A module and method for transmitting rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) encoded codewords in an incremental redundancy-hybrid automatic repeat request (IR-HARQ) system

Abstract

This disclosure describes a module and method for transmitting codewords in a wireless communication system using an incremental redundancy-hybrid automatic repeat request (IR- HARQ) scheme. Each of the codewords comprise information-bit sequences that have been encoded based on a parity check matrix (PCM) that was derived from a lifted base matrix of a rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) protograph.

Description

A MODULE AND METHOD FOR TRANSMITTING RATE-COMPATIBLE ROOT- PROTOGRAPH LOW-DENSITY PARITY-CHECK (RC-RP-LDPC) ENCODED CODEWORDS IN AN INCREMENTAL REDUNDANCY-HYBRID AUTOMATIC REPEAT REQUEST (IR-HARQ) SYSTEMCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority to Singapore patent application no. 10202401535 S which was filed on 30 May 2024, the contents of which are hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] This application relates to a module and method for transmitting codewords in a wireless communication system using an incremental redundancy -hybrid automatic repeat request (IR-HARQ) scheme. Each of the codewords comprise information-bit sequences that have been encoded based on a parity check matrix (PCM) that was derived from a lifted base matrix of a rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) protograph.BACKGROUND

[0003] Multi-data-stream (MDS) transmission techniques have garnered interest over the past few years due to the fact that such techniques are able to address diverse Quality -of- Service (QoS) requirements inherent in Internet of Things (loT) applications. In order to facilitate the timely delivery of critical data and to enable efficient scheduling of non-critical data, loT systems often rely on retransmission strategies, such as those provided by automatic repeat request (ARQ) mechanisms. Among these strategies, the incremental redundancy hybrid ARQ (IR-HARQ) approach has emerged as a widely adopted solution as this approach is able to enhance both the reliability of data transmission and the spectral efficiency, making it a suitable component of modem wireless standards, including in fifth generation (5G) communication systems.

[0004] In various wireless communication applications, such as orthogonal frequency division multiplexing (OFDM) systems, multiple-input multiple-output (MIMO) systems, and cellular networking technologies, the data transmission process is frequently impaired byslowly varying channel fading. In such scenarios, the fading gain remains constant over each block of a codeword yet varies across different blocks. This behavior gives rise to what is commonly known in the art as the block fading (BF) channel. In the BF environment, the channel fading gain (i.e., the independent and identically distributed random variable (RV)) will remain constant in an entire fading block, while distinct channel fading gains exist in different fading blocks.

[0005] Unlike fast-fading or ergodic fading channels, the block fading channel is categorized as a non-ergodic channel. As a result, it does not exhibit the information stability property; in particular, its Shannon capacity is theoretically zero. Consequently, coding schemes designed for ergodic fading environments, which rely on the existence of a positive Shannon capacity, often perform poorly when applied to non-ergodic BF scenarios.

[0006] To address this limitation, those skilled in the ait have developed specialized coding schemes that arc tailored to the characteristics of the non-crgodic BF channel. One analytical tool used in this context is the concept of outage probability, which reflects the irreducible probability of transmission failure and establishes an information-thcorctically lower bound on the word error rate (WER) of any coding scheme. In addition to outage probability, another critical performance metric in BF environments is the diversity order. This metric describes the rate at which the WER decreases with increasing signal-to-noise ratio (SNR). For example, in a coding scheme that has a rate of 1 / L, the maximum achievable diversity order, which is also known as full diversity, is L.

[0007] In order to approach the outage limit and to attain full diversity in non-ergodic BF channels, root-based low-density parity-check (LDPC) codes have been introduced as an effective class of error correction codes, particularly when paired with iterative decoding algorithms such as belief propagation (BP). These codes have demonstrated strong performance in overcoming the limitations of non-ergodic fading environments, where traditional LDPC schemes often fall short. To further enhance the performance and robustness of root-based LDPC codes under such channel conditions, additional techniques such as improved progressive-edge-growth (PEG) algorithms, turbo decoding approaches, and optimized power allocation strategies were also proposed.

[0008] Despite their promising error-correcting capabilities, root-based LDPC codes face challenges in terms of implementation. Specifically, their inherently irregular code structures introduce non-linear encoding complexity, rendering them less suitable for efficient hardwarebased applications. To overcome this limitation, a specialized subclass of root-based LDPC codes, referred to as root-protograph-based LDPC (RP-LDPC) codes has been developed by those skilled in the art. Such RP-LDPC codes preserve the structural advantages of protographbased LDPC codes, such as linear encoding complexity, while simultaneously retaining the outagc-limit-approaching and full-diversity characteristics of root-based designs.

[0009] Due to these intrinsic benefits, RP-LDPC codes have been the subject of extensive research across a variety of communication scenarios. Their applicability spans from binary modulation environments to high-order modulation systems, where careful bit-to-symbol mapping is essential. Additionally, RP-LDPC codes have demonstrated flexibility and effectiveness in more complex communication frameworks, including relay-assisted networks and incremental redundancy hybrid ARQ (IR-HARQ) systems. Notably, advancements in IR- HARQ design have led to the development of feedback encoding methods that enable RP- LDPC -coded IR-HARQ systems to achieve high levels of diversity, although not necessarily full diversity, in practical implementations.

[0010] Hence, those skilled in the ait are constantly looking for ways to encode codewords in such a manner that the resulting codewords arc able to achieve rate compatibility, achieve full diversity, and approach the outage performance limit when used in IR-HARQ systems operating over non-crgodic BF channels.SUMMARY

[0011] In one aspect, the present application discloses a transmitter module for transmitting codewords using an incremental redundancy -hybrid automatic repeat request (IR-HARQ) scheme whereby the disclosed module comprises a processing unit, and a non-transitory media readable by the processing unit. The media stores instructions that when executed by the processing unit causes the processing unit to encode, using an encoder module, an informationbit sequence into a codeword using a parity check matrix (PCM) derived from a lifted base matrix of a rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) protograph. In embodiments of this aspect, the RC-RP-LDPC protograph comprises K primary root-check connections, each primary root-check connection comprising (L-l) secondary root-check connections, wherein L is defined as a number of large transmission rounds of the IR- HARQ scheme; K information nodes and at least one set of unique parity nodes, wherein K is defined as a number of information nodes, and the number of information nodes is equal to a number of primary root-check connections. It is also disclosed that each secondary root-check connection is associated with exactly one information node, the at least one set of unique parity nodes, and a check node corresponding to the type of the secondary root-check connection. The codeword is then transmitted over L transmission rounds.

[0012] In embodiments of this aspect, it is disclosed that a number of parity nodes in each set of unique parity nodes is equal to the number of primary root-check connections, and that the RC-RP-LDPC protograph comprises (L-7) sets of unique parity nodes.

[0013] In embodiments of this aspect, it is disclosed that the transmission of the codeword over L transmission rounds further comprises instructions for directing the processing unit to vary a code rate of the transmission of the codeword by puncturing selected parity bits in the codeword based on a parity -bit proportional puncturing scheme, such that the punctured parity bits are excluded from being transmitted in one or more of (L-l) redundancy rounds.

[0014] In embodiments of this aspect, a wireless communication system for implementing a multilevel-priority incremental redundancy-hybrid automatic repeat request (MP-1R-HARQ) scheme is disclosed. The disclosed system comprises a plurality of transmitter modules configured according to this aspect, wherein each of the plurality of transmitter modules arc configured to transmit codewords to an adaptive modulator. It is disclosed that the adaptive modulator is then configured to generate a modulation symbol sequence for the codewords using a modulation scheme selected based on a number of active codewords to be modulated and transmit the modulation symbol sequence to a receiver module, wherein the receiver module is configured to decode the modulation symbol sequence. It is then disclosed that a controller module is configured to receive a feedback vector from the receiver module, wherein the feedback vector indicates codewords that remain undccodcd by the receiver module, identify transmitter modules associated with the undecoded codewords based on the feedback vector, trigger the identified transmitter modules to transmit a subsequent redundancy round of the respective codewords to the adaptive modulator, w'hereby the adaptive modulator is configured to generate a new modulation symbol sequence for the received codewords usingan updated modulation scheme selected based on an updated number of active codewords, and transmit the new modulation symbol sequence to a receiver module. The system then iteratively repeats the steps of receiving the feedback vector, identifying the transmitter modules, and triggering the transmission of subsequent redundancy rounds of the respective codewords to the adaptive modulator until the feedback vector indicates that all codewords have been decoded.

[0015] In embodiments of this aspect, it is disclosed that in the wireless communication system, each modulation symbol in the modulation symbol sequence is constructed using a priority-based bit-to-symbol mapping scheme that assigns higher-priority codewords to more significant positions in the modulation symbol sequence.

[0016] In another aspect, the present application discloses a method for transmitting codewords using an incremental redundancy -hybrid automatic repeat request (IR-HARQ) scheme. It is disclosed that the method comprises the steps of encoding, using an encoder module, an information-bit sequence into a codeword using a parity check matrix (PCM) derived from a lifted base matrix of a rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) protograph. In embodiments of this another aspect, the RC-RP-LDPC protograph comprises K primary root-check connections, each primary root-check connection comprising (L-l) secondary root-check connections, wherein L is defined as a number of large transmission rounds of the IR-HARQ scheme, K infonnation nodes and at least one set of unique parity nodes, wherein K is defined as a number of information nodes, and the number of information nodes is equal to a number of primary root-check connections. It is also disclosed that each secondary root-check connection is associated with exactly one information node, the at least one set of unique parity nodes, and a check node corresponding to the type of the secondary root-check connection. The method then comprises the step of transmitting, using a transmitter module, the codeword over L transmission rounds.

