Abstract: Methods for verifying rebuilt data in a dispersed storage network (DSN). In various examples, a storage unit of the DSN receives a rebuilt encoded data slice of a set of encoded data slices and a set of corresponding integrity values. An integrity function is performed on the set of integrity values to calculate an integrity value of the set of integrity values, which is then compared to a locally stored value. If the values match, the set of integrity values is validated. Another integrity function is performed on the rebuilt encoded data slice to produce a calculated integrity value of the received encoded data slice. The encoded data slice is validated and stored when the calculated integrity value compares favorably to the corresponding value of the validated set of integrity values. Proof of authenticity information from other storage units may be employed to further validate the set of integrity values.

Abstract: Features of the present disclosure implement a low complexity rate-matching design for polar codes that supports full rate-matching granularity, in some cases without good bit re-estimation after puncturing. In particular, features of the present disclosure provide techniques for adjusting the information bits allocation based on the number of punctured bits (P) for block puncturing polar codes. Particularly, features of the present disclosure determine the number of information bits for each sector based on a capacity formula after the puncturing.

Abstract: A transceiver, including a modulation circuit configured to modulate a first digital word into a first modulated time signal; and a demodulation circuit configured to demodulate a second modulated time signal into a second digital word, wherein the modulation and demodulation circuits are operable without an external clock source, and inseparably share one or more same circuit elements. Also, a tunable delay line may be configured to set a time rate of the modulation, wherein the modulation circuit and the demodulation circuit inseparably share the tunable delay line.

Abstract: A technology is provided for delivering a data object to device. Data delivery instructions to distribute a data object to a device may be received at a delivery service and include a storage location of the data object, a messaging topic, and a size of data receivable by the device. The data object is then divided into blocks corresponding to the size of data receivable by the device. A messaging topic is identified to which the device is subscribed via a messaging service. The blocks are sent to the device using the messaging topic and a network protocol installed on the device.

Abstract: In encoding, a frequency-domain sample sequence derived from an acoustic signal is divided by a weighted envelope and is then divided by a gain, the result obtained is quantized, and each sample is variable-length encoded. The error between the sample before quantization and the sample after quantization is quantized with information saved in this variable-length encoding. This quantization is performed under a rule that specifies, according to the number of saved bits, samples whose errors are to be quantized. In decoding, variable-length codes in an input sequence of codes are decoded to obtain a frequency-domain sample sequence; an error signal is further decoded under a rule that depends on the number of bits of the variable-length codes; and from the obtained sample sequence, the original sample sequence is obtained according to supplementary information.

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

Abstract: An apparatus for receiving broadcast signals includes a receiver configured to receive a broadcast signal; a time deinterleaver configured to time deinterleave a Time Interleaving (TI) block in the broadcast signal, the TI block including one or more Forward Error Correction (FEC) blocks, the broadcast signal includes information for a maximum number related to the one or more FEC blocks and information for a number of the one or more FEC blocks; a decoder configured to decode the broadcast signal, the decoded broadcast signal including a signal frame including: one or more components included in a content of a service and content information describing the content, the content information including component information including role information for at least one of an audio component, a video component or a closed caption component of the one or more components, the role information for the video component including an alternative view; and a display configured to display information related to the content

Abstract: Methods and devices are described for determining reliabilities of bit positions in a bit sequence for information bit allocation using polar codes. The reliabilities are calculated using a weighted summation over a binary expansion of each bit position, wherein the summation is weighted by an exponential factor that is selected based at least in part on the coding rate of the polar code. Information bits and frozen bits are allocated to the bit positions based on the determined reliabilities, and data is polar encoded as the information bits. The polar encoded data is then transmitted to a remote device.

Abstract: A transmitting apparatus is disclosed. The transmitting apparatus includes an encoder to perform channel encoding with respect to bits and generate a codeword, an interleaver to interleave the codeword, and a modulator to map the interleaved codeword onto a non-uniform constellation according to a modulation scheme, and the constellation may include constellation points defined based on various tables according to the modulation scheme.

