LLRs calculated for the bitstream  814 . In one example, a Viterbi decoder may compare and select the correct Viterbi path that defines a sequence of signaling states using a likelihood ratio test to generate LLRs from the bitstream  814 . Likelihood ratios can be used to statistically compare the fit of a plurality of candidate Viterbi paths using a likelihood ratio test that compares the logarithm of a likelihood ratio for each candidate Viterbi path (i.e. the LLR) to determine which path is more likely to account for the sequence of symbols that produced the bitstream  814 . The decoder  816  may then decode the bitstream  814  based on the LLRs to determine the message  818  containing data and/or encoded voice or other content transmitted from the base station (e.g., BS  110 ). 
       FIG. 9  is a diagram  900  showing an example of a DL-centric subframe, which may be used by one or more devices (e.g., BS  110  and/or UE  120 ) to communicate in the wireless network  100 . The DL-centric subframe may include a control portion  902 . The control portion  902  may exist in the initial or beginning portion of the DL-centric subframe. The control portion  902  may include various scheduling information and/or control information corresponding to various portions of the DL-centric subframe. In some configurations, the control portion  902  may be a physical DL control channel (PDCCH), as indicated in  FIG. 9 . The DL-centric subframe may also include a DL data portion  904 . The DL data portion  904  may sometimes be referred to as the payload of the DL-centric subframe. The DL data portion  904  may include the communication resources utilized to communicate DL data from the scheduling entity (e.g., UE or BS) to the subordinate entity (e.g., UE). In some configurations, the DL data portion  904  may be a physical DL shared channel (PDSCH). 
     The DL-centric subframe may also include a common UL portion  906 . The common UL portion  906  may sometimes be referred to as an UL burst, a common UL burst, and/or various other suitable terms. The common UL portion  906  may include feedback information corresponding to various other portions of the DL-centric subframe. For example, the common UL portion  906  may include feedback information corresponding to the control portion  902 . Non-limiting examples of feedback information may include an ACK signal, a NACK signal, a HARQ indicator, and/or various other suitable types of information. The common UL portion  906  may include additional or alternative information, such as information pertaining to random access channel (RACH) procedures, scheduling requests (SRs), and various other suitable types of information. As illustrated in  FIG. 9 , the end of the DL data portion  904  may be separated in time from the beginning of the common UL portion  906 . This time separation may sometimes be referred to as a gap, a guard period, a guard interval, and/or various other suitable terms. This separation provides time for the switch-over from DL communication (e.g., reception operation by the subordinate entity (e.g., UE)) to UL communication (e.g., transmission by the subordinate entity (e.g., UE)). One of ordinary skill in the art will understand that the foregoing is merely one example of a DL-centric subframe and alternative structures having similar features may exist without necessarily deviating from the aspects described herein. 
       FIG. 10  is a diagram  1000  showing an example of an UL-centric subframe, which may be used by one or more devices (e.g., BS  110  and/or UE  120 ) to communicate in the wireless network  100 . The UL-centric subframe may include a control portion  1002 . The control portion  1002  may exist in the initial or beginning portion of the UL-centric subframe. The control portion  1002  in  FIG. 10  may be similar to the control portion described above with reference to  FIG. 9 . The UL-centric subframe may also include an UL data portion  1004 . The UL data portion  1004  may sometimes be referred to as the payload of the UL-centric subframe. The UL portion may refer to the communication resources utilized to communicate UL data from the subordinate entity (e.g., UE) to the scheduling entity (e.g., UE or BS). In some configurations, the control portion  1002  may be a physical DL control channel (PDCCH). 
     As illustrated in  FIG. 10 , the end of the control portion  1002  may be separated in time from the beginning of the UL data portion  1004 . This time separation may sometimes be referred to as a gap, guard period, guard interval, and/or various other suitable terms. This separation provides time for the switch-over from DL communication (e.g., reception operation by the scheduling entity) to UL communication (e.g., transmission by the scheduling entity). The UL-centric subframe may also include a common UL portion  1006 . The common UL portion  1006  in  FIG. 10  may be similar to the common UL portion  1006  described above with reference to  FIG. 10 . The common UL portion  1006  may additional or alternative include information pertaining to channel quality indicator (CQI), sounding reference signals (SRSs), and various other suitable types of information. One of ordinary skill in the art will understand that the foregoing is merely one example of an UL-centric subframe and alternative structures having similar features may exist without necessarily deviating from the aspects described herein. 
     In some circumstances, two or more subordinate entities (e.g., UEs) may communicate with each other using sidelink signals. Real-world applications of such sidelink communications may include public safety, proximity services, UE-to-network relaying, vehicle-to-vehicle (V2V) communications, Internet of Everything (IoE) communications, IoT communications, mission-critical mesh, and/or various other suitable applications. Generally, a sidelink signal may refer to a signal communicated from one subordinate entity (e.g., UE1) to another subordinate entity (e.g., UE2) without relaying that communication through the scheduling entity (e.g., UE or BS), even though the scheduling entity may be utilized for scheduling and/or control purposes. In some examples, the sidelink signals may be communicated using a licensed spectrum (unlike wireless local area networks, which typically use an unlicensed spectrum). 
     A UE may operate in various radio resource configurations, including a configuration associated with transmitting pilots using a dedicated set of resources (e.g., a radio resource control (RRC) dedicated state, etc.) or a configuration associated with transmitting pilots using a common set of resources (e.g., an RRC common state, etc.). When operating in the RRC dedicated state, the UE may select a dedicated set of resources for transmitting a pilot signal to a network. When operating in the RRC common state, the UE may select a common set of resources for transmitting a pilot signal to the network. In either case, a pilot signal transmitted by the UE may be received by one or more network access devices, such as an AN, or a DU, or portions thereof. Each receiving network access device may be configured to receive and measure pilot signals transmitted on the common set of resources, and also receive and measure pilot signals transmitted on dedicated sets of resources allocated to the UEs for which the network access device is a member of a monitoring set of network access devices for the UE. One or more of the receiving network access devices, or a CU to which receiving network access device(s) transmit the measurements of the pilot signals, may use the measurements to identify serving cells for the UEs, or to initiate a change of serving cell for one or more of the UEs. 
     Example Polar Codes 
     As noted above, polar codes may be used to encode a stream of bits for transmission. Polar codes are the first provably capacity-achieving coding scheme with almost linear (in block length) encoding and decoding complexity. Polar codes are widely considered as a candidate for error-correction in the next-generation wireless systems. Polar codes have many desirable properties such as deterministic construction (e.g., based on a fast Hadamard transform), very low and predictable error floors, and simple successive-cancellation (SC) based decoding. 
     Polar codes are linear block codes of length N=2 n  where their generator matrix is constructed using the n th  Kronecker power of the matrix 
               G   =     (         1       0           1       1         )       ,         
denoted by G n , also referred to as a Hadamard matrix of order n. For example. Equation (1) shows the resulting generator matrix for n=3.
 