[0017] In embodiments of this another aspect, a method for implementing a multilevel- priority incremental redundancy -hybrid automatic repeat request (MP-IR-HARQ) scheme in a wireless communication system is disclosed. The disclosed method comprises the steps of configuring a plurality of transmitter modules to perform the method according to this another aspect, wherein each of the plurality of transmitter modules are configured to transmit codewords to an adaptive modulator; generating, using the adaptive modulator, a modulationsymbol sequence for the codewords using a modulation scheme selected based on a number of active codewords to be modulated; and transmitting, using the adaptive modulator, the modulation symbol sequence to a receiver module. It is also disclosed that the receiver module is configured to decode the modulation symbol sequence. The disclosed method then comprises the steps of receiving, using a controller module, a feedback vector from the receiver module, wherein the feedback vector indicates codewords that remain undecoded by the receiver module, identifying, using the controller module, transmitter modules associated with the undccodcd codewords based on the feedback vector, triggering, using the controller module, the identified transmitter modules to transmit a subsequent redundancy round of the respective codewords to the adaptive modulator, whereby the adaptive modulator is configured to generate a new modulation symbol sequence for the received codewords using an updated modulation scheme selected based on an updated number of active codewords, and transmit the new modulation symbol sequence to a receiver module. The method then includes the steps of iteratively repeating, using the controller module, the steps of receiving the feedback vector, identifying the transmitter modules, and triggering the transmission of subsequent redundancy rounds of the respective codewords to the adaptive modulator until the feedback vector indicates that all codewords have been decoded.BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Various embodiments of the present disclosure are described below with reference to the following drawings:Figure 1A illustrates a block diagram of an incremental redundancy-hybrid automatic repeat request (IR-HARQ) system as known in the prior art;Figure IB illustrates an IR-HARQ transmission model known in the prior art;Figure 2A illustrates a root-protograph LDPC code known in the prior art with the number of transmission rounds, L set to 2;Figure 2B illustrates parity check equations ci and C2 of the root-protograph LDPC code illustrated in Figure 2A;Figure 3 illustrates a block diagram of a IR-HARQ system that utilizes a rate-compatible root- protograph low-density parity -check (RC-RP-LDPC) encoder and decoder in accordance with embodiments of the present disclosure;Figure 4A illustrates a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the number of transmission rounds, L is set to 2;Figure 4B illustrates secondary root-check connections cn and C22 of the root-protograph RC- RP-LDPC code illustrated in Figure 4A;Figure 5A illustrates a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the number of transmission rounds, L is set to 3;Figure 5B illustrates a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the number of transmission rounds, L is set to 4;Figure 5C illustrates a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the number of transmission rounds is set as L;Figure 6A illustrates a base matrix of a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the code rate is set at 1 / 2 and the number of transmission rounds, L is set to 2;Figure 6B illustrates a base matrix of a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the code rate is set at 1 / 3 and the number of transmission rounds, L is set to 3;Figure 6C illustrates a base matrix of a root-protograph RC-RP-LDPC code in accordance with embodiments of the present disclosure when the code rate is set at 1 / 4 and the number of transmission rounds, L is set to 4;Figure 7 illustrates an example of the nested base matrix structures of the root-protograph RC- RP-LDPC codes where the rate- 1 / 2 base matrix is nested in the rate- 1 / 3 base matrix which in turn is nested in the rate 1 / 4 base matrix, when the number of information nodes K is set as 2; Figure 8 A illustrates an example of the rate- 1 / 3 base matrices when the number of information nodes K is set as 2 or 3, and when the number of transmission rounds, L is set as 3;Figure 8B illustrates an example of the rate- 1 / 4 base matrices when the number of information nodes K is set as 2 or 3, and when the number of transmission rounds, L is set as 4;Figure 9 illustrates an example of a general base matrix corresponding to a set of RC-RP-LDPC 1 1 1 codes for code rates R 6 *-2 3 LJ’Figure 10 illustrates an IR-HARQ transmission model when a parity-bit based proportional puncturing scheme is applied to the codeword in accordance with embodiments of the present disclosure;Figure 11 illustrates a block diagram of a multilevel-priority incremental redundancy-hybrid automatic repeat request (MP-IR-HARQ) system in accordance with embodiments of the present disclosure;Figure 12 illustrates a block diagram of a processing system for performing embodiments of the present disclosure;Figure 13 illustrates a flowchart of a process for transmitting codewords using an incremental redundancy-hybrid automatic repeat request (IR-HARQ) scheme in accordance with embodiments of the present disclosure;Figure 14A illustrates plots of frame error rates (FERs) for different types of protograph codes over a BF channel where the outage limits for different code rates are set out as the theoretical performance limits;Figure 14B illustrates plots of frame error rates (FERs) over a range of Eb / Nofor 5G NR, GRP LDPC, and RC-RP-LDPC protograph codes at various code rates;Figure 15A illustrates plots of bit error rates (BERs) and FERs for the RC-RP-LDPC protograph code over the BF channels with a code rate of 1 / 3 and when the values of the information nodes are between 2 and 3;Figure 15B illustrates plots of bit error rates (BERs) and FERs for the RC-RP-LDPC protograph code over the BF channels with a code rate of 1 / 4 and when the values of the information nodes are between 2 and 3;Figure 16A illustrates plots of BERs and FERs for the RC-RP-LDPC protograph code over the BF channels when the code rate is 1 / 3;Figure 16B illustrates plots of BERs and FERs for the RC-RP-LDPC protograph code over the BF channels when the code rate is 1 / 4;Figure 17A illustrates the word error rate (WER) performance of the RC-RP-LDPC protograph code in an IR-HARQ system operating over a non-ergodic block fading (BF) channel, for a code rate of 1 / 3, where the number of information nodes is set to 2 or 3, and the number of transmission rounds L is 2 or 3;Figure 17B illustrates the word error rate (WER) performance of the RC-RP-LDPC protograph code in an IR-HARQ system operating over a non-ergodic block fading (BF) channel, for a code rate of 1 / 4, where the number of information nodes is set to 2 or 3, and the number of transmission rounds L is 2, 3 or 4;Figure 17C illustrates the word error rate (WER) performance of the RC-RP-LDPC protograph code in an IR-HARQ system operating over a non-ergodic block fading (BF) channel, for a code rate of 1 / 4, where the number of information nodes is set to 3, while the plots for a GRPL4 code with and without feedback encoding is utilized as the benchmark;Figure 17D illustrates the word error rate (WER) performance of the RC-RP-LDPC protograph code in an IR-HARQ system operating over a non-ergodic block fading (BF) channel, for a code rates of 3 / 6, 3 / 8, 3 / 10, 3 / 12, and 1 / 3, where the number of transmission rounds, L is set as 2, 3 or 4;Figure 18A illustrates the throughput plots of various protograph codes in an IR-HARQ system operating over a non-ergodic BF channel, at a code rate of 1 / 2 with the number of transmission rounds, L set at 2;Figure 18B illustrates the throughput plots of various protograph codes in an IR-HARQ system operating over a non-ergodic BF channel, at a code rate of 1 / 3 with the number of transmission rounds, L set at 3;Figure 18C illustrates the throughput plots of various protograph codes in an IR-HARQ system operating over a non-ergodic BF channel, at a code rate of 1 / 4 with the number of transmission rounds, L set at 4;Figure 18D illustrates the throughput plots of the RC-RP-LDPC protograph code in an IR- HARQ system operating over a non-ergodic block fading (BF) channel, at code rates of 1 / 2, 1 / 3 and 1 / 4 with two fading blocks;Figure 19A illustrates the signal to noise ratio (SNR) outage boundaries of conventional P- LDPC codes operating over a non-ergodic BF channel when the code rate is 1 / 2 and the number of transmission rounds, L is set at 2;Figure 19B illustrates the signal to noise ratio (SNR) outage boundaries of conventional RP- LDPC codes and the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the code rate is 1 / 2 and the number of transmission rounds, L is set at 2;Figure 20A illustrates the signal to noise ratio (SNR) outage boundaries of conventional RP- LDPC codes and the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the number of information nodes is set as 2, the code rate is 1 / 3 and the number of transmission rounds, L is set at 3;Figure 20B illustrates the signal to noise ratio (SNR) outage boundaries of the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the number of information nodes is set as 2 or 3, the code rate is 1 / 3 and the number of transmission rounds, L is set at 3; Figure 21A illustrates plots of BERs and FERs of the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the codewords arc punctured resulting in code rates of 1 / 3, 3 / 8, and 2 / 5 and the number of transmission rounds, L is set as 2;Figure 2 IB illustrates throughput plots of the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the codewords are punctured resulting in code rates of 1 / 3, 3 / 8, and 2 / 5 and the number of transmission rounds, L is set as 2;Figure 22A illustrates plots of BERs and FERs of the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the codewords are punctured resulting in code rates of 1 / 4, 13 / 48, and 7 / 24 and the number of transmission rounds, L is set as 2;Figure 22B illustrates throughput plots of the RC-RP-LDPC protograph code operating over a non-ergodic BF channel when the codewords arc punctured resulting in code rates of 1 / 4, 13 / 48, and 7 / 24 and the number of transmission rounds, L is set as 2;Figure 23A illustrates WER plots of the MP-IR-HARQ system with four transmitted data streams, while the traditional TR-HARQ system is used as the benchmark, where the code rate is 1 / 2 and the number of transmission rounds, L is set as 2; andFigure 23B illustrates WER plots of the MP-IR-HARQ system with four transmitted data streams, while the traditional IR-HARQ system is used as the benchmark, where the code rate is 1 / 3 and the number of transmission rounds, L is set as 3.DETAILED DESCRIPTION

[0019] The following detailed description is made with reference to the accompanying drawings, showing details and embodiments of the present disclosure for the purposes of illustration. Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments, even if not explicitly described in these other embodiments. Additions and / or combinations and / or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0020] In the context of various embodiments, the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements.

[0021] In the context of various embodiments, the term “about” or “approximately” as applied to a numeric value encompasses the exact value and a reasonable variance as generally understood in the relevant technical field, e.g., within 10% of the specified value.

[0022] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0023] As used herein, “comprising” means including, but not limited to, whatever follows the word “comprising”. Thus, use of the term “comprising” indicates that the listed elements are required or mandatory, but that other elements are optional and may or may not be present.

