WO2021105548A1 - Design of fixed length coding scheme for probabilistic shaping applied to new radio physical layer - Google Patents

Abstract

A method, an apparatus and a computer program relating to a design of fixed length coding scheme for probabilistic shaping applied to new radio (NR) physical layer are disclosed, wherein an initialization of a lookup table with inconstancies is generated by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

Description

Design Of Fixed Length Coding Scheme For Probabilistic Shaping Applied To New Radio Physical Layer

TECHNICAL FIELD

[0001] The examples and non-limiting embodiments relate generally to communications and, more particularly, to a design of fixed length coding scheme for probabilistic shaping applied to new radio (NR) physical layer.

BACKGROUND

[0002] It is known to perform error correction over the physical layer during wireless transmission.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003] The foregoing aspects and other features are explained in the following description, taken in connection with the accompanying drawings, wherein:

[0004] FIG. 1 depicts a probabilistic amplitude shaping (PAS) coding scheme consistent with non-systematic new radio low density parity check code (NR-LDPC).

[0005] FIG. 2 shows an example of a probabilistic lookup table (LUT) with k=4, n=6, m=2 (8-ASK), and R_DM = 2 * 4/6 = 1.33 bits.

[0006] FIG. 3 shows the performance of probabilistic LUT compared to a reference and other existing solutions.

[0007] FIG. 4 shows a coding scheme comprising an add to NR-LDPC encoder hidden bits and non-linear check nodes. [0008] FIG. 5 is a flowchart based on the examples described herein.

[0009] FIG. 6 is an example apparatus configured to implement a distribution matcher based on the examples described herein.

[0010] FIG. 7 is an example method of implementing a distribution matcher based on the examples described herein.

[0011] FIG. 8 is a block diagram of one possible and non limiting system in which the example embodiments may be practiced.

[0012] FIG. 9 illustrates an example system of probabilistic amplitude shaping (PAS), according to one embodiment of the examples described herein.

[0013] FIG. 10 illustrates an example flow diagram of a method, according to an embodiment of the examples described herein.

[0014] FIG. 11 illustrates an example block diagram of an apparatus, according to an embodiment of the examples described herein.

[0015] FIG. 12 illustrates an example parity generator codeword, or shaped symbol sequence block, after puncturing in accordance with at least some embodiments of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0016] The following acronyms and abbreviations that may be found in the specification and/or the drawing figures are defined as follows: 3GPP third generation partnership project

5G fifth generation

5GC 5G core network

5GR17 5G release 17

6G sixth generation

ACM adaptive coding and modulation

AMF access and mobility management function

ASK amplitude shift-keying

B5G beyond 5G

BER bit error rate

BG base graph

BLER block error rate

CQI channel quality indicator

CU central unit

DM distribution matcher

DSP digital signal processor

DU distributed unit

Eb energy per bit eNB (or eNodeB) evolved Node B (e.g., an LTE base station)

EN-DC E-UTRA-NR dual connectivity en-gNB or En-gNB node providing NR user plane and control plane protocol terminations towards the UE, and acting as secondary node in EN-DC EPC evolved packet core

E-UTRA evolved universal terrestrial radio access, i.e., the LTE radio access technology FI control interface between CU and DU control gNB (or gNodeB) base station for 5G/NR, i.e., a node providing NR user plane and control plane protocol terminations towards the UE, and connected via the NG interface to the 5GC I/F interface i.i.d. independent and identically distributed

LDPC low density parity check

LTE long term evolution

LUT look up table

MAC medium access control

MB Maxwell Boltzmann

MCS modulation and coding scheme

MME mobility management entity

Ng or NG new generation ng-eNB or NG-eNB new generation eNB NG-RAN new generation radio access network NR new radio

N/W or NW network

OAI open air interface

OFDM orthogonal frequency-division multiplexing

PAS probabilistic amplitude shaping

PDA personal digital assistant

PDSCH physical downlink shared channel

PHY physical layer

PDCP packet data convergence protocol

PMF probability mass function

QAM quadrature amplitude modulation

RAN radio access network

RLC radio link control

RRC radio resource control

RRH remote radio head

RU radio unit

Rx or RX receiver SI interface between the LTE RAN and evolved packet core (EPC)

SDAP service data adaption protocol

SGW serving gateway

SMF session management function SNR signal noise ratio

Tx or TX transmitter

UE user equipment (e.g., a wireless, typically mobile device)

UPF user plane function

X2 interface between two eNodeBs in an LTE network

Xn interface defined between two NG-RAN nodes

[0017] The examples described herein relate to 5G/NR and coding, in particular PAS (Probabilistic Amplitude Shaping) coding schemes. The examples focus on the design of a distribution matcher (DM) mechanism. Look Up Tables (LUTs) with inconstancies are generated, whereby a single output is assigned to multiple inputs. The examples described herein adapt a PAS algorithm for fiber systems for use in future NR systems. The examples herein address the fact that QAM constellations have a non-optimal distributions with respect to maximizing the mutual information (throughput). The examples herein describe a specific hierarchical LUT based DM, with the goal to get a distribution close to an optimum one with a limited size of the input data blocks. This can be seen as a prerequisite for a typical NR scheduler with short data packets. Due to short data block length the LUT mapping ends in some cases in the same output codeword so that the decoder has to resolve this issue, which is then included into the already available decoder in one or more ways. As there are only a limited number of overlapping codewords the corresponding performance loss is small as well.

[0018] Capacity-approaching performance can be attained by a coded modulation if two conditions are satisfied: 1. The error-correcting code and the modulation should show a large coding gain. Here the coding gain refers to resilience to additive noise. The coded modulation codewords should be well separated in the Euclidean space in order to avoid errors due to additive noise. 2. The modulation exhibits a cost per bit, known as the average energy per bit Eb. The modulation in the Euclidean space should be as spherical as possible to minimize the energy cost Eb.