     
       
         
           
             
               
                 
                   
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     According to certain aspects, a codeword may be generated (e.g., by a BS) by using the generator matrix to encode a number of input bits (e.g., information bits). For example, given a number of input bits u=(u 0 , u 1 , . . . , u N-1 ), a resulting codeword vector x=(x 0 , x 1 , . . . , x N-1 ) may be generated by encoding the input bits using the generator matrix G. This resulting codeword may then be rate matched (e.g., using techniques described herein) and transmitted by a base station over a wireless medium and received by a UE. 
     When the received vectors are decoded (e.g., by the UE) using a Successive Cancellation (SC) decoder (e.g., decoder  816 ), every estimated bit, û 1 , has a predetermined error probability given that bits u 0   i-1  were correctly decoded, that tends towards either 0 or 0.5. Moreover, the proportion of estimated bits with a low error probability tends towards the capacity of the underlying channel. Polar codes exploit a phenomenon called channel polarization by using the most reliable K bits to transmit information, while setting, or freezing, the remaining (N−K) bits to a predetermined value such as 0, for example as explained below. 
     For very large N, polar codes transform the channel into N parallel “virtual” channels for the N information bits. If C is the capacity of the channel, then there are almost N*C channels which are completely noise free and there are N(1−C) channels which are completely noisy. The basic polar coding scheme then involves freezing (i.e., not transmitting) the information bits to be sent along the completely noisy channel and sending information only along the perfect channels. For short-to-medium N, this polarization may not be complete in the sense there could be several channels which are neither completely useless nor completely noise free (i.e., channels that are in transition). Depending on the rate of transmission, these channels in the transition are either frozen or they are used for transmission. 
     Example Unified Pattern for Puncturing and Shortening Polar Codes 
     Aspects of the present disclosure relate to a rate-matching scheme for transmission of information using polar codes. Rate matching is a process whereby the number of bits to be transmitted is matched to the available bandwidth of the number of bits allowed to be transmitted (e.g., the number of bits that can be carried in an allocation of transmission resources). In certain instances, the amount of data to be transmitted is less than the available bandwidth, in which case all the data to be transmitted (and one or more copies of the data) will be transmitted (a technique called repetition). In other instances, the amount of data to be transmitted exceeds the available bandwidth, in which case a certain portion of the data to be transmitted will be omitted from the transmission using a technique called puncturing and/or a technique called shortening. 
       FIG. 11  illustrates an example process  1100  for polar encoding and rate matching information, according to aspects of the present disclosure. Information bits  1102  may be encoded with a polar encoder  1104  to produce encoded bits at  1106 . The encoded bits may be collected (e.g., bit collection at  1108 ) into a circular buffer (e.g., a virtual circular buffer implemented in memory of a device). Some of the encoded bits may be selected for puncturing, shortening, or repetition at  1110 . The stream of encoded bits that is produced is then interleaved at  1112  and provided to a transmit chain for transmission. 
       FIG. 12  illustrates an exemplary circular buffer  1200 , according to aspects of the present disclosure. For example, in LTE, a tail biting convolutional code (TBCC) of rate ⅓ may be used for rate matching control channels and other types of channels, which is typically performed using a circular buffer. In the example, the bits of the channel may be encoded using three polynomials. Still in the example, after encoding a stream of bits, the resultant encoded bits from the three polynomials are put into the circular buffer one by one. For example, with reference to  FIG. 12 , code bits from the first polynomial are placed in the circular buffer in the range of [0, N−1]. Further, code bits from the second polynomial are placed in the circular buffer in the range of [N, 2N−1], and code bits from the third polynomial are placed in the circular buffer in the range of [2N, 3N−1]. 
     Once the coded bits are stored in the circular buffer, rate matching may be performed. For example, assuming an allocated block size of ‘M’, if M=3N, then no repetition, puncturing, or shortening (i.e., rate matching) is performed. However, if M&gt;3N, then repetition may be performed clockwise from 3N around the circular buffer. Additionally, if M&lt;3N, then puncturing and/or shortening may be performed counter-clockwise from 3N−1 around the circular buffer. 