[0024] As used herein, “consisting of’ means including, and limited to, whatever follows the phrase “consisting of’. Thus, use of the phrase “consisting of’ indicates that the listed elements are required or mandatory, and that no other elements may be present.

[0025] One skilled in the art will recognize that certain functional units in this description have been labelled as modules throughout the specification. The person skilled in the art will also recognize that a module may be implemented as circuits, logic chips or any sort of discrete component. Still further, one skilled in the art will also recognize that a module may be implemented in software which may then be executed by a variety of processor architectures. In embodiments of the disclosure, a module may also comprise computer instructions or executable code that may instruct a computer processor to carry out a sequence of events based on instructions received. The choice of the implementation of the modules is left as a design choice to a person skilled in the ait and does not limit the scope of the claimed subject matter in any way.

[0026] Incremental-redundancy hybrid automatic repeat request (IR-HARQ) transmission.

[0027] A block diagram of a protograph based low-density-parity-check (P-LDPC) coded IR-HARQ transmission system 100 is illustrated in Figure 1A. As illustrated in Figure 1A, an information-bit sequence m is first encoded by P-LDPC encoder 102 to generate a corresponding coded-bit sequence which is then mapped to a modulated symbol sequence x, also referred to as the data stream. This data stream is subsequently partitioned into L sequential blocks, denoted a

[0028] During the first transmission round, the transmitter sends only the first block x, . which comprises all information bits along with a portion of the parity bits. The receiver collects the transmitted signal yt, which has traversed non-ergodic BF channel 104. P-LDPC decoder 106 then performs a de-mapping operation on jq, producing extrinsic log -likelihood ratios (LLRs), which serve as a-priori inputs for decoding.

[0029] If decoding is successful, a feedback signal F, in the form of an acknowledgment (ACK) is sent to IR-HARQ controller 112 (that is located at the transmitter side) through IR- HARQ controller 108 (that is located at the receiver side) via feedback channel 110, indicating that the remaining blocks (i.c. , the remaining parity bits) need not be transmitted. The decoded signal m is then further processed as required. Conversely, if decoding fails, the IR-HARQ controller 108 transmits a feedback signal F, in the form of a negative acknowledgment (NACK) to IR-HARQ controller 112, prompting IR-HARQ controller 112 to trigger P-LDPC encoder 102 to send the second block x2. The newly received block y2is similarly processed by P-LDPC decoder 106, and its corresponding extrinsic LLRs are combined with those obtained from prior transmission rounds to form a refined LLR sequence. This updated LLR sequence is then used in the subsequent decoding attempt. This iterative process repeats itself until decoding is successful or all L transmission blocks have been delivered to P-LDPC decoder 106.

[0030] A corresponding P-LDPC coded IR-HARQ transmission model comprising L transmission rounds is illustrated in Figure IB. Figure IB shows the transmission of a complete codeword, comprising a set of information bits 114 and the transmission of corresponding parity bits 116 (i.e., comprising subsets 116a- 116L) being incrementally transmitted over multiple rounds.

[0031] In the first transmission round 122, information bits 1 14 are initially transmitted. Following a first decoding attempt at the receiver, if decoding is unsuccessful, a subset 116a of the parity bits will be transmitted in a second transmission round 124. These bits arc then jointly decoded with the previously received bits during a second decoding process. If decoding is unsuccessful, a subset 116b of the parity bits will be transmitted in a third transmission round 126. These bits are then jointly decoded with the previously received bits during a third decoding process. This iterative process repeats itself until the codeword has been decodedsuccessfully or until all L transmission rounds 128 have been completed and all subsets 116L have been delivered to the receiver.

[0032] Root-protograph low-density-parity-check (RP-LDPC) codes.

[0033] A protograph Q — (V, C, £) is a small Tanner graph consisting of three different sets, including the variable-node (VN) set 'V, the check-node (CN) set C. and the edge set £. Each edge etj E £ connects a VN Vj E V (j — 1, 2, .... Np') to a CN ctE C (i =The protograph can also be represented by a base matrix B = (b[ y) of sizeMpX Np , where bij denotes the number of edges connecting Vj to c;. Unlike the traditional LDPC codes, protographs allow parallel edges. By performing the “copy-and-permute” (i.e., lifting) operation on a given protograph, these parallel edges can be eliminated, thus yielding a larger graph, called derived graph.

[0034] The derived graph can then be used to generate a parity -check matrix (PCM) corresponding to a protograph-based LDPC (P-LDPC) code. Specifically, the lifting operation expands the base matrix associated with a protograph into a full PCM, which is then used during encoding to map an information-bit sequence into a codeword. This encoding process may be implemented using an encoder module that is configured to encode the information-bit sequence into a codeword based on the PCM constructed from the lifted base matrix of a protograph code.

[0035] The lifting operation may be implemented by a modified progressive-edge-growth (PEG) algorithm. Different from the P-LDPC codes, the RP-LDPC codes have a relatively rigid protograph structure, called root protograph. Moreover, the RP-LDPC code with a code rate of R — 1 / L can be constructed only from a root protograph that includes L different rootcheck types. For example, the base matrix of a general rate-1 / 2 RP-LDPC code is shown as:. . . equation (1) where Np= 2Mp= 2LMRand MR6 N_ is the number of each rootcheck type. Additionally, I (resp. 0) is the identity (resp. zero) matrix with a size of MRX MR. The VN set V may bedivided into four subsets, including two information-node subsetsand vi2) and two paritynode subsets (i.e., vpland vp2)- The information nodes (resp. parity nodes) are the VNs corresponding to the information bits (resp. parity bits) in an RP-LDPC code. The coded bits (i.e., VNs) are composed of the information bits and parity bits (i.e., information nodes and parity nodes). In particular, the VNs Vj G vi;U vpiarc affected by the fading ahwhere j = ( / — 1)B + 1, (7 — 1)B + 2, ..., IB,B — N / 2, and I — 1, 2. The CN set C is divided into two subsets cy and c2, where c;is the typc-Z rootcheck subset. The weight per row in a combined sub-matrixmust be at least

[0036] Based on the base-matrix structure, a rate- 1 / 2 RP-LDPC code with full diversity (i.e., the diversity order is 2) can be generated. The diversity order may be defined as:...equation (2) where Pwis the WER at the decoder output and y = ^(Es / N^ai ) is the average received SNR of the Z-Lh block.

[0037] The achievable diversity order d of a coded system is also limited by the Singleton bound:...equation (3) where 1 + |L(1 — / ?)] is the maximum diversity order provided by a coding scheme. In the case of d = de = L , it can be concluded that the code is able to achieve full diversity. Additionally, it can be observed that the RP-LDPC codes have a symmetric property. Thus, it can be said that their performance is independent of the order of the L fading gains.

[0038] A conventional rate- 1 / 2 RP-LDPC code 201 as used in the IR-HARQ system with L = 2 transmission rounds (i.e., a codeword is divided into L - 2 blocks for L - 2 separate transmissions) is illustrated in Figure 2A. In accordance with the IR-HARQ mechanism, the 1stblock composed of all information bits must be sent in the 1sttransmission round. In other words, the information bits associated with the information nodes vLland vi2are first sent over a noisy channel characterized by a Nakagami fading gain a±. When ayis a deep fading gain, the information bits have a very high probability of being received incorrectly. Thisnecessitates the 2ndtransmission round, during which the parity bits associated with the parity nodes vpland vp2are sent over the noisy channel with a different Nakagami fading gain cr2. The currently received parity bits then will be combined with the previously received information bits for a joint decoding, to assist with the recovery' of the original information bits. Unfortunately, the traditional RP-LDPC-code structure is not able to correct the error occurring in the received information bits.

[0039] Figure 2B illustrates parity check equations ci - 202 and ci - 203 of root-protograph LDPC code 201 as illustrated in Figure 2A. As can be seen, even though both vpland vp2may be received correctly under an ideal channel condition, their error-correction capabilities are limited because bothand Vt2are involved in the same parity-check equations c, and c2, as given by:...equation (4) where G {0, 1} and b(vpj) G {0, 1} denote the binary bit representation of the information node Vij and the parity node vpj, respectively, for j = 1, 2. According to c1(it can be assumed that the bit associated with vp2is received correctly (i.e., b(vp2) ’sdetermined), but the bits associated with virand vi-2are not due to a deep fading. In such a situation, the decoder would not be able to infer the original values of b(v(| ) and h(Vj2). In other words, the error propagation between vL1and vt2cannot be eliminated. Also, a similar phenomenon can be observed from c2. From the above message-passing analysis, it can be seen that the correctly received block 2 is ineffective in correcting the errors in block 1. As a result, the traditional RP-LDPC codes then fail to achieve full diversity in the IR-HARQ scenarios.

[0040] Rate-compatible root-protograph low-density-parity-check (RC-RP-LDPC) protograph codes.

[0041] A block diagram of a rate-compatible root-protograph low-density-parity-check (RC-RP-LDPC) coded IR-HARQ transmission system 300 in accordance with embodiments of the disclosure is illustrated in Figure 3. As illustrated in Figure 3, an information-bit sequence m is first encoded by RC-RP-LDPC encoder 302 to generate a corresponding coded-bit sequence which is then mapped to a modulated symbol sequence x. This data stream is subsequently partitioned into L sequential blocks.

[0042] During a first transmission round, a transmitter (not shown) sends only the first block. A receiver (not shown) receives the transmitted signal y, which has traversed non- ergodic BF channel 304. RC-RP-LDPC decoder 306 then performs a decoding operation on the received signal to produce decoded signal m. If the decoding operation is successful, a feedback signal F, in the form of an acknowledgment (ACK) is sent to the transmitter by TR- HARQ controller 308 (that is located at the receiver side) via feedback channel 310, indicating that the remaining blocks (i.e., the remaining parity bits) need not be transmitted. Conversely, if decoding fails, the IR-HARQ controller 308 transmits a feedback signal F, in the form of a negative acknowledgment (NACK) to the transmitter, prompting the transmitter to trigger RC- RP-LDPC encoder 302 to transmit the next sequential block. The newly received block is similarly processed by RC-RP-LDPC decoder 306, and the received block is combined with the information obtained from prior transmission rounds. This iterative process repeats itself until decoding is successful or all L transmission blocks have been delivered to RC-RP-LDPC decoder 306.