[0019] Coding structures such as low-density parity-check codes (LDPC), polar codes, and turbo codes are well understood nowadays in Coding Theory and are examples of error-correcting codes with excellent coding gains. Hence, we may consider that the first condition stated above can be easily satisfied. However, the spherical shaping of a modulation was still an open problem until the recent discovery of Probabilistic Amplitude Shaping (PAS). PAS has been introduced in the context of versatile and flexible optical networks where the net information rates shall be optimized and as close to the theoretical limits as possible. Engineers had two options for shaping, whether the modulation is directly built with a geometrical spherical shape (non-uniform constellation) or the modulation symbols are given a spherically-shaped probability distribution (non-uniform probability distribution). The second method appears to be easier for practical implementations. The modulation symbols are made non- equiprobable with a distribution that mimics a discrete Gaussian distribution. This shaping method based on a non- uniform probability distribution of modulation symbols is called PAS. The discrete Gaussian-like distribution to be achieved or approached by the modulation symbols, called Maxwell-Boltzmann (MB) distribution, is given by probability masses that are proportional to exp (-ʋ *|s|^Λ2), where s is a symbol and ʋ is an MB-distribution parameter. The MB distribution applies only on the symbol amplitude due to the IsI in its expression, this explains the word Amplitude in the PAS abbreviation. The symbol sign is left to be free, i.e. +1 and -1 are equiprobable for a given amplitude.

[0020] The distribution matcher (DM) is a key component of the PAS design. The goal of the DM is to transform a uniformly distributed flow of bits and make it match to a desired MB distribution. A small deviation from the optimal MB distribution at the output of the distribution matcher leads to important loss in performance. Most of the coding schemes proposed in the literature for DM are optimal for very long length and are not implementable in practice. The examples herein describe a new fixed length DM coding structure relevant for PAS applied to 5G NR-LDPC. The proposed solution achieves near-capacity (optimal) performance and is implementable in practice.

[0021] Features described herein include building a practical coding scheme for modulations to achieve the best possible performance on a digital transmission channel. A common measure for the quality of the digital transmission is the bit error probability P_eb as a function of the signal-to- noise ratio SNR. For a given transmission rate R expressed in bits per channel use (bpcu) or in bits per real dimension, the signal-to-noise ratio should be large enough to let the system guarantee a vanishing error probability, e.g. P_eb=10^-6. Information Theory founded by C.E. Shannon established limits that cannot be exceeded by the rate R and the signal-to-noise ratio SNR. According to Information Theory, the highest achievable information rate in presence of additive white Gaussian noise, referred to as channel capacity, is C=1/2 log₂(1+SNR) bpcu. At fixed SNR, we must have R<C to let P_eb go to zero. At fixed rate R=C, we must have SNR > (2^2R-1) for a vanishing P_eb· Thus, the capacity formula gives a maximal achievable rate or equivalently a minimal achievable SNR. Our target is to build a coding scheme such that our transmission system achieves a signal-to-noise ratio and a transmission rate as close as possible to Shannon limits, i.e. a capacity- approaching system.

[0022] In the context of LTE and 5G communications the net information rates are to be optimized and as close to the theoretical limits as possible. In order to reach the theoretical limits, constellation shaping is used to approach the Shannon limit. An attractive solution to achieve this limit is the Probabilistic Amplitude Shaping (PAS) scheme. PAS was first proposed for optical communications. A scheme has been proposed to adapt PAS to an NR-LDPC coding scheme in Patent Application Number: PCT/FI2019/050290. The block diagram of this scheme is shown in FIG. 12 (FIG. 12 corresponds to FIGURE 2 of PCT/FI2019/050290). PCT/FI2019/050290 is incorporated herein by reference in its entirety.

[0023] FIG. 12 illustrates an example parity generator codeword, or shaped symbol sequence block, after puncturing in accordance with at least some embodiments of the present invention. Shaped symbols are present in the block as the information bits. Here n_LDPC is the length of the LDPC coded block, and k_LDPC is the number of information bits going into the LDPC encoder. As can be seen, the encoded block comprises, after the puncturings, as parity bits the sign bits and also extra parity bits, which are not signs of any amplitudes/symbols. The number of the extra parity bits is given by. For transmission the extra parity bits may be mapped to at least one QAM symbol, such that the number of these non- shaped QAM symbols is given by

The number of extra symbols is given by the number

of bits divided by m_R. Indeed, m_R — 1 bits are used to create an amplitude and one bit is used as a sign, so a symbol is defined by m_Rbits.

[0024] FIG. 1 depicts a probabilistic amplitude shaping (PAS) coding scheme 1000 consistent with non-systematic new radio low density parity check code (NR-LDPC). The key component of this system is the distribution matcher (DM) 1002 [Refer to Schulte, P.; Bocherer, G.: Constant Composition Distribution Matching. IEEE Trans. Inf. Theory, Dec 2015]. This device takes U₁ uniformly distributed input bits and generates V₁ symbols belonging to the set A := {A₁,A₂,...,AM } where M := 2^m-1 and m denotes the number of bits mapped to the final (real-valued) constellation. The DM 1002 imposes a probability distribution P_A(A_i) on the symbols, which can be selected such that the information-theoretic capacity is maximized. The rate of the DM 1002 is defined as

[0025] Ideally, the distribution matcher 1002 yields R_DM ≈ H(A), where H(A) denotes the entropy of the output distribution. If R_DM < H(A) then there is a rate loss leading to performance degradation.

[0026] R_DM is the rate of the distribution matcher 1002. U₁ is the number of input bits. V₁ is the number of output symbols. m_R is defined as log₂ (SizeQAM). The distribution matcher

1002 generates 2^mR-1 different amplitudes and m_R — 1 bits are associated to each amplitude. The total system generates the real or imaginary part of an 2^2mR -QAM. k_LDPC is the number of information bits going to the NR-LDPC encoder 1004 and n_LDPC is the length of the NR-LDPC block code. R_LDPC is the rate of the parity generator 1004 (NR-LDPC code). 3GPP's NR-LDPC parity check matrices are quasi cyclic, i.e. a row of this matrix follows from a cyclic right shift of the previous row in submatrices of size Zc*Zc.