     In NR, polar codes of size (N) may be used to encode a stream of bits for transmission. However, in some cases, using the rate matching scheme described above (e.g., for TBCC codes) may lead to performance loss when used with polar codes, for example, when the size of the circular buffer is not a power of 2 (e.g., the block length constraint of polar codes). 
     As noted above, rate-matching may involve puncturing, repeating, or shortening certain bits of the encoded bits stored in the circular buffer, for example, as illustrated in  FIG. 13 . Whether puncturing, repeating, or shortening is used may be determined by the wireless communications device based, at least in part, on the allocated coded block size, M, and the target coded block size, N. 
     For example, if M&gt;N, the wireless communications device performs rate matching by repeating M−N(M minus N) encoded bits (e.g., R bits ) based on the Polar code of size N starting from the zeroth position in the circular buffer and proceeding clockwise around the circular buffer until position R bits −1 in the circular buffer, for example, as illustrated in  FIG. 13 . According to aspects of the present disclosure, R bits  may be repeated at the end of the stream of encoded bits stored in the circular buffer. 
     In aspects of the present disclosure, if M&lt;N, then the wireless communications device may perform rate matching by either puncturing or shortening certain bits of the stored encoded bits. For example, if M&lt;N and M&gt;=βK (where β is an integer and represents the reciprocal of the effective coded rate used to encode the stream of bits), then the wireless communications device punctures N-M encoded bits (e.g., P bits ) based on the Polar code of size N, starting at the zeroth position in the circular buffer and proceeding clockwise around the circular buffer, as illustrated in  FIG. 13 . 
     According to aspects of the present disclosure, if M&lt;N and M&lt;βK, the wireless communications device shortens N-M encoded bits (e.g., P bits ) based on the Polar code N, starting from position N−1 in the circular buffer and proceeding counter-clockwise around the circular buffer, for example, as illustrated in  FIG. 13 . 
       FIG. 14  is a diagram  1400  illustrating a block-level interlacing technique for rate matching, according to previously known techniques. The polar encoder  1402  uses a polar code of size N to encode a stream of bits to generate a stream of encoded output bits  1404 . That stream of encoded output bits is divided into 16 blocks at  1406 . The blocks are then interlaced by being placed in a circular buffer in a different order at  1408 . An allocation of transmission resources of size M is allocated for transmission of the stream of bits. If M is less than N, then some of the blocks may be punctured, as shown at  1410 , or shortened, as shown at  1412 . If M is greater than N, then some of the blocks may be repeated, as shown at  1414 . This technique of rate matching has a granularity of N/16 (e.g., an entire block of size N/16 may be punctured or shortened), and this can be very large when N is very large, which may be a drawback in some cases. 
       FIG. 15  is a diagram  1500  illustrating a bit-level interlacing technique for rate matching, according to previously known techniques. The polar encoder  1502  uses a polar code of size N to encode a stream of K bits (e.g., information bits and a CRC) to generate a stream of encoded output bits  1504 . That stream of encoded output bits is divided into 4 blocks at  1506 . The bits of the middle two blocks are then interlaced by at  1508 . An allocation of transmission resources (e.g., a coded bit length) of size M is allocated for transmission of the stream of bits (at  1516 ). If M is greater than N, then some of the bits may be repeated, as shown at  1510 . If M is less than N, then some of the bits may be punctured, as shown at  1512 , or shortened, as shown at  1514 . This technique of rate matching may have decreased performance when a number of bits to puncture or shorten is greater than N/4. The bits produced are then interleaved (at  1518 ). 
     Thus, aspects of the present disclosure propose an efficient rate-matching scheme for channels using polar codes. In aspects of the present disclosure, bits are selected for modification (e.g., puncturing and/or shortening) based on row weights of a Hadamard matrix. According to aspects of the present disclosure, bits corresponding to the smallest row weights may be punctured to provide better performance than previously known techniques. In aspects of the present disclosure, bits corresponding to the largest row weights may be shortened to provide better performance than previously known techniques. 
     In the discussion below the following parameters are used:
         K: the number of information bits   M: the number of coded bits for transmission   N: mother code size
           P: the number of blocks used for rate-matching. The value of P is an integral power of 2   
               