[0043] In embodiments of the disclosure, puncturing controller 312 may be used in IR- HARQ transmission system 300 to puncture certain parity bits in each transmission round so that IR-HARQ transmission system 300 may achieve a wider code rate range. Puncturing controller 312 operates by varying the code rate of the transmission of the various blocks of the codeword by puncturing selected parity bits in the codeword based on a parity-bit proportional puncturing scheme, such that the punctured parity bits are excluded from being transmitted in one or more of (L — 1) redundancy rounds. In other words, the puncturing scheme for the rate-l / L RC-RP-LDPC codes allow the system to realize code rates ranging between 1 / L and 1 / (L — 1).

[0044] In embodiments of the disclosure, a RC-RP-LDPC code will feature K different primary rootchecks (i.e., type- / ’ rootcheck, i — 1, 2, ... , K). Moreover, each typc-z rootcheck includes ( L — 1 ) secondary rootchecks (i.e., type-zj rootcheck, j — 1, 2, . . ., L — 1 ). Consequently, the proposed RC-RP-LDPC structure contains K X (L — 1) different secondary rootchecks, with each secondary rootcheck connecting an information nodebelonging to the 1sttransmission round by a single edge and any parity nodes belonging to the yh(k — 2, 3, ..., L) transmission round by a single edge or parallel edges. For instance, under the assumption that there are K information nodes, the 1stinformation node will connect to L — 1 secondary rootchecks (i.e., the type-11, type-12, . . ., type-l(L — 1) rootchecks) via ! — 1 edges. Then, the L — 1 secondary rootchecks respectively connect to any parity nodes belonging to the remaining L - 1 transmission rounds. To be specific, the type- 1 / secondary rootcheck connects to the parity nodes within the (j + l)-th transmission round, where j —1, 2, . .., L — 1. Similarly, the 2-nd information node also connects to L — 1 secondary rootchecks (i.e., type-21, type- 22, . . ., type-2(L - 1) rootchecks) via L — 1 edges, while the type-2 / secondary rootcheck connects to the parity nodes within the (j + l)-th transmission round. By repeating this rootcheck connection process for all K information nodes, the protograph and base matrix structures corresponding to a RC-RP-LDPC code may then be constructed.

[0045] Figure 4 A illustrates protograph structure 401 of the RC-RP-LDPC code having K - 2 (i.e., 2 information nodes) and with the number of transmission rounds L — 2. In this figure, it can be seen that a single edge (which implies that the corresponding number in the base matrix is 1 ) is used to connect each of the information nodesand v,2) with their respective check nodes (i.e., cltand c21). The edges connecting the parity nodes (i.e., vpl, vp2) and the check nodes can be a single edge or parallel edges (which imphes that the corresponding number in the base matrix is greater than 1).

[0046] Figure 4B illustrates two primary rootcheck connections, i.e., Type-1 and Type-2, and two secondary rootcheck connections, i.e., Type-1 1 and Type-21. Secondary rootcheck connection Type- 11 comprises check node c1±that is connected to information nodeand also to a set of unique parity nodes comprising parity nodes vpland vp2while secondary rootcheck connection Type-21 comprises check node c21that is connected to information node vi2and to a set of unique parity nodes comprising parity nodes vpland vp2.

[0047] Figure 5 A illustrates another example of the protograph structure of the RC-RP- LDPC code having K = 2 (i.e., 2 information nodes) and with the number of transmission rounds L set to 3. In this figure, it can be seen that a single edge is used to connect each of the information nodes (i.e.,and vi2) with their respective check nodes (i.e., clx, c21, c12andc22) while the edges (i.e., the dashed lines) connecting the parity nodes (i.e., vpl, vp2, vp3, vp4) with their respective check nodes can be a single edge or parallel edges. This protograph structure illustrates two primary rootcheck connections, i.e., Type-1 and Type-2, and four secondary rootcheck connections, i.e., Type-11, Type-21, Type-12 and Type-22. Secondary rootcheck connection Type- 11 comprises check node cixthat is connected to information node vi4and also to a set of unique parity nodes comprising parity nodes vpland vp2while secondary rootcheck connection Type-21 comprises check node c21that is connected to information node V{2and to a set of unique parity nodes comprising parity nodes vpland vp2. Secondary rootcheck connection Type- 12 comprises check node c12that is connected to information nodeand also to a set of unique parity nodes comprising parity nodes vp3and vp4while secondary rootcheck connection Type-22 comprises check node c22that is connected to information node vi2and to a set of unique parity nodes comprising parity nodes vp3and vp4.

[0048] Figure 5B illustrates another example of the protograph structure of the RC-RP- LDPC code having K = 2 (i.e., 2 information nodes) and with the number of transmission rounds L set to 4. In this figure, it can be seen that a single edge is used to connect each of the information nodes (i.e., 1% and vx2) with their respective check nodes (i.e., c41, c21, c12, c22, c13, c23) while the edges (i.e., the dashed lines) connecting the parity nodes (i.e., vpl,vp2>vp3-vp\>Vpz>vp&) with their respective check nodes can be a single edge or parallel edges. This protograph structure illustrates two primary rootcheck connections, i.e., Type-1 and Type-2, and six secondary rootcheck connections, i.e., Type-11, Type-21, Type-12, Type- 22, Typc-13 and Typc-23. Secondary rootcheck connections Typc-11, Typc-21, Typc-12 and Type-22 are as described above. Secondary rootcheck connection Type- 13 comprises check node c13that is connected to information node vi4and also to a set of unique parity nodes comprising parity nodes vp5and vp6while secondary rootcheck connection Type-23 comprises check node c23that is connected to information node iy2and to a set of unique parity nodes comprising parity nodes vp5and vp6.

[0049] Lastly, as illustrated in Figure 5C, it can be seen that the protograph structure of the RC-RP-LDPC code may be extended to any number of transmission rounds L , and as a consequence, may result in various transmission code rates.

[0050] The base matrices corresponding to the protograph structures in Figures 4A, 5A and 5B are shown in Figures 6A, 6B and 6C, respectively. In particular, base matrix 602 as shown in Figure 6 A is tailored for protograph structure 401 of the RC-RP-LDPC code having K = 2 (i.e., 2 information nodes) and with the number of transmission rounds L set as 2, base matrix 604 as shown in Figure 6B is tailored for protograph structure 501 of the RC-RP-LDPC code having K = 2 (i.e., 2 information nodes) and with the number of transmission rounds L set as 3, and base matrix 606 as shown in Figure 6C is tailored for protograph structure 502 of the RC-RP-LDPC code having K = 2 (i.e., 2 information nodes) and with the number of transmission rounds L set as 4. It should be noted that the rate of the base matrices 602, 604 and 606 are 1 / 2, 1 / 3 and 1 / 4, respectively.[0051J As can be seen from Figures 6A, 6B and 6C, the rate- 1 / 2 base matrix 602 is included in the rate- 1 / 3 base matrix 604, which in turn is included in the rate- 1 / 4 base matrix 606. Figure 7 illustrates an embodiment where the base matrices 602, and 604 are nested within base matrix 606 with the condition that the degree of each check node is set as 6.

[0052] In embodiments of the disclosure, for a given HARQ condition (e.g., L = 3 or 4), the parameter K may be enlarged to attain a larger base matrix. It is worth noting that a larger base matrix offers more flexibility to be optimized to achieve desirable performance. Thereby, the RC-RP-LDPC codes may be constructed with a larger parameter K (i.e., with better performance). Figure 8A illustrates rate-1 / 3 base matrices 802 and 804 for K — 2 and 3 respectively as tailored for the HARQ scenario with L = 3 while Figure 8B illustrates rate- 1 / 4 base matrices 806 and 808 for K - 2 and 3 respectively as tailored for the HARQ scenario with L = 4.

[0053] In embodiments of the disclosure, when the code-design methodology described above is adopted, it should be noted that a family of RC-RP-LDPC codes can be systematically constructed to support a wide range of code rates R E {1 / 2, 1 / 3, ...,1 / L}, where L denotes the total number of transmission rounds in an IR-HARQ system. These RC-RP-LDPC codes may be characterized by a general protograph structure, or equivalently, a corresponding base matrix, as illustrated in Figure 9. Given specific design parameters K (the number of information nodes) and L, an appropriate base matrix can be selected from Figure 9. In particular, the variables bij, where i G {1,2, ... , K * (1 — 1)} and j G {1,2,may bedetermined using a computer-aided exhaustive search method to ensure that the resulting RC- RP-LDPC code achieves a desirable outage performance boundary. Such a method is described in Algorithm 1 below.

[0054] Further, as illustrated in Figure 9, during HARQ-bascd data transmission over BF channels, all information bits corresponding to the K information nodes are transmitted during the 1sttransmission round and are subjected to a fading gain a1. If these information bits cannot be correctly decoded, a second transmission round is initiated in which additional parity bits corresponding to the 1sLK parity nodes are transmitted over a new fading block with gain a2. These parity bits are jointly decoded with the previously received information bits. If decoding remains unsuccessful, another set of parity bits associated with the next K parity nodes is transmitted under a new fading gain (c.g., cr3), and the decoding is again performed using all previously received information and parity bits. This retransmission and joint decoding process continues until cither successful decoding is achieved or the maximum number of retransmission rounds L is reached.

[0055] In embodiments of the disclosure, when a code rate R G ( 1 / L, 1 / (L — 1)) in an 1R- HARQ transmission system needs to be achieved, this may be accomplished by adopting a parity-bit based proportional puncturing scheme. In this scheme, the rate-l / Z. RC-RP-LDPC code is first obtained according to the methods described above. Subsequently, selected parity bits in the 2-nd, 3-rd, . .., L transmission rounds may then be punctured, i.e., these punctured parity bits will not be transmitted over the BF channels. The pseudo-code of this puncturing scheme is set out below in Algorithm 2. Through the use of this scheme, a larger range of code rates may be achieved, while ensuring that the full diversity characteristic of the RC-RP-LDPC code is preserved.