[0027] In order to fully take advantage of the PAS coding scheme 1000, the design of the distribution is a key point. Consider an amplitude shift-keying (ASK) modulation with M real symbols centered around the origin. The distribution matcher 1002 can be implemented, and good performance can be achieved for instance if very long sequences of bits are treated, and one method that has been proposed in [Schulte, P.; Bocherer, G.: Constant Composition Distribution Matching. IEEE Trans. Inf. Theory, Dec 2015] is to use a variant of arithmetic coding to generate constant composition codes that closely approach H (A). This approach has however the drawback that it is not easily implementable for high-speed wireless communication systems requiring a massive amount of parallelization. Also, to be near-optimal those methods required a very large number of information bits. Therefore an elegant solution is used to build a distribution matcher 1002 with small complexity and compliant with the number of bits at the input of the NR-LDPC code 1004. The examples herein describe a solution based on lookup with inconstancy to generate non-uniform ASK symbols such that near-capacity performance is attained with low implementation complexity.

[0028] The PAS coding scheme is mainly studied for optical communications. Refer, for example, to Schulte, P.; Bocherer, G.: Constant Composition Distribution Matching. IEEE Trans. Inf. Theory, Dec 2015. In the release of the world's first 6G white paper [Key drivers and research challenges for 6G ubiquitous wireless intelligence, https://www.oulu .fi/6gflagship/news/6g-white-paper (last accessed November 12, 2019)], PAS has been recognized as one of the key enablers/drivers of 6G.

[0029] The assignee of the examples herein proposed in U.S.

Patent Application No. 16/248234 (hereinafter "US16/248234"), a PAS coding system that can be applied to narrowband (e.g. flat fading channels within each OFDM sub-carriers) in the context of the needs of the 3GPP standard for 5G. US16/248234 is incorporated herein by reference in its entirety.

[0030] In PCT/FI2019/050290, the assignee of the examples herein proposed an enhanced probabilistic shaping scheme consistent with non-systematic 5G new radio LDPC codes. PAS coding scheme was only defined with systematic parity generator LDPC codes. An adapted scheme to non-systematic codes is proposed. It is compared to the standard adaptive coding and modulation (ACM) as defined in 3GPP 38.214 Table 5.2.2.1-2. The proposed PAS coding scheme outperforms from at least 1.5 dB the performance of the ACMs with uniform signaling. A PAS coding scheme for 5G has also been proposed using polar codes (Huawei Munich) [0. Iscan, R. Bohnke, W. Xu, "Probabilistic shaping using 5G new radio polar codes", IEEE Access, Feb. 2019.]. They also proposed a design of DM based on arithmetic coding [M. Pikus, W. Xu , and G. Kramer, "Finite- Precision Implementation of Arithmetic Coding Based Distribution Matchers", https://arxiv.org/pdf/1907.12066.pdf, Jan 19.]

[0031] The examples described herein provide for the design of a new structure of DM coding scheme for probabilistic shaping. The solution is approaching near-optimal capacity. The examples described herein are based on Look Up Tables (LUTs) with inconstancies, i.e. non-invertible LUTs wherein a single output may be assigned to multiple inputs.

[0032] The first part of the proposed solution involves creating a LUT based on a one-to-one mapping where k source symbols are assigned to n ouput symbols, where k > n. The aim is to approach as far as possible the MB distribution at the output. Then, the non-invertible (probabilistic) LUT is built. Its aim is also to shape (or match) perfectly the output probability distribution R_DM = H(A)= H(MB). This method allows construction of a look up table that fulfills all the distribution matcher constraints. This LUT is not fully invertible. The error correcting decoder can solve this ambiguity. To solve the ambiguities created by the probabilistic LUT, side information or parts of information, that are not sent through the channel, are hidden in the 5G NR-LDPC coded information and can be retrieved after decoding.

[0033] The examples described herein based on LUTs are fixed- length wherein the number of amplitudes generated at the output of the distribution matcher is fixed. Previously the best solution was variable length, and this is an issue regarding the implementation development. In the examples described herein, there is no rate loss and the matching to MB distribution is perfect. Therefore, the examples described herein show outstanding performance compared to the one proposed in the literature.

[0034] The two following aspects are described herein: 1) Implementation point of view - The proposed algorithm is highly parallelizable and exhibits near optimal capacity performance for a limited number of input bits; 2) Standard point of view: The resulting LUT is used at the transmitter to shape a uniform distribution into the desired MB distribution and also at the receiver side to decode and retrieve the original data.

[0035] Description of the Algorithm

[0036] Let k denote the number of bits at the matcher input and n denote the number of bits at the matcher output. It is assumed that input bits are i.i.d. and Bernoulli(1/2). The task of the matcher is to make the distribution non-uniform at its output. The following vocabulary is used:

[0037] Binary digits or bits are the main elements handled by the distribution matcher (DM). Input bits are called b = (b₁b₂ ...b_k) and output bits are calledc= (c₁ c₂ ...c_n). A symbol is a group of m consecutive bits at the DM output. The word c of n bits at the DM output is called a codeword. This is a word belonging to the codebook used by the DM. A codeword c includes n/m symbols. It is assumed that m divides n.

[0038] 1 - Initialization of the LUT parameters. The DM codebook has 2^k codewords which is eguivalent to

symbols. Each symbol is being converted into an amplitude for a 2^m+1-ASK modulation. Let {p₁,p₂,...,p₂ ^m} be a Probability Mass Function (PMF) to be approximated by the DM output PMF. Define S_t = [p_iS],i= 1...2^m, and ensure that

[0039] For each i,i= 1...2^m — 1, select S_i random symbol positions N_i among the S, where N_i is a subset of {1,2,...,5} and |N_i|=S_i. The remaining positions N_2m correspond to the remaining S_2m symbols. Finally, for all i, replace the m bits of the symbols in positions N_i by the m-bit representation of the index i. [0040] Now the codebook is built and the DM is ready to read k input bits and output n bits with PMF that approximates as well as possible the distribution {p_1,p₂,..., p₂ ^m}· Taking 5 large enough, i.e. k and n large enough, improves the accuracy of the output PMF.

[0041] The subsets N₁, N₂, ..., N_2m form a partition of {1,2,...,S} .If this partition results in equal codewords then the random selection of N_i's should be repeated. Hence, the codebook is guaranteed to be invertible.

[0042] Without any loss of generality, in the sequel, we are presenting the construction of a fixed-length DM for 8-ASK modulation (256-QAM). The DM is based on a lookup table (LUT) of size 256 words. Each word has 10 bits which is equivalent to 5 symbols of 8-ASK. Here, the LUT is represented by a table of 256 rows and 5 columns. The 5 amplitudes are labeled by symbols 0, 1, 2, and 3, each symbol carries 2 bits (at the modulation level).