       FIG. 16  illustrates example operations  1600  for wireless communications, for example, for rate-mating of a control channel using polar codes. Operations  1600  may be performed by a wireless communications device, such as a base station (BS  110 ), user equipment  120 , and/or wireless communications device  602 . 
     Operations  1600  begin at  1602  by encoding K information bits using a polar code with a mother code length, N, to generate a stream of encoded bits. 
     At  1604 , the wireless communications device stores a portion of the encoded bits in a circular buffer of size N. 
     At  1606 , the wireless communications device reorders P blocks of the circular buffer according to row weights of a Hadamard matrix J. 
     At  1608 , the wireless communications device interlaces the encoded bits of the blocks having a same row weight. 
     At  1610 , the wireless communications device selects, based on the row weights, a subset of the encoded bits in the blocks to modify. 
     At  1612 , the wireless communications device modifies the selected subset of the encoded bits. 
     At  1614 , the wireless communications device transmits the encoded bits in the P blocks, subsequent to modifying the selected subset of the encoded bits, via transmission resources. 
       FIG. 17  is a diagram  1700  of an exemplary algorithm for determining bits to be punctured and/or shortened for rate-matching, in accordance with certain aspects of the present disclosure. The encoded (e.g., polar encoded) bits are represented at  1702 . At  1704 , a wireless communications device divides the mother code length N bits into P blocks, each containing N/P bits. i.e., block1 has bits 0 through (N/P)−1, block2 has bits N/P through (N/P)*2−1, etc.  FIG. 17  is illustrated using a typical value of P of 8, but other values of P that are integral powers of 2 may be used. At  1706 , the wireless communications device reorders the blocks according to the row weights of a Hadamard matrix. The Hadamard matrix J may be constructed with order of log 2 (P). The row weights of J may be calculated by adding the values in each row of J. The Hadamard matrix of order 3 is reproduced below, with a table showing the row weights. 
     