[0056] The puncturing scheme described in Algorithm 2 may also be described as follows. For a current redundancy round, an error rate associated with a previously transmitted round is first calculated. A puncturing pattern associated with a current redundancy round is selected and applied to parity bits corresponding to the current redundancy round, wherein the puncturing pattern specifies parity bits that are to be omitted from being transmitted in the current redundancy round. For a subsequent redundancy round, a new error rate is then calculated based on all previous transmission rounds. The steps of selecting and applying the puncturing pattern, and the step of calculating the new error rate is iteratively repeated until the new error rate exceeds a predetermined error rate. Subsequently, in response to the determination that the new error rate exceeds a predetermined error rate, the puncturing patternassociated with a previously transmitted redundancy round is set as an optimal puncturing pattern for the parity-bit proportional puncturing scheme to achieve the desired code rate.

[0057] Figure 10 illustrates an IR-HARQ transmission mechanism 1001 that incorporates the parity-bit-based proportional puncturing scheme described above. The codeword to be transmitted comprises information bits 1002 and parity bits 1004. During a first transmission round 1006, all information bits 1002 are transmitted. In the subsequent transmission rounds 1008, 1010, ..., 1012, parity bits 1004a, 1004b, ..., 1004 / ? arc transmitted incrementally, where p denotes the number of unique sets or blocks of parity bits, hi each redundancy round, a puncturing process is applied. For example, in the second transmission round 1008, specific parity bits 1005 associated with the set 1004a are punctured and thus omitted from transmission. After each redundancy round, a decoding attempt is performed using all previously received bits. If decoding is unsuccessful, the next set of parity bits (e.g., 1004b) is transmitted in the following transmission round 1010, again subject to puncturing of certain associated parity bits 1005. This process continues iteratively until all the information bits 1002 have been successfully decoded or all sets of parity bits have been transmitted. By selectively omitting parity bits, system 1001 adaptively varies the code rate in response to channel conditions and decoding outcomes, thereby improving spectral efficiency while maintaining reliable communication between the transmitter and receiver.

[0058] Rate-compatible root-protograph low-density-parity-check (RC-RP-LDPC) coded multilevel-priority IR-HARQ (MP-IR-HARQ) system.

[0059] Wireless applications with diverse QoS requirements, especially 6G-enabled loTs, require a transmission technique that can support multiple data streams, offer unequal protection, and incorporate ARQ strategies. A block diagram of a rate -compatible root- protograph low-density-parity-check (RC-RP-LDPC) coded multilevel-priority IR-HARQ (MP-IR-HARQ) system that can achieve this objective is illustrated in Figure 11. The proposed MP-IR-HARQ system comprises transmitter 1101 that is configured to transmit a modulation symbol sequence to receiver 1107 via BF channel 1106.

[0060] At transmitter 1 101 , it is assumed that there are m-number different information-bit sequences. . ,, mm, and that they may be re-ranked sequentially according to theirpriorities. In other words, mthas higher priority than m(-+ l, where i = 1, 2, . . m — 1. These m information bit sequences will be passed to RC-RP-LDPC encoders 1102a, 1102b,..., 1102m, which then produce the corresponding coded-bit sequences c1, c2, .. ., cm. Subsequently, every coded-bit sequence is divided into L different blocks i, Cj2, . . ,, CjLwhere j = 1, 2,In the 1-st transmission round, a feedback signal sequence F — {Fi, F2, . . . , Fm] is first set and initialized to an all-zero vector (i.e., Fj = 0). Based on the m NACK signals, each of these m RC-RP-LDPC encoders 1102a-1102m outputs the 1-st block of its codeword (i.e., Cjx) to adaptive modulator 1104, which can continuously extract m bits from the m different blocks to generate an Af-ary modulation symbol sequence x by an M-ary constellation (M — 2m~). During the bit-to symbol procedure, the coded bits with the highest priority, second highest priority, . . ., lowest priority are respectively assigned into the most significant bit (MSB), second MSB, . . ., least significant bit (LSB) positions in the constellation to achieve the Unequal Error Protection (UEP) property.

[0061] It should be noted that in the subsequent (i.e., the / -th for I > 1) transmission round, the updated F may no longer be an all zero vector since the receiver should be able to correctly decode some data streams in the previous transmission round. As such, based on the updated F with m' ‘Os’ (i.e., NACK) and m-m' ‘Is’ (i.e., ACK), only the m'RC-RP-LDPC encoders that receive the NACK will output the / -th block of their corresponding codeword ck tto adaptive modulator 1104, where k is the indicator of the m' codewords that have not been successfully decoded yet. Then, the adaptive modulator 1104 also continuously extracts m' bits from the m' different blocks to generate an A / '-ai'y modulation symbol sequence x by an A / -ary constellation (. It should be noted that adaptive modulator 1104 adopts different constellations based on the numbers of input blocks to implement the bit-to-symbol procedure.

[0062] At receiver 1107, the received signal sequence y is processed by a multi-level concatenated structure, which is formulated by adaptive detector 1108 and m RC-RP-LDPC decoders 1 1 10a, 1 1 10b,.. , 1 1 10m. The proposed MP-IR-HARQ decoding principle is set out in Algorithm 3 below, while the specific soft information (i.e., LLRs) update is described as follows in the following steps. Additionally, each m1;m2inmrepresents the estimated or recovered message at the side of receiver 1107, derived from the noisy and possibly incomplete signals received over the block fading (BF) channel.

[0063] Step 1: In the 1-st transmission round, the initial feedback signal sequence F of size 1 X m in receiver 1107 is also an all-zero vector, indicating that m data streams need to be processed. Thereby, adaptive detector 1108 will make the detection according to a 2m-ary bit- to-symbol mapping relationship. After that, for the LLRs output from adaptive detector 1108, those LLRs corresponding to the data stream with the highest priority are sent to its corresponding RC-RP-LDPC decoder (i.e., H lOa-l l lOm). The corresponding decoding is then performed. If the decoding fails, F remains unchanged (i.e., it’s all elements are still 0), while the receiver sends F to transmitter 1101 via feedback channel 1114 using IR-HARQ controller 1112, requesting to start a new transmission round. F is received by IR-HARQ controller 1116 which then triggers transmitter 1101 accordingly. It should be noted that since F is still an all-zero vector in next transmission round, the LLR update process is the same as above, except that the decoding considers the incremental redundancy principle (i.e., thecurrent LLRs will be merged with those obtained in the previous transmission rounds into a new LLR sequence for decoding)

[0064] If the decoding is done correctly, the first element within F is updated to 1, while the remaining elements remain at 0. The 1-st RC-RP-LDPC decoder 1110a then feeds the extrinsic LLRs of the decoded bits transmitted in the current transmission round back to the adaptive detector. Based on the channel output and feedback LLRs, adaptive detector 1108 initiates a new detection, and then sends the LLRs corresponding to the sccond-highcst-priority data stream to the 2-nd RC-RP-LDPC decoder 1110b for decoding. If the decoding fails, go to Step 2, else go to Step 3.

[0065] Step 2: When the decoding fails, F is kept unchanged, and then sent to transmitter 1101, which will start a new transmission round. It should be noted that based on the current F in receiver 1107, adaptive detector 1108 executes the detection according to a 2m'- ary bit-to- symbol mapping relationship, and sends the LLRs of the data stream with the highest priority among the currently transmitted data streams to its corresponding RC-RP-LDPC decoder for decoding, where m' = m —When the decoding fails, the steps described above are repeated, else proceed to Step 3.

[0066] In particular, if the decoding fails and the maximum number of transmission rounds (i.c., L) is reached, the LLR update is terminated and returns to Step 1 with the initiation of a new transmission. However, if the decoding is done correctly and m' — 1, the LLR update is terminated and an all-one vector F is sent to the transmitter, indicating that all data streams are received correctly.

[0067] Step 3: If the k-th (k < m) data stream is decoded correctly, the k-th element within F is updated to 1 . Meanwhile, the k-th RC-RP-LDPC decoder feeds the extrinsic LLRs of the decoded bits transmitted in the current transmission round back to adaptive detector 1108. Based on the channel output and feedback LLRs, adaptive detector 1108 initiates a new detection, and then sends the LLRs of the (k + l)-th data stream to the corresponding (k + 1)- th RC-RP-LDPC decoder for decoding. Go to Step 4.

[0068] Step 4: For k + 1 < m, when the (k + l)-th RC-RP-LDPC decoding fails, k is set as k = k + 1 and return to Step 2. For k + 1 = m , when the (k + 1 )-th RC-RP-LDPC decoding fails, return to Step 2. Otherwise, terminate the LLR update and send an all-one vector F to transmitter 1101, indicating that all data streams are received correctly.

[0069] It should be noted that both proposed adaptive modulator 1104 and adaptive detector 1108 must employ the 2m' -ary ( 1 < m1< m ) bit-to-symbol mapping and dc-mapping, respectively, according to the number of zero elements (i.e., m') within F. Based on the proposed successive decoding, the low priority data stream is processed only after the high priority data stream has been correctly decoded because the latter is given priority protection and is more reliable. In other words, if the high-priority data stream cannot be decoded correctly, there is a high probability that the low priority one cannot be decoded correctly. This mechanism significantly reduces the computational overhead of the system.

[0070] In accordance with embodiments of the present disclosure, a block diagram representative of components of processing system 1200 that may be provided within any of the modules shown in Figures 3 and 11 to carry' out the computing and processing functions in accordance with embodiments of the disclosure. One skilled in the art will recognize that the exact configuration of each processing system provided within these modules may be different and the exact configuration of processing system 1200 may vary' and the arrangement illustrated in Figure 12 is provided by way of example only.