[0043] The rate of this DM is bits per

ASK amplitude.

[0044] After a quick optimization it is found that a DM of rate R_DM = 1-6 should match as much as possible the following Maxwell-Boltzmann (MB) distribution: P_MB(0) = 0.4995, P_MB(1) = 0.3250,P_MB (2) = 0.1376,P_MB (3) = 0.0379.

[0045] The entropy H_MB of the above PMF is H_MB = 1.6 bits. We expect that the entropy H of the constructed LUT be slightly greater than 1.6 (R_DM ≤ H). The total number of symbols in the LUT is S = 256 * 5 = 1280 symbols. The frequency of the 4 symbols 0,1, 2, 3 in the LUT should be S_MB [i]= P_MB(i)*S, which is found to be equal to

S_MB [0]= 639 S_MB [1]= 416 S_MB [2]= 176 S_MB [3]= 49.

[0046] Then, the target is to build a DM table such that the effective frequency S[i] is as close as possible to S_MB [i], i= 0,1,2,3. In all cases,

S[0]+ S[1]+ S[2]+ S[3]= S = 1280.

[0047] A trivial approach is to write a sequence of 630 symbols at 0, 416 symbols at 1, 176 symbols at 2, 49 symbols at 3 and then make random permutations of the 1280 symbols such that the 256x5 table is invertible. Given the high number of Os and Is, the probability of getting an invertible table is extremely low, i.e. it never happened after a large number of random instances. In fact, for S [0]=639, S[1]=416, S[2]=176, and S[3]=49 it is proven within this description that such an invertible LUT does not exist. Firstly, start by building an invertible LUT with the best S[i], i=0,1,2,3. The proposed construction is applied directly on the 5 symbols of a LUT codeword. Hence, results derived from this construction are valid for any other method of LUT construction.

[0048] 2 - The optimal invertible length-256 LUT A LUT codeword is written in a vector form or in integer form as = (X₀,X₁,X₂,X₃,X₄)= X₀ + X₁M + X₂M² + X₃M³ +X₄ ⁴ where M=4 in this construction. A symbol X_i takes values in{0,1,2,3}.The codeword X can be represented as a vector of 5 symbols or simply as an integer from 0 to 45-1=1023. A list of all possible 1024 codewords is built. The LUT is a sub- table of 256 codewords selected among the 1024 in the total list. In this way, the construction itself guarantees that a 256-length LUT is always invertible because all integers X₀ + X₁M + X₂M² + X₃M³ + X₄M⁴ in the list are distinct. Now the LUT invertibility is not an issue anymore. However, the matching should be tuned to make S[i] as close as possible to S_MB [i], i= 0,1, 2, 3.

[0049] The first step is to generate a list of all possible 1024 codewords sorting according to a special alphabetical order: in descending order of number of Os. Indeed, the MB distribution privileged the number of Os. If the number of Os is identical in two codewords, then sort in descending order of number of Is. Again, if the number of Is is identical in two codewords then sort in descending order of number of 2s. Finally, if the number of 2s is identical in two codewords then sort in descending order of number of 3s.

[0050] In order to maximize the number of 0, we consider in a first time, the first 256 rows of this sorted list of size 1024.In this way, we create a LUT of length-256 with frequencies S[0]= 635,S[1]= 295,S[2]= 205,and S[3]= 145. The table below shows this association:

[0051] This initial length-256 LUT should be modified to reduce the number of 2s and 3s, i.e. mainly increase the number of Is.

[0052] The initial LUT is tuned to increase S[1], and decrease both S[2] and S[3] by bringing codewords from the remaining part of the list of size 1024. The frequency distribution of the second length-256 LUT is given by the third row of the next table.

[0053] This second LUT is the best invertible length-256 LUT in terms of matching S[i] to S_MB [i]. It is clear that the limitation comes from the codeword length. Five symbols per codeword do not allow to guarantee invertibility while reducing the gap between the attained frequency and Maxwell- Boltzmann frequency.

[0054] 3 - The optimal non-invertible (probabilistic) length-256 LUT. The symbols distribution of the second LUT is still too different from the Target MB distribution. The second LUT is tuned to decrease S[3] and increase S[0] and S [1]. For this purpose, 493s are turned into Os and 22 3s are changed in Is. The frequency distribution of the third length-256 LUT is given by the fourth row of the next table.

[0055] By changing 71 symbols, it is possible to almost perfectly reach the target distribution and there is no rate loss, R_DM = 1.6= H(MB)≈ H(LUT₃).

[0056] In order to achieve the distribution of the third LUT, some LUT output is merged, i.e. some LUT inputs have the same output. This LUT is thus not fully invertible: A single output may be assigned to multiple inputs. The third LUT is named Probabilistic/Stochastic Look Up Table due to its non- invertibility .

[0057] Consider the example shown in FIG. 2. FIG. 2 shows an example of a probabilistic look up table (LUT) 200 with k=4, n=6, m=2 (8-ASK), and R_DM = 2 * 4/6 = 1.33 bits. In order to have R_DM = 1.33= H(MB) ≈ H(LUT_example), two symbols 3s are changed in Is. After this operation the LUT input labels '0000' and ' 0110 ' have the same output label ' 00 1 ' , in the same way the input labels '1110' and '1111' have the same output label ' 110'.

[0058] The main challenge with Probabilistic LUTs is to find a way to remove ambiguities due to labels merging. The performance of the probabilistic 256-LUT based on non-linear check-nodes is shown FIG. 3. In particular, FIG. 3 shows the performance of probabilistic LUT compared to a reference and other existing solutions. FIG. 3 plots the bit error rate (BER) against the energy per symbol to noise power spectral density (E_s/N₀ (dB)). Notice in FIG. 3 that the performance of the prob. 256-LUT (item 306) is very close to the performance of the ideal DM (item 302). The performance of the prob. 256-LUT 306 is closer to the ideal DM 302 than the former proposed solution based on variable length coding (item 304).

[0059] 4 - Removing ambiguities with non linear-check nodes.