Abstract: An encoding method and apparatus are provided. The method by a transmit end includes: performing check encoding on to-be-encoded information to obtain a check encoding codeword that comprises K information bits and J check bits; performing an interleaving operation on the check encoding codeword with an interleaving sequence including J subsequences, and an ith subsequence includes a position index of an element 1 in an intermediate result vector Ti and a value of (K+i), where 1?i?J, i is an integer, Ti=(˜M)&(Vi), M=M|(Vi), M is a masked vector, Vi is a column vector of a checking part matrix P, P is a submatrix of a generator matrix G for check encoding, ˜ represents a bit-by-bit NOT operation, & represents a bit-by-bit AND operation, and | represents a bit-by-bit OR operation; and performing polar encoding on a check encoding codeword obtained after the interleaving operation.

Abstract: A transmitting apparatus is disclosed. The transmitting apparatus includes an encoder to perform channel encoding with respect to bits and generate a codeword, an interleaver to interleave the codeword, and a modulator to map the interleaved codeword onto a non-uniform constellation according to a modulation scheme, and the constellation may include constellation points defined based on various tables according to the modulation scheme.

Abstract: A method for encoding a quasi-cyclic low-density parity-check (LDPC) code according to an embodiment of the present invention may comprise the steps of: generating a multi-edge LDPC code matrix including a high rate code matrix and a single parity check code matrix; and encoding a signal by using the multi-edge LDPC code matrix, wherein the single parity check code matrix includes a first matrix having a non-row-orthogonal structure matrix and a second matrix having a pure row-orthogonal structure, which are concatenated.

Abstract: A transmitting device may identify a set of bit locations of a polar code for encoding an input vector based at least in part on a reliability order of the bit locations, where the input vector includes a set of payload bits. The transmitting device may map bits of the input vector to respective bit locations of the identified set of bit locations and may apply a masking operation to a subset of bits of the input vector that is mapped to a most reliable subset of the set of bit locations. The transmitting device may perform an encoding operation according to the mapped input vector to generate a codeword for transmission. A receiving device may perform complementary operations to obtain the payload bits of the input vector. Based on the described techniques, a false alarm rate for the receiving device may be suppressed.

Abstract: A parity puncturing apparatus and method for variable length signaling information are disclosed. A parity puncturing apparatus according to an embodiment of the present invention includes memory configured to provide a parity bit string for parity puncturing for the parity bits of an LDPC codeword whose length is 16200 and whose code rate is 3/15, and a processor configured to puncture a number of bits corresponding to a final puncturing size from the rear side of the parity bit string.

Abstract: The present disclosure relates to polar encoding methods and apparatus. One example method includes obtaining locations of information bits and frozen bits based on a reliability order of polar channels, where reliability of a polar channel corresponding to the information bits is higher than reliability of a polar channel corresponding to the frozen bits, performing cyclic redundancy check (CRC) encoding on an information block, mapping bits obtained after the CRC encoding to the information bits, determining at least one bit of the frozen bits as a check frozen bit, where a value of the check frozen bit is determined based on values of P information bits that are in information bits prior to the check frozen bit and that meet a preset condition, and performing polar encoding on the information bits, the check frozen bit, and a frozen bit other than the check frozen bit.

Abstract: In accordance with aspects of the disclosure, systems and methods are provided for normalizing data representing entities and relationships linking the entities including defining one or more graph rules describing searchable characteristics for the data representing the entities and relationships linking the entities, applying the one or more graph rules to the data representing the entities and the relationships linking the entities, identifying one or more matching instances between the one or more graph rules and the data representing the entities and the relationships linking the entities, and performing one or more actions to update the one or more matching instances between the one or more graph rules and the data representing the entities and the relationships linking the entities.

Abstract: LDPC coding is executed using a check matrix of an LDPC code whose code length is 736 bits and whose code rate is 1/4, and modulation is executed using a repetition unit that has an LDPC code obtained by the LDPC coding, repeatedly arranged therein. The LDPC code includes information bits and parity bits, the check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the parity matrix portion has a stepwise structure, the information matrix portion is indicated by a check matrix initial value table, and the check matrix initial value table is a predetermined table indicating positions of elements of “1” of the information matrix portion for each eight columns. This technique is applicable to, for example, information transmission using the LDPC code.