       
         
           
             
               [ 
               
                 
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     0 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     0 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     1 
                   
                   
                     0 
                   
                   
                     1 
                   
                   
                     0 
                   
                 
                 
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                   
                     1 
                   
                 
               
               ] 
             
               
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Row 
                 Row weight 
               
               
                   
                   
               
             
            
               
                   
                 1 
                 1 
               
               
                   
                 2 
                 2 
               
               
                   
                 3 
                 2 
               
               
                   
                 4 
                 4 
               
               
                   
                 5 
                 2 
               
               
                   
                 6 
                 4 
               
               
                   
                 7 
                 4 
               
               
                   
                 8 
                 8 
               
               
                   
                   
               
            
           
         
       
     
     Thus, as shown at  1706 , sorting the blocks according to row weights of the Hadamard matrix J results in the fifth block being placed before the fourth block. When sorting the blocks, the blocks remain in the natural order for blocks corresponding to rows with a same row weight. 
     At  1708 , the wireless communications device may perform a bit-level interlace of the bits, after the block reordering at  1706 . The interlacing interlaces bits of blocks having a same row weight. Thus, in  FIG. 17 , the bits from blocks  2 ,  3 , and  5  are interlaced, and the bits from blocks  4 ,  6 , and  7  are interlaced. 
     At  1710 , if bits are to be punctured, the bits selected for puncturing are the 1st N−M bits from  1708 . If bits are to be shortened, the bits selected for shortening are the end N−M bits from  1708 . The bits selected for shortening are labeled at  1712 . 
     According to aspects of the present disclosure, the modification operation in block  1612  of  FIG. 16  may be a repetition operation. The wireless communications device may select the first N−M bits in the blocks for repetition. 
     As mentioned above, other values of P may be used with the disclosed techniques. According to aspects of the present disclosure, row weights of a Hadamard matrix of order 4, for P=16, are shown in the table below. 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Row 
                 Row weight 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 1 
                 1 
               
               
                   
                 2 
                 2 
               
               
                   
                 3 
                 2 
               
               
                   
                 4 
                 4 
               
               
                   
                 5 
                 2 
               
               
                   
                 6 
                 4 
               
               
                   
                 7 
                 4 
               
               
                   
                 8 
                 8 
               
               
                   
                 9 
                 2 
               
               
                   
                 10 
                 4 
               
               
                   
                 11 
                 4 
               
               
                   
                 12 
                 8 
               
               
                   
                 13 
                 4 
               
               
                   
                 14 
                 8 
               
               
                   