[0071] In embodiments of the disclosure, processing system 1200 may comprise controller1201 and user interface 1202. User interface 1202 is arranged to enable manual interactions between a user and the computing module as required and for this purpose includes the input / output components required for the user to enter instructions to provide updates to each of these modules. A person skilled in the art will recognize that components of user interface1202 may vary from embodiment to embodiment but will typically include one or more of display 1240, keyboard 1235 and optical device 1236.

[0072] Controller 1201 is in data communication with user interface 1202 via bus 1215 and includes memory 1220, processing unit or processor 1205 mounted on a circuit board that processes instructions and data for performing the method of this embodiment, an operatingsystem 1206, an input / output (I / O) interface 1230 for communicating with user interface 1202 and a communications interface, in this embodiment in the form of a network card 1250. Network card 1250 may, for example, be utilized to send data from these modules via a wired or wireless network to other processing devices or to receive data via the wired or wireless network. Wireless networks that may be utilized by network card 1250 include, but are not limited to, Wireless-Fidelity (Wi-Fi), Bluetooth, Near Field Communication (NFC), cellular networks, satellite networks, telecommunication networks, Wide Area Networks (WAN) and etc.

[0073] Memory 1220 and operating system 1206 are in data communication with processor 1205 via bus 1210. The memory components include both volatile and non-volatile memory and more than one of each type of memory, including Random Access Memory (RAM) 1223, Read Only Memory (ROM) 1225 and a mass storage device 1245, the last comprising one or more solid-state drives (SSDs). One skilled in the art will recognize that the memory components described above comprise non-transitory computer- read able media and shall be taken to comprise all computer-readable media except for a transitory, propagating signal. Typically, the instructions are stored as program code in the memory components but can also be hardwired. Memory 1220 may include a kernel and / or programming modules such as a software application that may be stored in either volatile or non-volatile memory.

[0074] Herein the term “processor” or “processing unit” is used to refer generically to any device or component that can process such instructions and may include: a microprocessor, a processing unit, a microcontroller, a programmable logic device or other computational device. That is, processor 1205 may be provided by any suitable logic circuitry for receiving inputs, processing them in accordance with instructions stored in memory and generating outputs (for example to the memory components or on display 1240). In this embodiment, processor 1205 may be a single core or multi-core processor with memory addressable space. In one example, processor 1205 may be multi-core, comprising — for example — an 8 core CPU. In another example, it could be a cluster of CPU cores operating in parallel to accelerate computations.

[0075] A flowchart which sets out the process for transmitting codewords using an incremental redundancy-hybrid automatic repeat request (IR-HARQ) scheme in accordance with embodiments of the present disclosure is illustrated in Figure 13. In embodiments of theT1disclosure, process 1300 as illustrated in Figure 13 may be performed by any combination of modules provided within IR-HARQ system 300.

[0076] Process 1300 begins at step 1302 with process 1300 encoding an information-bit sequence into a codeword using a parity check matrix (PCM) derived from a lifted base matrix of a rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) protograph. In embodiments of the disclosure, the RC-RP-LDPC protograph comprises K primary root-check connections with each primary root-check connection comprising (L — 1) secondary rootcheck connections, wherein L is defined as a number of large transmission rounds of the IR- HARQ scheme and K information nodes and at least one set of unique parity nodes, wherein K is defined as a number of information nodes, and the number of information nodes is equal to a number of primary root-check connections. Further, each secondary root-check connection is associated with exactly one information node, the at least one set of unique parity nodes, and a check node corresponding to the type of the secondary root-check connection. Process 1300 then proceeds to transmit the codeword over L transmission rounds at step 1304.

[0077] In embodiments of the disclosure, a number of parity nodes in each set of unique parity nodes is equal to the number of primary root-check connections, and wherein the RC- RP-LDPC protograph comprises (L — 1) sets of unique parity nodes and the RC-RP-LDPC protograph is one of a plurality of RC-RP-LDPC protographs that each correspond to a different coding rate. In embodiments of the disclosure, each of the plurality of RC-RP-LDPC protographs corresponds to an associated lifted base matrix, and a lifted base matrix derived from a RC-RP-LDPC protograph having a higher code rate is structurally included as a submatrix within a lifted base matrix derived from another RC-RP-LDPC protograph having a lower code rate.

[0078] In embodiments of the disclosure, at step 1306, process 1300 varies a code rate of the transmission of the codeword by puncturing selected parity bits in the codeword based on a parity-bit proportional puncturing scheme, such that the punctured parity bits are excluded from being transmitted in one or more of (L — 1) redundancy rounds.

[0079] In embodiments of the disclosure, process 1300 implements the parity-bit proportional puncturing scheme by calculating, for a current redundancy round, an error rateassociated with a previously transmitted round. This takes place at step 1308. At step 1310, process 1300 then selects and applies a puncturing pattern associated with a current redundancy round to parity bits corresponding to the current redundancy round, wherein the puncturing pattern specifies parity bits that are to be omitted from being transmitted in the current redundancy round. Process 1300 then calculates, for a subsequent redundancy round, a new error rate based on all previously transmission rounds. This occurs at step 1312. At step 1314, process 1300 determines if the new error rate exceeds a predetermined error rate. If the new error rate docs not exceed a predetermined error rate, process 1300 returns to step 1310 and the steps of selecting and applying the puncturing pattern at step 1310, and the step of calculating the new error rate at step 1312 repeats until the new error rate exceeds a predetermined error rate. Conversely, if process 1300 determines at step 1314 that the new error rate exceeds a predetermined error rate, process 1300 proceeds to step 1316 where process 1300 sets the puncturing pattern associated with a previously transmitted redundancy round as the optimal puncturing pattern for the parity -bit proportional puncturing scheme.

[0080] Simulation results of the RC-RP-LDPC protograph codes.

[0081] In the following simulations, it is assumed that the information length of the codes used in the simulations is 1020, the maximum number of belief -propagation iterations is 100, and that the channels suffer from Nakagami BF.

[0082] Figure 14A illustrates plots that compare the Frame Error Rate (FER) performance of four different rate-1 / 2 protograph codes, including the regular-(3, 6) protograph LDPC (P- LDPC) code, the accumulate-repeat-4-jagged-accumulate (AR4JA) code, the irregular root protograph code (IRP2), and the RC-RP-LDPC code as described in embodiments of the disclosure, over a BF channel with two fading blocks. As illustrated, it can be seen that the rate- 1 / 2 RC-RP-LDPC code was able to achieve a gain of about 6.0 dB with respect to the other three rate- 1 / 2 protograph-based codes in the high SNR region (even if the performance degrades slightly in low SNR region). It can also be seen that the rate- 1 / 2 RC-RP-LDPC code was also able to achieve the full diversity property. Moreover, the rate- 1 / 2 RC-RP-LDPC code only exhibits a gap of about 3.0 dB to its corresponding outage limit. Because the scale of SNR of error correction codes over BF channels is approximately 10 times larger than the standard scale over additive white Gaussian noise (AWGN) channels, the 3.0 dB gap to the outage limitover a BF channel is similar to a 0.3 dB gap to the Shannon limit over an AWGN channel. This small gap indicates that the rate- 1 / 2 RC-RP-LDPC code has near outage-limit performance. Figure 14A also illustrates the FER plots of the RC-RP-LDPC code with code rates of 1 / 3 and 1 / 4 over the BF channel, in which there are respectively three and four fading blocks (i.e., L — 3 and L = 4). The outage limits corresponding to each code rate is also included as benchmark plots in Figure 14A.

[0083] Plots showing the performance of the RC-RP-LDPC code, the existing RP code (i.e., GRP code) designed for a HARQ transmission model, and existing 5G NR LDPC code are plotted in Figure 14B. It can be seen that the existing 5G NR LDPC code is not able to achieve full diversity under the given channel conditions. In contrast, the proposed RC-RP-LDPC code successfully achieves full diversity and demonstrates superior error performance compared to the GRP code. It is also noteworthy that the RC-RP-LDPC codes were able to maintain excellent performance characteristics even when applied to scenarios involving short block lengths.

[0084] Figure 15A illustrates the Bit Error Rate (BER) and Frame Error Rate (FER) curves for two RC-RP-LDPC rate- 1 / 3 codes, where each of these codes have three transmission rounds (i.e., L — 3), an information length of 1020 and when the number of information nodes K is 2 or 3. The RC-RP-LDPC rate- 1 / 3 code with K = 2 corresponds to base matrixas shown below and the RC-RP-LDPC rate- 1 / 3 code with K = 3 corresponds to base matrix B2as shown below:

[0085] As illustrated in Figure 15A, when the information length, code rate, and frame length are constant, an increase in the value of parameter K results in an improved overallsystem performance. This improvement is evidenced by both the BER and FER curves, which demonstrate a consistent reduction in the error rates as K increases.

[0086] Figure 15B illustrates the Bit Error Rate (BER) and Frame Error Rate (FER) curves for two RC-RP-LDPC rate- 1 / 4 codes, where each of these codes have four transmission rounds (i.e., L — 4), an information length of 1020 and when the number of information nodes K is 2 or 3. The RC-RP-LDPC ratc-1 / 4 code with K = 2 corresponds to base matrix B3as shown below and the RC-RP-LDPC rate- 1 / 4 code with K = 3 corresponds to base matrix B4as shown below:

[0087] Similarly, it can be seen that when the information length, code rate, and frame length are constant, an increase in the value of parameter K results in an improved overall system performance. In summary, it can be said that for a given number of transmission rounds, L, an increase in the parameter K results in an enhanced code that in turn results in a better performance.

[0088] Figure 16A illustrates the BER and FER plots of the rate- 1 / 3 RC-RP-LDPC code based on base matrix B2and when the parameter K is set as 3, and as transmitted over a BF channel with two fading blocks (i.e., L = 2). It can be seen that such a base matrix was able to achieve the full diversity (i.e., dc— 2). Figure 16B illustrates the BER and FER of the rate-1 / 4 RC-RP-LDPC code based on base matrix B4when the parameter K is set as 3, and as transmitted over a BF channel with two or three fading blocks (i.e., L = 2 or 3). It can be seenthat such a base matrix was able to achieve the full diversity (i.e., dc— 2 for L — 2 and dc— 3 for L = 3). From the above observations, it can be inferred that the rate-l / L RC-RP-LDPC codes may achieve full diversity with L blocks and is also able to maintain this full diversity property with (L — 1) blocks, (L — 2) blocks, 2 blocks.