In this part, an example is provided to remove ambiguities due to labels merging in the probabilistic LUT. The example presented here is based on non-linear check nodes and hidden bits (side information).

[0060] In the example embodiment, the probabilistic LUT has

256 words. Each word has 10 bits (output). Some words are repeated two or three times in the probabilistic LUT. Let π₀₀ be the probability of an original LUT word, i.e. π₀₀ is the number of words in the LUT which have not been changed to match the MB distribution divided by 256:

[0061] If a word is repeated twice in the LUT of course the two copies are equiprobable. Similarly, if a word shows up in 3 rows in the LUT, these three rows are equiprobable. In all cases, (1— π₀₀) is the probability that a word appears more than once in the LUT.

[0062] The table below, corresponding to Example 1, shows three identical rows at the output of the probabilistic LUT.

Example 1: 3 identical rows at the output of the probabilistic

LUT

[0063] a_i ∈ F₂, i = 1 ... 10. Row 1 is assumed to correspond to the exact information (exact input). Its apriori is π₀₀. The two other rows have apriori

[0064] Suppose that three different LUT indexes have the same output word, i.e. two LUT output words were modified (the first word is the original one) to match the Maxwell Boltzmann distribution. An apriori is associated to each LUT index. The highest probability, π₀₀ , is associated to the original index. From this assumption, the probability of LUT words which have been changed is ( 1- π₀₀ ) . In this example, two LUT words were modified, and they are equiprobable, then the probability of these words is

[0065] The hidden bits may not be transmitted on the channel. The coding scheme is described in FIG. 4. In particular, FIG. 4 shows a coding scheme 400 comprising an add to NR-LDPC encoder hidden bits and non-linear check nodes. The NR-LDPC encoder considers the parity bits b_i (including, as shown in FIG. 4, b_{1 ,} b₂ , b₃ , b , and b₅ ) are not sent through the channel, extra information is hidden with the parity bits b_i.

[0066] In an example, two hidden bits h₁ and h₂ are generated: h₁ = h₂ = 0, the original label is sent (corresponding to the 1st row in Example 1). h₁ = 0 and h₂ = 1, the first merged label is sent (corresponding to the 2nd row in Example 1). h₁ = 1 and h₂ = 0, the second merged label is sent (corresponding to the 3rd row in Example 1). h₁ = 1 and h₂ = 1, is forbidden, only 3 rows in the LUT can be merged. [0067] Then, new check nodes 402 are created to sum the b_i parity bits and the hidden bits. These new parity bits contain information on the previous parity bits b_i and on the hidden bits. It is important to notice that the previous parity bits b_iare not transmitted, It is important to notice that for this step, the NR-LDPC encoder is not modified. An external box can be added to create the new parity bits c_i .

[0068] Consider the construction illustrated FIG. 4. This is the Tanner graph representation of the code. The circles represent the variable nodes (in this subgraph of the code the parity bits are represented). Each of them corresponds to a bit of the codewords. The square (rectangular) nodes describe the parity-check equations (constraints). This is the baseline Tanner graph that is usually used for NR-LDPC decoding.

[0069] Notice that the information of the first three parity bits b_i are linked to h₁ and the two last parity bits b₄ and b₅ are linked to h₂ . It's a very simple and naive way to create the graph: repetition coding. This can be seen as a repetition code: h₁ is added to b_{1 ,} b₂ and b ₃ , i.e. the information is replicated three times and h₂ to b₄ and b₅ . The hidden bits contain the information to remove ambiguities on LUT merged labels. Therefore, the information they contain is very important to remove ambiguities.

[0070] In order to have a better protection of the hidden bits, an extra-parity bit 412 can be sent. This extra-parity adds some extra information on the hidden bits. In order to avoid a modification of the NR-LDPC encoder, this step can be skipped, i.e., this extra information is not mandatory to ensure good performance, In fact, hidden bits are already protected by a non-linear check node 410. This non-linear check contains the apriori on hidden bits and have to be implemented at the NR-LDPC decoder level. Therefore, an extra information is needed at NR-LDPC decoder side to realize this method based on non-linear check node 410.

[0071] The apriori on the non-linear check node 410 is given by the table:

Extr h₁ and Extr h₂ are extrinsic information needed at the NR- LDPC decoder part. This solution allows removal of a large proportion of ambiguities and reaches very good performance (see FIG. 3.).

[0072] 5 - General case: Flowchart of the proposed solution.

FIG. 5 is a flowchart 500 based on the examples described herein. At 502, the process starts. At 504, the used modulation is SizeQAM, and the rate of the DM R_DM=2*k/n. Input bits are called b = (b₁ b₂ ... b_k) and output bits are called c = {c₁ c₂ ... c_n) . At 506, the step is to find the optimal MB distribution, P_MB, given R_DM , and Initialize the LUT parameters (total number of symbols S in the LUT and number of each symbols S_MB given P_MB ) . At 508, the step is to fill the LUT with codeword enumeration from 0 to 2ⁿ sorted by descending order of 0s.

[0073] At 510, the method determines whether there is a perfect match with the number of symbols S_MB set by P_MB . If at 510 the determination is positive (e.g., "Yes"), then at 512, parity bits b_i are sent through the channel and the process ends at 524.

[0074] If, on the other hand, the determination at 510 is negative, then the method proceeds to 514 to merge some symbols to perfectly match the MB distribution. At 516, the method proceeds to, given the number of changed symbols and merges labels, define apriori on each LUT index. Apriori are calculated given π₀₀ : the number of words in the LUT which have not been changed to match the MB distribution divided by the length of the LUT. At 518, the method proceeds to generate two hidden bits h₁ and h₂ given the fact that the LUT index is merged or not, wherein h₁ = h₂ = 0, the original label is sent, h₁ = 0 and h₂ = 1, the first merged label is sent, and h₁ = 1 and h₂ = 0, the second merged label is sent. At 520, the method proceeds to sum the b_i parity bits and the hidden bits to create new parity bits c_i. At 522, new parity bits c_i are sent through the channel. At 524, the method ends.

[0075] Use of the constructed LUTs at the transmitter and receiver

[0076] The resulting LUT is used at the transmitter to shape a uniform distribution into the desired MB distribution and also at the receiver side to decode and retrieve the original data.