Abstract: The embodiments of the application provides a polar code rate matching method and apparatus. The method includes: obtaining, by a communications device, to-be-encoded information; determining, by the communications device, a to-be-used rate matching manner based on the code rate, a code rate threshold, a target code length, and a target code length threshold, where the rate matching manner is a puncturing manner or a shortening manner; and rate matching, by the communications device based on the determined rate matching manner, a polar code of the to-be-encoded information.

Abstract: A wireless transmit receive unit (WTRU) may receive a Physical Downlink Control Channel (PDCCH) transmission and perform early termination on the PDCCH transmission. Transmissions that are not intended for the WTRU may be terminated. The WTRU may perform a first decode of the PDCCH transmission based on a first scrambling sequence. The first scrambling sequence may be generated using a Gold sequence, which may be initialized based on a WTRU identifier. If the first decode is not successful, the WTRU may determine that the PDCCH transmission is not intended for the WTRU. The WTRU may perform an assistance bit added (ABA) polar decode of the PDCCH transmission based on a second scrambling sequence (e.g., a cell radio network temporary ID (C-RNTI)). The WTRU may perform a CRC on the output of the ABA polar decode to obtain downlink control information (DCI).

Abstract: A memory device includes a memory component that stores data and a processor. The processor may receive requests from a requesting component to perform a plurality of data operations, generate a plurality of packets associated with the plurality of data operations, and continuously transmit each of the plurality of packets until each of the plurality of packets are transmitted. Each of the plurality of packets after the first packet of the plurality of packets is transmitted on a subsequent clock cycle immediately after a previous packet is transmitted.

Abstract: This application provides an encoding method and apparatus in wireless communications between a network device and a terminal. The method includes: performing CRC encoding on A to-be-encoded information bits based on a CRC polynomial, to obtain a first bit sequence, where the first bit sequence includes L CRC bits and A information bits, L=6; and performing polar encoding on the first bit sequence. Based on an improved CRC polynomial, encoding satisfying an FAR requirement is implemented.

Abstract: A broadcast signal receiver is disclosed. A broadcast signal receiver according to an embodiment of the present invention comprises a synchronization & demodulation module performing signal detection and OFDM demodulation on a received broadcast signal; a frame parsing & deinterleaving module performing parsing and deinterleaving of a signal frame of the broadcast signal; a demapping & decoding module performing conversion of data of at least one Physical Layer Pipe (PLP) of the broadcast signal into the bit domain and FEC decoding of the converted PLP data; and an output processing module outputting a data stream by receiving the at least one PLP data.

Abstract: A low density parity check (LDPC) encoder, an LDPC decoder, and an LDPC encoding method are disclosed. The LDPC encoder includes first memory, second memory, and a processor. The first memory stores an LDPC codeword having a length of 64800 and a code rate of 7/15. The second memory is initialized to 0. The processor generates the LDPC codeword corresponding to information bits by performing accumulation with respect to the second memory using a sequence corresponding to a parity check matrix (PCM).

Abstract: The embodiments of the application provides a polar code rate matching method and apparatus. The method includes: obtaining, by a communications device, to-be-encoded information; determining, by the communications device, a to-be-used rate matching manner based on the code rate, a code rate threshold, a target code length, and a target code length threshold, where the rate matching manner is a puncturing manner or a shortening manner; and rate matching, by the communications device based on the determined rate matching manner, a polar code of the to-be-encoded information.

Abstract: A system has a plurality of memory devices arranged in a fly-by topology, each having on-die termination (ODT) circuitry for connecting to an address and control (RQ) bus. The ODT circuitry of each memory device includes a set of one or more control registers for controlling on-die termination of one or more signal lines of the RQ bus. A memory controller sends register values, for storage in a plurality of registers of a respective memory device. The register values include register values that represent one or more impedance values of on-die termination (ODT) impedances to apply to the respective inputs of the respective memory device that receive the CA signals, and one or more register values to selectively enable application of a chip select ODT impedance to the chip select input of the respective memory device.