                 15 
                 8 
               
               
                   
                 16 
                 16 
               
               
                   
                   
               
            
           
         
       
     
     As mentioned above, other values of P may be used with the disclosed techniques. According to aspects of the present disclosure, row weights of a Hadamard matrix of order 5, for P=32, are shown in the table below. 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Row 
                 Row weight 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 1 
                 1 
               
               
                   
                 2 
                 2 
               
               
                   
                 3 
                 2 
               
               
                   
                 4 
                 4 
               
               
                   
                 5 
                 2 
               
               
                   
                 6 
                 4 
               
               
                   
                 7 
                 4 
               
               
                   
                 8 
                 8 
               
               
                   
                 9 
                 2 
               
               
                   
                 10 
                 4 
               
               
                   
                 11 
                 4 
               
               
                   
                 12 
                 8 
               
               
                   
                 13 
                 4 
               
               
                   
                 14 
                 8 
               
               
                   
                 15 
                 8 
               
               
                   
                 16 
                 16 
               
               
                   
                 17 
                 2 
               
               
                   
                 18 
                 4 
               
               
                   
                 19 
                 4 
               
               
                   
                 20 
                 8 
               
               
                   
                 21 
                 4 
               
               
                   
                 22 
                 8 
               
               
                   
                 23 
                 8 
               
               
                   
                 24 
                 16 
               
               
                   
                 25 
                 4 
               
               
                   
                 26 
                 8 
               
               
                   
                 27 
                 8 
               
               
                   
                 28 
                 16 
               
               
                   
                 29 
                 8 
               
               
                   
                 30 
                 16 
               
               
                   
                 31 
                 16 
               
               
                   
                 32 
                 32 
               
               
                   
                   
               
            
           
         
       