[0077] 1 Transmitter side . At the transmitter side, the probabilistic LUT needs to be known to process the matching to the MB distribution. For example, one LUT can be associated to one MB parameter which depends on the CQI index feedback from the RX. The LUT should be updated each time the MB is updated given the channel condition. For more details on the MB refreshment please refer to the filed specification of US16/248234, which is incorporated herein by reference in its entirety, and PCT/FI2019/050290, which is incorporated herein by reference in its entirety. In particular, the MB refreshment is discussed in US16/248234 in Fig. 1 and description of Fig. 1 at paragraph [0027], Fig. 2 and description of Fig. 2 at paragraph [0030], and Fig. 3 and description of Fig. 3 at paragraph [0044].

[0078] FIG. 9 illustrates an example system 900 of probabilistic amplitude shaping (PAS), according to one embodiment of the examples described herein. (FIG. 9 corresponds to or is similar to Fig. 1 of US16/248234, and the description of FIG. 9 herein corresponds to or is similar to the description in paragraph [0027] of US16/248234). In an embodiment of the examples described herein, once the MB- parameter ʋ has been chosen for the given estimated fading factor, the process may continue according to the example system 900 of FIG. 9. The distribution matcher 901 depicted in FIG. 9 may include a coding process that can transform the uniform distribution into the given shaped distribution depending on the chosen ʋ parameter. Then, a parity generator 902 may apply a uniform parity, which is used as a sign +1 or -1, to create the symmetric part of the shaped constellation. In certain embodiments, the modulated data may be sent through the fading channel and transmitted to a receiver. The distribution matcher 901 of FIG. 9 may function similar to the distribution matcher 608 shown in FIG. 6 and/or the distribution matcher 1002 shown in FIG. 1. The parity generator 902 of FIG. 9 may function similar to the parity generator 1004 shown in FIG. 1.

[0079] FIG. 10 illustrates an example flow diagram of a method, according to an embodiment of the examples described herein (FIG. 10 corresponds to or is similar to Fig. 2 of US16/248234, and the description of FIG. 10 herein corresponds to or is similar to the description in paragraph [0030] of US16/248234). In one embodiment of the examples described herein, the method of Fig. 10 may include, at 1010, estimating a flat fading channel for one constellation in a communications system (e.g., 5G system). In one example, the one constellation may be 256QAM or 1024QAM, for instance. In other examples, the one constellation may include QPSK, 16QAM, or 64QAM. The method of Fig. 10 may also include, at 1020, selecting a distribution parameter of the constellation depending on one or more flat fading channel(s). When the flat fading channel has been estimated for the constellation, then the selecting 1020 may include selecting the distribution parameter for the constellation based on the estimated flat fading channel. According to an embodiment, the distribution parameter may include a Maxwell-Boltzmann (MB) distribution parameter. In one example, the MB distribution may be given by probability masses that are proportional to exp (-ʋ*|s|^Λ2), where s is a QAM symbol and ʋ is the MB distribution parameter. The method may further include, at 1030, transforming the uniform distribution of the constellation into a shaped distribution using the selected distribution parameter (e.g., MB distribution parameter) to produce modulated data. In one example, the shaped distribution may include a spherically shaped probability distribution. According to certain embodiments, the method may also include, at 1040, applying a uniform parity, such as +1 or -1, to create a symmetric part of the shaped distribution. The method may then include, at 1050, passing the modulated data through a fading channel and, at 1060, transmitting the modulated data to a receiver.

[0080] FIG. 11 illustrates an example block diagram of an apparatus, according to an embodiment of the examples described herein (FIG. 11 corresponds to or is similar to Fig. 3 of US16/248234, and the description of FIG. 11 herein corresponds to or is similar to the description in paragraph [0044] of US16/248234). In one embodiment of the examples described herein, apparatus 1110 may be controlled by memory 1114 and processor 1112 to estimate a flat fading channel for one constellation in a communications system (e.g., 5G system). In one example, the one constellation may be 256QAM or 1024QAM, for instance. In other examples, the one constellation may include QPSK, 16QAM, or 64QAM. According to an embodiment, apparatus 1110 may be controlled by memory 1114 and processor 1112 to select a distribution parameter of the constellation depending on one or more flat fading channel(s). When the flat fading channel has been estimated for the constellation, then apparatus 1110 may be controlled by memory 1114 and processor 1112 to select the distribution parameter for the constellation based on the estimated flat fading channel. In one embodiment, the distribution parameter may include a Maxwell-Boltzmann (MB) distribution parameter. In one example, the MB distribution may be given by probability masses that are proportional to exp (-ʋ*IsI^Λ2), where s is a QAM symbol and ʋ is the MB distribution parameter. According to an embodiment, apparatus 1110 may be further controlled by memory 1114 and processor 1112 to transform the uniform distribution of the constellation into a shaped distribution using the selected distribution parameter (e.g., MB distribution parameter) to produce modulated data. In one example, the shaped distribution may include a spherically shaped probability distribution. According to certain embodiments, apparatus 1110 may also be controlled by memory 1114 and processor 1112 to apply a uniform parity, such as +1 or -1, to create a symmetric part of the shaped distribution. In an embodiment, apparatus 1110 may then be controlled by memory 1114 and processor 1112 to pass the modulated data through a fading channel, and to transmit the modulated data to a receiver, which can demodulate the data based on the selected distribution parameter. In some embodiments, apparatus 1110 may also include or be coupled to one or more antennas 15 for transmitting and receiving signals and/or data to and from apparatus 1110.

[0081] Also, an item processing the sum of the original parities and the hidden information generated to identify the merging of LUT labels should be added to the NR-LDPC decoder. The apriori on the merges labels should be constructed.

[0082] 2 - Receiver side. At the receiver side, the probabilistic LUT should be known to decode and retrieve the original data. For example, the same LUT should be used at the transmitter and receiver side. It is working as communicating the choice of MCS from the TX to the RX. The LUT table depends on the MB parameter. Then, in one example, the LUT can be communicated by the TX to the RX through PDCSH. The LUT should be updated each time the MB is updated given the channel condition. For more details refer to US16/248234 and PCT/FI2019/050290 or to the previous paragraphs 0078-0080. Also, the apriori on the merged labels should be known at the decoder of the NR-LDPC to identify the hidden bits and retrieve the original information.