Abstract: Disclosed in an embodiment of the present invention are a polar code encoding method and device, the method comprising: utilizing a common information bit set to represent each of m polar code blocks, the polar codes in each polar code block having the same code length and different code rates, and m being greater than or equal to 2; according to the common information bit set corresponding to the polar code block, acquiring an information bit set corresponding to each polar code in the polar code block; and according to the information bit set corresponding to each polar code in the polar code block, conducting polar code encoding on information to be encoded, thus reducing polar code representation overhead, and solving the problem in the prior art of excessively high polar code representation overhead.

Abstract: Methods, systems, and devices for wireless communications are described. Efficient low-density parity-check (LDPC) scheduling of layered decoding may include receiving a message encoded as an LDPC code that includes a number of check nodes and a number of bit nodes, applying a first number of decoding iterations to decoding the message, applying a second number of decoding iterations to decoding the message after the first number of decoding iterations are applied, and decoding the message through completion of both the first number of decoding iterations and the second number of decoding iterations. In some cases, only a portion of the number of check nodes is decoded during each of the first number of decoding iterations and all of the number of check nodes are decoded during each of the second number of decoding iterations.

Abstract: Certain aspects of the present disclosure provide techniques and apparatus for low density parity check (LDPC) interleaving with improved error floor performance. A method for wireless communications that may be provided by a transmitting device is provided. The method generally includes encoding one or more information bits using a LDPC code to produce a coded bit sequence comprising systematic bits and parity bits. The transmitting device stores the coded bit sequence in a circular buffer. The transmitting device performs rate matching on the coded bit sequence. The rate matching includes interleaving the parity bits with a partial interleaver and interleaving the systematic bits and interleaved parity bits with a systematic bit priority mapping (SBPM) interleaver. The transmitting device maps the SBPM interleaved bit sequence to constellation points according to a modulation scheme and transmits the modulated bit sequence.

Abstract: Data to be transmitted over a channel from a transmitter to a receiver is encoded to obtain a codeword. The codeword is defined by a plurality of variable nodes associated with a plurality of the check nodes of a bipartite graph representing the code. The codeword is transmitted over the channel such that certain variable nodes are transmitted prior to other variable nodes. The certain variable nodes are associated with a subset of the check nodes of the bipartite graph and define a subcodeword known at the receiver. At the receiver, a decodability of the transmitted codeword is estimated using the subcodeword prior to receiving all variable nodes of the codeword.

Abstract: Systems, methods, and computer-readable media are disclosed for determining and applying a timeout for streaming video. Processing circuitry of a device may request video fragments to be downloaded and played, and if a requested fragment is not downloaded entirely before expiration of a timeout, the device may adjust the timeout to allow the download to complete. A timeout may be set based on available bandwidth and a size of a fragment requested for download, and the timeout may be extended based on network and/or device conditions.

Abstract: A transmitting apparatus and a receiving apparatus are provided. The transmitting apparatus includes an encoder configured to generate a low density parity check (LDPC) codeword by performing LDPC encoding, an interleaver configured to interleave the LDPC codeword, and a modulator configured to modulate the interleaved LDPC codeword according to a modulation method to generate a modulation symbol. The interleaver performs interleaving by dividing the LDPC codeword into a plurality of groups, rearranging an order of the plurality of groups in group units, and dividing the plurality of rearranged groups based on a modulation order according to the modulation method.

Abstract: A method by which a base station transmits a physical broadcast channel (PBCH) can comprise the steps of: generating the same encoded data bit for each of two symbols of a predetermined subframe for PBCH transmission by using a polar code; and transmitting the generated same encoded data bit from each of the two symbols of the predetermined subframe through the PBCH.

Abstract: A transmitter is provided. The transmitter includes: a Low Density Parity Check (LDPC) encoder configured to encode input bits to generate parity bits; a parity permutator configured to perform parity permutation by interleaving the parity bits and group-wise interleaving a plurality of bit groups including the interleaved parity bits; and a puncturer configured to puncture some of the parity bits in the group-wise interleaved bit groups, wherein the parity permutator group-wise interleaves the bit groups such that some of the bit groups are positioned at predetermined positions, respectively, and a remainder of the bit groups are positioned without an order within the group-wise interleaved bit groups.