     
     The methods disclosed herein comprise one or more steps or actions for achieving the described method. The method steps and/or actions may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of steps or actions is specified, the order and/or use of specific steps and/or actions may be modified without departing from the scope of the claims. 
     According to aspects of the present disclosure, the techniques described above provide an efficient rate-matching algorithm(s) with a good trade-off between decoding complexity and decoding performance. For example, by using the techniques described above to puncture, repeat, or shorten encoded bits before transmission, decoding complexity and latency at a receiving device may be reduced because these bits do not need to be decoded, which, in turn, saves processing resources and power at the receiving device. 
     As used herein, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover a, b, c, a-b, a-c, b-c, and a-b-c, as well as any combination with multiples of the same element (e.g., a-a, a-a-a, a-a-b, a-a-c, a-b-b, a-c-c, b-b, b-b-b, b-b-c, c-c, and c-c-c or any other ordering of a, b, and c). 
     As used herein, the term “determining” encompasses a wide variety of actions. For example, “determining” may include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Also, “determining” may include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Also, “determining” may include resolving, selecting, choosing, establishing and the like. 
     In some cases, rather than actually transmitting a frame, a device may have an interface to output a frame for transmission. For example, a processor may output a frame, via a bus interface, to an RF front end for transmission. Similarly, rather than actually receiving a frame, a device may have an interface to obtain a frame received from another device. For example, a processor may obtain (or receive) a frame, via a bus interface, from an RF front end for transmission. 
     The various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and/or software component(s) and/or module(s), including, but not limited to a circuit, an application specific integrated circuit (ASIC), or processor. Generally, where there are operations illustrated in figures, those operations may have corresponding counterpart means-plus-function components with similar numbering. 
     For example, means for transmitting, means for receiving, means for determining, means for performing (e.g., rate-matching), means for encoding, means for, puncturing, means for repeating, means for shortening, and/or means for generating may comprise one or more processors or antennas at the BS  110  or UE  120 , such as the transmit processor  220 , controller/processor  240 , receive processor  238 , or antennas  234  at the BS  110  and/or the transmit processor  264 , controller/processor  280 , receive processor  258 , or antennas  252  at the UE  120 . 
     The various illustrative logical blocks, modules and circuits described in connection with the present disclosure may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device (PLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any commercially available processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. 
     If implemented in hardware, an example hardware configuration may comprise a processing system in a wireless node. The processing system may be implemented with a bus architecture. The bus may include any number of interconnecting buses and bridges depending on the specific application of the processing system and the overall design constraints. The bus may link together various circuits including a processor, machine-readable media, and a bus interface. The bus interface may be used to connect a network adapter, among other things, to the processing system via the bus. The network adapter may be used to implement the signal processing functions of the PHY layer. In the case of a user terminal  120  (see  FIG. 1 ), a user interface (e.g., keypad, display, mouse, joystick, etc.) may also be connected to the bus. The bus may also link various other circuits such as timing sources, peripherals, voltage regulators, power management circuits, and the like, which are well known in the art, and therefore, will not be described any further. The processor may be implemented with one or more general-purpose and/or special-purpose processors. Examples include microprocessors, microcontrollers, DSP processors, and other circuitry that can execute software. Those skilled in the art will recognize how best to implement the described functionality for the processing system depending on the particular application and the overall design constraints imposed on the overall system. 
     If implemented in software, the functions may be stored or transmitted over as one or more instructions or code on a computer-readable medium. Software shall be construed broadly to mean instructions, data, or any combination thereof, whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise. Computer-readable media include both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. The processor may be responsible for managing the bus and general processing, including the execution of software modules stored on the machine-readable storage media. A computer-readable storage medium may be coupled to a processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. By way of example, the machine-readable media may include a transmission line, a carrier wave modulated by data, and/or a computer readable storage medium with instructions stored thereon separate from the wireless node, all of which may be accessed by the processor through the bus interface. Alternatively, or in addition, the machine-readable media, or any portion thereof, may be integrated into the processor, such as the case may be with cache and/or general register files. Examples of machine-readable storage media may include, by way of example, RAM (Random Access Memory), flash memory, ROM (Read Only Memory), PROM (Programmable Read-Only Memory), EPROM (Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory), registers, magnetic disks, optical disks, hard drives, or any other suitable storage medium, or any combination thereof. The machine-readable media may be embodied in a computer-program product. 
     A software module may comprise a single instruction, or many instructions, and may be distributed over several different code segments, among different programs, and across multiple storage media. The computer-readable media may comprise a number of software modules. The software modules include instructions that, when executed by an apparatus such as a processor, cause the processing system to perform various functions. The software modules may include a transmission module and a receiving module. Each software module may reside in a single storage device or be distributed across multiple storage devices. By way of example, a software module may be loaded into RAM from a hard drive when a triggering event occurs. During execution of the software module, the processor may load some of the instructions into cache to increase access speed. One or more cache lines may then be loaded into a general register file for execution by the processor. When referring to the functionality of a software module below, it will be understood that such functionality is implemented by the processor when executing instructions from that software module. 
     Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared (IR), radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray® disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Thus, in some aspects computer-readable media may comprise non-transitory computer-readable media (e.g., tangible media). In addition, for other aspects computer-readable media may comprise transitory computer-readable media (e.g., a signal). Combinations of the above should also be included within the scope of computer-readable media. 
     Further, it should be appreciated that modules and/or other appropriate means for performing the methods and techniques described herein can be downloaded and/or otherwise obtained by a user terminal and/or base station as applicable. For example, such a device can be coupled to a server to facilitate the transfer of means for performing the methods described herein. Alternatively, various methods described herein can be provided via storage means (e.g., RAM, ROM, a physical storage medium such as a compact disc (CD) or floppy disk, etc.), such that a user terminal and/or base station can obtain the various methods upon coupling or providing the storage means to the device. Moreover, any other suitable technique for providing the methods and techniques described herein to a device can be utilized. 
     It is to be understood that the claims are not limited to the precise configuration and components illustrated above. Various modifications, changes and variations may be made in the arrangement, operation and details of the methods and apparatus described above without departing from the scope of the claims.