[0083] The examples described herein have exhibited excellent performance, and enable a practical PAS coding scheme. Distribution matcher coding schemes proposed in the literature are not implementable in practice, whereas the examples described herein are implementable in practice, designed. The solution is applicable at least for 5GR17, B5G and 6G. The algorithm of PAS coding scheme for non-systematic codes may be implemented with OAI (Open Air Interface). [0084] FIG. 6 is an example apparatus 600 configured to implement a distribution matcher based on the examples described herein. The apparatus 600 comprises a processor 602 a non-transitory memory 604 including computer program code 606, wherein the memory 604 and the computer program code 606 are configured to, with the at least one processor 602, cause the apparatus 600 at least to perform: generate an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher 608, to a plurality of output labels of the distribution matcher 608, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel 622 used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

[0085] The example apparatus 600 provides the lookup table to the transmitter 612 and/or the receiver 624. The transmitter 612 encodes the input 601 provided to the distribution matcher 608 using the encoder 614. The transmitter 612 transmits the encoded data to the receiver 624 over the channel 622 (e.g., PDSCH) via transmission circuitry 616. The receiver 624 decodes the encoded input data to generate the input data 601, or an approximation of the input data 601 using the decoder 626. The receiver 624 receives the encoded data over the channel 622 via the receiver circuitry 628.

[0086] In some examples, the transmitter 612 and receiver 624 may each be an electronic device such as a mobile smartphone or other user equipment (UE). In other examples, the transmitter 612 and receiver 624 may be a base station. While in the example shown in FIG. 6, the apparatus 600 is separate from the transmitter 612 and receiver 624, in other examples the apparatus 600 may reside within the transmitter 612 (e.g., such that the LUT is communicated by the TX 612 to the RX 624 through physical downlink shared channel (PDSCH)) or the receiver 624.

[0087] FIG. 7 is an example method 700 of implementing a distribution matcher based on the examples described herein. At 702, the method includes generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols. At 704, the method includes wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception. At 706, the method includes wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols. [0088] Turning to FIG. 8, this figure shows a block diagram of one possible and non-limiting example in which the examples may be practiced. A user equipment (UE) 110, radio access network (RAN) node 170, and network element(s) 190 are illustrated. In the example of FIG. 8, the user equipment (UE) 110 is in wireless communication with a wireless network 100. A UE is a wireless device that can access the wireless network 100. The UE 110 includes one or more processors 120, one or more memories 125, and one or more transceivers 130 interconnected through one or more buses 127. Each of the one or more transceivers 130 includes a receiver, Rx, 132 and a transmitter, Tx, 133. The one or more buses 127 may be address, data, or control buses, and may include any interconnection mechanism, such as a series of lines on a motherboard or integrated circuit, fiber optics or other optical communication equipment, and the like. The one or more transceivers 130 are connected to one or more antennas 128. The one or more memories 125 include computer program code 123. The UE 110 includes a module 140, comprising one of or both parts 140-1 and/or 140-2, which may be implemented in a number of ways. The module 140 may be implemented in hardware as module 140-1, such as being implemented as part of the one or more processors 120. The module 140-1 may be implemented also as an integrated circuit or through other hardware such as a programmable gate array. In another example, the module 140 may be implemented as module 140-2, which is implemented as computer program code 123 and is executed by the one or more processors 120. For instance, the one or more memories 125 and the computer program code 123 may be configured to, with the one or more processors 120, cause the user equipment 110 to perform one or more of the operations as described herein. The UE 110 communicates with RAN node 170 via a wireless link 111. [0089] The RAN node 170 in this example is a base station that provides access by wireless devices such as the UE 110 to the wireless network 100. The RAN node 170 may be, for example, a base station for 5G, also called New Radio (NR). In 5G, the RAN node 170 may be a NG-RAN node, which is defined as either a gNB or an ng-eNB. A gNB is a node providing NR user plane and control plane protocol terminations towards the UE, and connected via the NG interface to a 5GC (such as, for example, the network element(s) 190). The ng-eNB is a node providing E-UTRA user plane and control plane protocol terminations towards the UE, and connected via the NG interface to the 5GC. The NG-RAN node may include multiple gNBs, which may also include a central unit (CU) (gNB-CU) 196 and distributed unit(s) (DUs) (gNB-DUs), of which DU 195 is shown. Note that the DU may include or be coupled to and control a radio unit (RU). The gNB-CU is a logical node hosting radio resource control (RRC), SDAP and PDCP protocols of the gNB or RRC and PDCP protocols of the en-gNB that controls the operation of one or more gNB-DUs. The gNB-CU terminates the FI interface connected with the gNB-DU. The FI interface is illustrated as reference 198, although reference 198 also illustrates a link between remote elements of the RAN node 170 and centralized elements of the RAN node 170, such as between the gNB-CU 196 and the gNB-DU 195. The gNB-DU is a logical node hosting RLC, MAC and PHY layers of the gNB or en-gNB, and its operation is partly controlled by gNB-CU. One gNB-CU supports one or multiple cells. One cell is supported by only one gNB-DU. The gNB-DU terminates the FI interface 198 connected with the gNB-CU. Note that the DU 195 is considered to include the transceiver 160, e.g., as part of a RU, but some examples of this may have the transceiver 160 as part of a separate RU, e.g., under control of and connected to the DU 195. The RAN node 170 may also be an eNB (evolved NodeB) base station, for LTE (long term evolution), or any other suitable base station or node.

[0090] The RAN node 170 includes one or more processors 152, one or more memories 155, one or more network interfaces (N/W I/F(s)) 161, and one or more transceivers 160 interconnected through one or more buses 157. Each of the one or more transceivers 160 includes a receiver, Rx, 162 and a transmitter, Tx, 163. The one or more transceivers 160 are connected to one or more antennas 158. The one or more memories 155 include computer program code 153. The CU 196 may include the processor(s) 152, memories 155, and network interfaces 161. Note that the DU 195 may also contain its own memory/memories and processor(s), and/or other hardware, but these are not shown.