Abstract: An apparatus and method for generating a broadcast signal frame corresponding to a time interleaver supporting a plurality of operation modes are disclosed. An apparatus for generating broadcast signal frame according to an embodiment of the present invention includes a combiner configured to generate a multiplexed signal by combining a core layer signal and an enhanced layer signal; a power normalizer configured to reduce the power of the multiplexed signal to a power level corresponding to the core layer signal; a time interleaver configured to generate a time-interleaved signal by performing interleaving that is applied to both the core layer signal and the enhanced layer signal; and a frame builder configured to generate a broadcast signal frame including a preamble for signaling time interleaver information corresponding to the time interleaver, the preamble includes a field indicating a start position of a first complete FEC block corresponding to each of physical layer pipes.

Abstract: The present invention relates to a wireless communication system. More specifically, the present invention relates to a method and a device for indicating a ciphering indication for a sidelink radio bearer in a D2D communication system, the method comprising: receiving a PDCP SDU when the UE is configured to communicate with one or more other UEs directly; deciding whether to apply ciphering or not for the received PDCP SDU; generating a PDCP data PDU including the received PDCP SDU and a PDCP PDU header including one or more fields for ciphering parameters; and transmitting the PDCP data PDU to the one or more other UEs over PC5 interface, wherein at least one of the one or more fields for ciphering parameters is set to a fixed value when the ciphering is not applied for the received PDCP SDU.

Abstract: A communication apparatus includes: a PPDU generation circuit that sets a time equal to or greater than a total of a non-legacy STF, a non-legacy CEF, multiple non-legacy header fields, and multiple data fields as a nominal data field length, computes a nominal data octet size based on the nominal data field length, stores the nominal data octet size in a legacy header, and sets an Additional PPDU field in the legacy header to 0; a signal processing circuit that forms an A-PPDU in the nominal data field length or less; and a transmission circuit that transmits the A-PPDU.

Abstract: The present technology relates to a transmission method and a reception device capable of ensuring good communication quality in data transmission by using an LDPC code. In group-wise interleaving, an LDPC code with a code length N of 69120 bits is interleaved in units of bit groups of 360 bits. In group-wise deinterleaving, an arrangement of the LDPC code after the group-wise interleaving is returned to an original arrangement. The present technology can be applied, for example, to the case of performing data transmission by using an LDPC code or the like.

Abstract: Systems and methods related to data encoders that can perform error detection or correction. The encoders and decoders may minimize the addition of errors due to aliasing in error correction codes by implementing operators associated with reduced aliasing parity generating or reduced aliasing error checking matrices.

Abstract: A transmitter for transmitting an encoded codeword over a communication channel includes a source to accept source data, an irregular polar encoder operated by a processor to encode the source data with at least one polar code to produce the encoded codeword, a modulator to modulate the encoded codeword, and a front end to transmit the modulated and encoded codeword over the communication channel. The polar code is specified by a set of regular parameters including one or combination of parameters defining a number of data bits in the codeword, a parameter defining a data index set specifying locations of frozen bits in the encoded codeword, and a parameter defining a number of parity bits in the encoded codeword.

Abstract: A storage device includes a nonvolatile memory including a plurality of physical blocks, a communication interface connectable to a host, and a controller. The controller is configured to generate metadata of host data, which include user data and metadata of the user data, and write, in a physical block of the nonvolatile memory, the metadata of the host data, the metadata of the user data, and the user data continuously in this order, when the host data are received through the communication interface in association with a write command.

Abstract: An encoding apparatus includes a processor a non-transitory computer-readable storage medium storing a program for encoding data into a codeword. The program includes instructions to encode the data x using a code that is a product of a matrix generated using the Kronecker product of the Q with itself and factors generated according to frozen bit indices of the code and a constraint matrix generated according to a precoding matrix.

Abstract: An infrastructure equipment that transmits signals representing data via a wireless access interface to a communications device and receives signals representing data via the wireless access interface from the communications device in accordance with a time divided structure in which the wireless access interface is divided into a plurality of repeating time units. The infrastructure equipment provides, in each of a first plurality of the time units, one of a plurality of control channels each configured to schedule one of a plurality of data channels, and provides, in each of a second plurality of time units of the signal transmitted to the communications device, one of the plurality of data channels, the plurality of data channels being formed of one or more bundles of data channels, wherein the infrastructure equipment transmits a bundle status indicator in one or more of the plurality of control channels.