[0089] Figure 17A illustrates the WER performance of the rate- 1 / 3 RC-RP-LDPC codes with K = 2 and 3 for three transmission rounds (i.e., L = 3). Both these codes exhibit the fulldiversity property, but the rate- 1 / 3 RC-RP-LDPC code with K = 3 exhibits a better WER performance than that with K = 2. The WER performance of the rate- 1 / 3 NRP code with K = 3 in the IR-HARQ system with L = 2 is also plotted in Figure 17A. It can be seen that the RC- RP-LDPC code was also able to achieve full diversity (i.e., d = dc= L = 2). This implies that the proposed rate-l / L RC-RP-LDPC code possesses the full-diversity property in both i) IR- HARQ system with L transmission rounds (i.e., only information bits are included in the 1-st transmission round) and ii) IR-HARQ system with L' transmission rounds (i.e., all information bits and partial parity bits are included in the 1-st transmission round), where 2 < L' < L is a positive integer.

[0090] Figure 17B illustrates the WER performance of the rate-1 / 4 RC-RP-LDPC codes with K = 2 and 3 for four transmission rounds (i.e., L = 4). Similarly, it can be observed that the performance of the RC-RP-LDPC code with K — 3 is better than that with K — 2 when the number of transmission rounds is set to four (i.e., L = 4). Additionally, as illustrated, it can be seen that the RC-RP-LDPC code with K — 3 is able to exhibit the full-diversity property for L = 4, 3, and 2.

[0091] Figure 17C illustrates the WER performance of the proposed rate- 1 / 4 RC-RP-LDPC code with K = 3, while the GRPL4 code with and without feedback encoding is used as the benchmark. It is obvious that the GRPL4 code with L — 4, 5, 6 is not able to achieve full diversity in the proposed system, whereas the RC-RP-LDPC code is able to do so.

[0092] Additionally, Figure 17D illustrates the WER performance of a family of NRP codes having a wide range of rational code rates R = K / P, where K = 3 and P = 6, 7, . . . , 12. As illustrated, it can be seen that the proposed rate-K / L’ RC-RP-LDPC code may achieve fulldiversity in the case of 2 < L1< [P / / 6J , where L’ is a positive integer and [-J is a floor operation.

[0093] The throughput performance comparison among various protograph codes in the IR- HARQ system over a non-ergodic BF channel is illustrated in Figure 18A, where the rate- 1 / 2 regular-(3,6) code, accumulate-repeat-4-jagged-accumulate (AR4JA) code, IRP2 code, and RC-RP-LDPC code with K = 2 are considered. As illustrated, it can be seen that when L = 2, only the RC-RP-LDPC code was able to approach the theoretical maximum throughput as the SNR (i.e., Eb / N0) increases.

[0094] Similarly, in Figure 18B, where the rate-1 / 3 regular-(4, 6) code, accumulate-repeat- jagged-accumulate (ARJA) code, and proposed RC-RP-LDPC code with K = 2 are considered, it can be seen that there is similar throughput performance trend among the three types of codes. Based on the plots in Figure 18C, where the rate- 1 / 4 regular-(6, 8) code, ARJA code, and RC-RP-LDPC code with K = 2 arc considered, it can be seen that there is also a similar throughput performance trend among these codes. It is useful to note that although there is a relatively large gap between the throughput performance of the RC-RP-LDPC codes and the BPSK capacity in the low SNR range (i.e., 0 ~ 24 (dB)), this gap can be narrowed by optimizing the HARQ mechanism, c.g., the cross-packet HARQ.

[0095] Figure 18D illustrates the simulated RC-RP-LDPC code at code rates of 1 / 2, 1 / 3, and 1 / 4, as transmitted over a BF channel with two fading blocks (i.e., L — 2). It can be seen that the three proposed codes consistently achieved their respective theoretical maximum throughputs as the SNR increases. These plots show that the proposed codes are able to achieve near-optimal throughput performance across a wide range of code rates and fading blocks.

[0096] Figure 19A illustrates the SNR outage boundaries of the regular-(3, 6) and AR4JA P-LDPC codes with a code rate of R = 1 / 2 over a BF channel with L = 2. In particular, y(= (Es / N0)a.2 denotes the received SNR of the / -th block, and both codes are conventional nonroot P-LDPC codes. In this figure, the corresponding outage bound and the ergodic line are also plotted, which are defined as yx= y2. The intersection of the SNR outage boundary and the ergodic line is defined as the ergodic SNR threshold yth. The ergodic SNR threshold of a protograph-based code only depends on its corresponding decoding threshold over an AWGNchannel. With reference to Figure 19 A, it can be seen that the ergodic SNR threshold of the AR4JA P-LDPC code is smaller than that of the regular- (3, 6) P-LDPC code, but the AR4JA P-LDPC code converges slower than the regular (3, 6) P-LDPC code as yxincreases.

[0097] Accordingly, the AR4JA P-LDPC code may be outperformed by the regular-(3, 6) P-LDPC code due to a larger outage region. Furthermore, both P-LDPC codes may have not excellent performance over BF channels because they cannot converge as1approaches infinity. Figure 19B illustrates the SNR outage boundaries of three RP codes (RP code, IRP1 code, and TRP2 code) and the RC-RP-LDPC code in accordance with embodiments of the disclosure. The four codes have a code rate of 1 / 2 and are transmitted over a BF channel with L — 2. From these plots, it can be seen that for the three conventional RP codes, when the received SNR on information nodes approaches 0, their outage region does not converge, even if the SNR experienced on parity nodes increases. Tn contrast, the RC-RP-LDPC code exhibits convergence as both y-t and y2approach infinity. This suggests that the RC-RP-LDPC code should provide a higher coding gain compared to the prior-art RP codes and may possess superb error performance over BF channels.

[0098] Figures 20A and 20B set out the results of the outage boundary analysis for the conventional RP codes and the RC-RP-LDPC codes for a code rate of 1 / 3 and three fading blocks (i.e., L = 3). ytis employed for the information nodes, while y2and y3are used for the respective blocks of the parity nodes. Based on the plots in Figure 20A, it can be seen that as Yi approaches 0, the outage region of the conventional RP code fails to converge, while the RC-RP-LDPC code was able to achieve convergence for an arbitrary value of yt. This observation further substantiates the superior performance of the RC-RP-LDPC code compared to conventional RP codes over BF channels in the low code -rate scenario. Figure 20B illustrates the simulated plots for the RC-RP-LDPC codes using different parameters K within the protograph. As shown, it can be seen that a RC-RP-LDPC code constructed with a larger K exhibits a lower SNR threshold and faster convergence speed. This verifies the efficacy of the RC-RP-LDPC code-design scheme, affirming the theory that by enlarging the parameter K, this results in a RC- RC-RP-LDPC code with enhanced performance.

[0099] Figures 21A and 21B illustrate the simulated error performance and throughput performance of two proposed punctured RC-RP-LDPC codes. These two punctured RC-RP-LDPC codes have code rates of 3 / 8 and 2 / 5, and both of them arc constructed by puncturing a rate- 1 / 3 RC-RP-LDPC code in accordance with embodiments of the present disclosure. For example, when a rate- 1 / 3 RC-RP-LDPC code with a frame length of 18 bits, containing 6 information bits and 12 parity bits is considered, the resulting punctured RC-RP-LDPC code with a rate of 3 / 8 can be generated by puncturing 2 parity bits in the last two transmission rounds (i.e., P — 1).

[0100] As illustrated in Figure 21A, the two punctured codes have almost the same BER and FER performance as the unpunctured rate- 1 / 3 code, implying that these codes exhibit full diversity. Furthermore, as shown in Figure 2 IB, both the rate-3 / 8 code and the rate-2 / 5 code are able to achieve their theoretical maximum throughputs of T — 0.75 and T = 0.8 , respectively. This suggests that the proposed puncturing scheme can also generate codes with maximum throughput.

[0101] Further simulations were performed on three different puncturing patterns: (i) where the highest-degree VNs are punctured; (ii) the lowest-degree VNs are punctured; and (iii) random VNs are punctured. The resulting plots are illustrated in Figure 21 B and it can be seen that all three patterns yield nearly identical throughput results, signifying that puncturing patterns have little impact on the performance of the RC-RP-LDPC code.

[0102] Figures 22A and 22B illustrate the BER and FER of punctured codes with rates of 13 / 48 and 7 / 24, as generated by puncturing a rate-1 / 4 RC-RP-LDPC code in accordance with embodiments of the disclosure. These punctured codes are transmitted over a BF channel with two fading blocks, i.e. L = 2. From the BER and FER performance plots and the throughput results shown in Figures 22 A and 22B, it can be seen that the proposed punctured codes exhibit full diversity and achieve maximum throughput, respectively. Similarly, it can be observed that both codes were also able to achieve the theoretical maximum throughput as SNR increases when the three different puncturing patterns ae applied to generate both the rate-7 / 24 code and rate- 13 / 48 code.

[0103] In summary, based on the simulation results, it can be said that the puncturing scheme for the RC-RP-LDPC codes not only enables the generation of codes with flexible code rates, but also preserves near-optimum throughput performance and full diversity property.

[0104] Figures 23A and 23B illustrate the WER performance comparison between the MP- IR-HARQ system as described in accordance with embodiments of the present disclosure and the traditional IR-HARQ system. In particular, the Gray-labeled 4-ary phase shift keying (PSK), 8-ary PSK, and 16-ary quadrature amplitude modulation (QAM) are considered, with 2, 3, or 4 coded bits being transmitted in every time slot. As can be seen from Figure 23A, where rate- 1 / 2 RC-RP-LDPC code and L — 2 are assumed, the proposed MP-1R-HARQ system can provide UEP for 4 different data streams and exhibits better WER performance than the traditional IR-HARQ system. Specifically, in the proposed MP-IR-HARQ system, the high- priority data streams 1 and 2 significantly outperform the low-priority data streams 3 and 4 due to the UEP property. Additionally, as the SNR increases, the low-priority data streams 3 and 4 of the proposed MP-IR-HARQ system are able to achieve the same WER performance as the traditional IR-HARQ system due to the successive decoding property. With reference Figure 23 A, where rate- 1 / 3 RC-RC-LDPC code and L = 3 are assumed, it can be seen that a similar WER performance trend can be observed.

[0105] Numerous other changes, substitutions, variations, and modifications may be ascertained by the skilled in the art and it is intended that the present application encompass all such changes, substitutions, variations, and modifications as falling within the scope of the appended claims.

Claims

CLAIMS:

1. A transmitter module for transmitting codewords using an incremental redundancy -hybrid automatic repeat request (IR-HARQ) scheme, the module comprising: a processing unit; and a non-transitory media readable by the processing unit, the media storing instructions that when executed by the processing unit causes the processing unit to: encode, using an encoder module, an information-bit sequence into a codeword using a parity check matrix (PCM) derived from a lifted base matrix of a rate-compatible root-protograph low-density parity-check (RC-RP-LDPC) protograph, wherein the RC- RP-LDPC protograph comprises:K primary root-check connections, each primary root-check connection comprising (A- / ) secondary root-check connections, wherein A is defined as a number of large transmission rounds of the IR-HARQ scheme;K information nodes and at least one set of unique parity nodes, wherein K is defined as a number of information nodes, and the number of information nodes is equal to a number of primary root-check connections; wherein each secondary root-check connection is associated with exactly one information node, the at least one set of unique parity nodes, and a check node corresponding to the type of the secondary root-check connection, and transmit the codeword over the A transmission rounds.

2. The transmitter module according to claim 1, wherein a number of parity nodes in each set of unique parity nodes is equal to the number of primary root-check connections, and wherein the RC-RP-LDPC protograph comprises (L-l) sets of unique parity nodes.

3. The transmitter module according to claim 1 , wherein in each secondary root-check connection, each check node is connected to the exactly one information node through a single edge.

4. The transmitter module according to claims 1 or 2, wherein in each secondary root-check connection, each check node is connected to each set of unique parity nodes through a single or parallel edge.

5. The transmitter module according to claim 1, wherein the RC-RP-LDPC protograph is one of a plurality of RC-RP-LDPC protographs that each correspond to a different coding rate.

6. The transmitter module according to claim 5, wherein each of the plurality of RC-RP-LDPC protographs corresponds to an associated lifted base matrix, and wherein a lifted base matrix derived from a RC-RP-LDPC protograph having a higher code rate is structurally included as a submatrix within a lifted base matrix derived from another RC-RP-LDPC protograph having a lower code rate.

7. The transmitter module according to claim 1 , wherein the transmitting of the codeword over / . transmission rounds further comprises instructions for directing the processing unit to: vary a code rate of the transmission of the codeword by puncturing selected parity bits in the codeword based on a parity-bit proportional puncturing scheme, such that the punctured parity bits are excluded from being transmitted in one or more of (L-l) redundancy rounds.

8. The transmitter module according to claim 7, wherein the parity -bit proportional puncturing scheme comprises instructions for directing the processing unit to: calculate, for a current redundancy round, an error rate associated with a previously transmitted round; select and apply a puncturing pattern associated with a current redundancy round to parity bits corresponding to the current redundancy round, wherein the puncturing pattern specifies parity bits that are to be omitted from being transmitted in the current redundancy round; calculate, for a subsequent redundancy round, a new error rate based on all previously transmission rounds; iteratively repeat the steps of selecting and applying of the puncturing pattern, and the calculating of the new error rate until the new error rate exceeds a predetermined error rate; and in response to the determination that the new error rate exceeds a predetermined error rate, set the puncturing pattern associated with a previously transmitted redundancy round as an optimal puncturing pattern for the parity-bit proportional puncturing scheme.

9. A wireless communication system for implementing a multi level -priority incremental redundancy-hybrid automatic repeat request (MP-IR-HARQ) scheme, the system comprising: a plurality of transmitter modules according to claim 1 , wherein each of the plurality of transmitter modules are configured to transmit codewords to an adaptive modulator; the adaptive modulator being configured to:generate a modulation symbol sequence for the codewords using a modulation scheme selected based on a number of active codewords to be modulated; and transmit the modulation symbol sequence to a receiver module, wherein the receiver module is configured to decode the modulation symbol sequence; a controller module configured to: receive a feedback vector from the receiver module, wherein the feedback vector indicates codewords that remain undecoded by the receiver module; identify transmitter modules associated with the undecoded codewords based on the feedback vector; trigger the identified transmitter modules to transmit a subsequent redundancy round of the respective codewords to the adaptive modulator, whereby the adaptive modulator is configured to generate a new modulation symbol sequence for the received codewords using an updated modulation scheme selected based on an updated number of active codewords, and transmit the new modulation symbol sequence to a receiver module; iteratively repeat the steps of receiving the feedback vector, identifying the transmitter modules, and triggering the transmission of subsequent redundancy rounds of the respective codewords to the adaptive modulator until the feedback vector indicates that all codewords have been decoded.

10. The wireless communication system according to claim 9, wherein each modulation symbol in the modulation symbol sequence is constructed using a priority-based bit-to- symbol mapping scheme that assigns higher-priority codewords to more significant positions in the modulation symbol sequence.

11. A method for transmitting codewords using an incremental redundancy -hybrid automatic repeat request (IR-HARQ) scheme, the method comprising: encoding, using an encoder module, an information-bit sequence into a codeword using a parity check matrix (PCM) derived from a lifted base matrix of a rate-compatible root- protograph low-density parity-check (RC-RP-LDPC) protograph, wherein the RC-RP- LDPC protograph comprises:K primary root-check connections, each primary root-check connection comprising (A- / ) secondary root-check connections, wherein A is defined as a number of large transmission rounds of the IR-HARQ scheme;K information nodes and at least one set of unique parity nodes, wherein K i s defined as a number of information nodes, and the number of information nodes is equal to a number of primary root-check connections;wherein each secondary root-check connection is associated with exactly one information node, the at least one set of unique parity nodes, and a check node corresponding to the type of the secondary root-check connection, and transmitting, using a transmitter module, the codeword over the L transmission rounds.

12. The method according to claim 11, wherein a number of parity nodes in each set of unique parity nodes is equal to the number of primary root-check connections, and wherein the RC-RP-LDPC protograph comprises ( / .- / ) sets of unique parity nodes.

13. The method according to claim 11, wherein in each secondary root-check connection, each check node is connected to the exactly one information node through a single edge.

14. The method according to claims 11 or 12, wherein in each secondary root-check connection, each check node is connected to each set of unique parity nodes through a single or parallel edge.

15. The method according to claim 11, wherein the RC-RP-LDPC protograph is one of a plurality of RC-RP-LDPC protographs that each correspond to a different coding rate.

16. The method according to claim 15, wherein each of the plurality of RC-RP-LDPC protographs corresponds to an associated lifted base matrix, and wherein a lifted base matrix derived from a RC-RP-LDPC protograph having a higher code rate is structurally included as a submatrix within a lifted base matrix derived from another RC-RP-LDPC protograph having a lower code rate.

17. The method according to claim 11, wherein the transmitting of the codeword over L transmission rounds further comprises the steps of: varying a code rate of the transmission of the codeword by puncturing selected parity bits in the codeword based on a parity-bit proportional puncturing scheme, such that the punctured parity bits are excluded from being transmitted in one or more of (L-l) redundancy rounds.

18. The method according to claim 17, wherein the parity-bit proportional puncturing scheme further comprises the steps of: calculating, for a current redundancy round, an error rate associated with a previously transmitted round; selecting and applying a puncturing pattern associated with a current redundancy round to parity bits corresponding to the current redundancy round, wherein the puncturingpattern specifies parity bits that are to be omitted from being transmitted in the current redundancy round; calculating, for a subsequent redundancy round, a new error rate based on all previously transmission rounds; iteratively repeating the steps of selecting and applying of the puncturing pattern, and the calculating of the new error rate until the new error rate exceeds a predetermined error rate; and in response to the determination that the new error rate exceeds a predetermined error rate, setting the puncturing pattern associated with a previously transmitted redundancy round as an optimal puncturing pattern for the parity-bit proportional puncturing scheme.

19. A method for implementing a multilevel -priority incremental redundancy-hybrid automatic repeat request (MP-IR-HARQ) scheme in a wireless communication system, the method comprising: configuring a plurality of transmitter modules to perform the method according to claim 11, wherein each of the plurality of transmitter modules are configured to transmit codewords to an adaptive modulator; generating, using the adaptive modulator, a modulation symbol sequence for the codewords using a modulation scheme selected based on a number of active codewords to be modulated; and transmitting, using the adaptive modulator, the modulation symbol sequence to a receiver module, wherein the receiver module is configured to decode the modulation symbol sequence, receiving, using a controller module, a feedback vector from the receiver module, wherein the feedback vector indicates codewords that remain undecoded by the receiver module; identifying, using the controller module, transmitter modules associated with the undecoded codewords based on the feedback vector; triggering, using the controller module, the identified transmitter modules to transmit a subsequent redundancy round of the respective codewords to the adaptive modulator, whereby the adaptive modulator is configured to generate a new modulation symbol sequence for the received codewords using an updated modulation scheme selected based on an updated number of active codewords, and transmit the new modulation symbol sequence to a receiver module; and iteratively repeating, using the controller module, the steps of receiving the feedback vector, identifying the transmitter modules, and triggering the transmission of subsequent redundancy rounds of the respective codewords to the adaptive modulator until the feedback vector indicates that all codewords have been decoded.

0. The method according to claim 19, wherein each modulation symbol in the modulation symbol sequence is constructed using a priority -based bit-to-symbol mapping scheme that assigns higher-priority codewords to more significant positions in the modulation symbol sequence.

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