Abstract: Embodiments of the present invention include an apparatus that receives date from multiple lanes, which are then aligned and synchronized for transcoding and encoding.

Abstract: A zero padding apparatus and method for variable length signaling information are disclosed. A zero padding apparatus according to an embodiment of the present invention includes a processor configured to generate a LDPC information bit string by deciding a number of groups whose all bits are to be filled with 0 using a difference between a length of the LDPC information bit string and a length of a BCH-encoded bit string, selecting the groups using a shortening pattern order to fill all the bits of the groups with 0, and filling at least a part of remaining groups, which are not filled with 0, with the BCH-encoded bit string; and memory configured to provide the LDPC information bit string to an LDPC encoder.

Abstract: Disclosed are a polar code encoding method and device and a polar code decoding method and device. The polar code encoding method comprises: reading a known first sequence; and for an information sequence to be encoded, combining the information sequence with the first sequence, and performing polar code encoding on the combined sequence. In the polar code encoding method provided by embodiments of the present disclosure, a known first sequence is read and polar code encoding is performed on an information sequence and the first sequence. Thus, polar code encoding on the information sequence to be encoded is implemented, and a new polar code encoding solution is provided.

Abstract: The transmission apparatus maps a plurality of code blocks obtained from data to a time-frequency resource, and transmits the plurality of code blocks therefrom. The time-frequency resource comprises L number of time symbols in the time domain, where L is an integer greater than 1. Each of the L number of time symbols comprises one or more different code blocks from among the plurality of code blocks. The plurality of code blocks is mapped in the time-frequency resource so that one complete code block is one time symbol.

Abstract: A rate matching method for a polar code is provided, to improve performance. The method includes: encoding, based on an N*N encoding matrix of a polar code, a sequence including N first bits, to generate a mother code including N second bits, where the N first bits are in a one-to-one correspondence with N rows in the encoding matrix in sequence, and the N second bits are in a one-to-one correspondence with N columns in the encoding matrix in sequence; determining N?M to-be-punctured second bits from the N second bits, where at least one first bit in N?M first bits participating in encoding of the N?M second bits belongs to the first M first bits in the N first bits, and the N?M first bits are fixed bits; and puncturing the N?M second bits, to obtain a target polar code including M second bits.

Abstract: A method and an apparatus for transmitting broadcast signals thereof are disclosed. The apparatus for transmitting broadcast signals, the apparatus comprises an encoder to encode service data corresponding to each of a plurality of physical paths, a time interleaver to the encoded service data in each physical path by a TI (Time Interleaving) block, wherein at least one virtual FEC block is ahead of FEC blocks in at least one TI block, wherein each TI block includes a variable number of FEC blocks of the encoded service data, wherein a number of the at least one virtual FEC block is defined based on a maximum number of FEC blocks of a TI block, a frame builder to build at least one signal frame including the time interleaved DP data, a modulator to modulate data in the built at least one signal frame by an OFDM (Orthogonal Frequency Division Multiplex) scheme and a transmitter to transmit the broadcast signals having the modulated data.

Abstract: A communication method and system for converging a 5th-generation (5G) communication system for supporting higher data rates beyond a 4th-generation (4G) system with a technology for internet of things (IoT) are provided. The disclosure may be applied to intelligent services based on the 5G communication technology and the IoT-related technology, such as smart home, smart building, smart city, smart car, connected car, health care, digital education, smart retail, security and safety services. The method and apparatus for polar encoding and rate-matching are disclosed.

Abstract: A low density parity check (LDPC) channel encoding method is used in a wireless communications system. A communication device encodes an input bit sequence by using an LDPC matrix, to obtain an encoded bit sequence for transmission. The LDPC matrix is obtained based on a lifting factor Z and a base matrix. The base matrix may be one of eight exemplary designs. The encoding method can be used in various communications systems including fifth generation (5G) telecommunication systems, and can support various encoding requirements for information bit sequences with different code lengths.