[0091] The RAN node 170 includes a module 150, comprising one of or both parts 150-1 and/or 150-2, which may be implemented in a number of ways. The module 150 may be implemented in hardware as module 150-1, such as being implemented as part of the one or more processors 152. The module 150-1 may be implemented also as an integrated circuit or through other hardware such as a programmable gate array. In another example, the module 150 may be implemented as module 150-2, which is implemented as computer program code 153 and is executed by the one or more processors 152. For instance, the one or more memories 155 and the computer program code 153 are configured to, with the one or more processors 152, cause the RAN node 170 to perform one or more of the operations as described herein. Note that the functionality of the module 150 may be distributed, such as being distributed between the DU 195 and the CU 196, or be implemented solely in the DU 195. [0092] The one or more network interfaces 161 communicate over a network such as via the links 176 and 131. Two or more gNBs 170 may communicate using, e.g., link 176. The link 176 may be wired or wireless or both and may implement, for example, an Xn interface for 5G, an X2 interface for LTE, or other suitable interface for other standards.

[0093] The one or more buses 157 may be address, data, or control buses, and may include any interconnection mechanism, such as a series of lines on a motherboard or integrated circuit, fiber optics or other optical communication equipment, wireless channels, and the like. For example, the one or more transceivers 160 may be implemented as a remote radio head (RRH) 195 for LTE or a distributed unit (DU) 195 for gNB implementation for 5G, with the other elements of the RAN node 170 possibly being physically in a different location from the RRH/DU, and the one or more buses 157 could be implemented in part as, for example, fiber optic cable or other suitable network connection to connect the other elements (e.g., a central unit (CU), gNB-CU) of the RAN node 170 to the RRH/DU 195. Reference 198 also indicates those suitable network link(s).

[0094] It is noted that description herein indicates that "cells" perform functions, but it should be clear that equipment which forms the cell may perform the functions. The cell makes up part of a base station. That is, there can be multiple cells per base station. For example, there could be three cells for a single carrier frequency and associated bandwidth, each cell covering one-third of a 360 degree area so that the single base station's coverage area covers an approximate oval or circle. Furthermore, each cell can correspond to a single carrier and a base station may use multiple carriers. So if there are three 120 degree cells per carrier and two carriers, then the base station has a total of 6 cells.

[0095] The wireless network 100 may include a network element or elements 190 that may include core network functionality, and which provides connectivity via a link or links 181 with a further network, such as a telephone network and/or a data communications network (e.g., the Internet). Such core network functionality for 5G may include access and mobility management function (s) (AMF(S)) and/or user plane functions (UPF(s)) and/or session management function (s) (SMF(s)). Such core network functionality for LTE may include MME (Mobility Management Entity)/SGW (Serving Gateway) functionality. These are merely example functions that may be supported by the network element(s) 190, and note that both 5G and LTE functions might be supported. The RAN node 170 is coupled via a link 131 to the network element 190. The link 131 may be implemented as, e.g., an NG interface for 5G, or an SI interface for LTE, or other suitable interface for other standards. The network element 190 includes one or more processors 175, one or more memories 171, and one or more network interfaces (N/W I/F(s)) 180, interconnected through one or more buses 185. The one or more memories 171 include computer program code 173. The one or more memories 171 and the computer program code 173 are configured to, with the one or more processors 175, cause the network element 190 to perform one or more operations.

[0096] The wireless network 100 may implement network virtualization, which is the process of combining hardware and software network resources and network functionality into a single, software-based administrative entity, a virtual network. Network virtualization involves platform virtualization, often combined with resource virtualization. Network virtualization is categorized as either external, combining many networks, or parts of networks, into a virtual unit, or internal, providing network-like functionality to software containers on a single system. Note that the virtualized entities that result from the network virtualization are still implemented, at some level, using hardware such as processors 152 or 175 and memories 155 and 171, and also such virtualized entities create technical effects.

[0097] The computer readable memories 125, 155, and 171 may be of any type suitable to the local technical environment and may be implemented using any suitable data storage technology, such as semiconductor based memory devices, flash memory, magnetic memory devices and systems, optical memory devices and systems, fixed memory and removable memory. The computer readable memories 125, 155, and 171 may be means for performing storage functions. The processors 120, 152, and 175 may be of any type suitable to the local technical environment, and may include one or more of general purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs) and processors based on a multi-core processor architecture, as non-limiting examples. The processors 120, 152, and 175 may be means for performing functions, such as controlling the UE 110, RAN node 170, network element(s) 190, and other functions as described herein.

[0098] In general, the various embodiments of the user equipment 110 can include, but are not limited to, cellular telephones such as smart phones, tablets, personal digital assistants (PDAs) having wireless communication capabilities, portable computers having wireless communication capabilities, image capture devices such as digital cameras having wireless communication capabilities, gaming devices having wireless communication capabilities, music storage and playback appliances having wireless communication capabilities, Internet appliances permitting wireless Internet access and browsing, tablets with wireless communication capabilities, as well as portable units or terminals that incorporate combinations of such functions.

[0099] The distribution matcher as described herein, such as the distribution matcher 1002 shown in FIG. 1, the distribution matcher 608 shown in FIG. 6, and/or the distribution matcher 901 shown in FIG. 9 may, in some examples, be implemented in either the UE 110 (for example within or as module 140-2), the RAN node 170 (for example within or as module 150-2), and/or the network element 190 (for example within or as computer program code 173).

[00100] An example apparatus is provided, the apparatus comprising at least one processor; and at least one non- transitory memory including computer program code; wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus at least to perform: generate an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

[00101] The apparatus may further include wherein the lookup table with inconstancies is fixed-length, and a number of amplitudes generated at an output of the distribution matcher is fixed.

[00102] The apparatus may further include wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: in response to the output probability distribution being within a threshold of closeness to the channel probability distribution: transmit a plurality of parity bits through the channel; and in response to the output probability distribution not being within a threshold of closeness to the channel probability distribution: assign at least one of the output labels to two or more index labels by changing at least one output symbol of the at least one output label to perform the shaping of the output probability distribution to more closely match the channel probability distribution.

[00103] The apparatus may further include wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: define an apriori probability for each index label that has been merged, wherein the apriori probability is calculated as a number of codewords that have not been changed to more closely match the channel probability distribution divided by a length of the lookup table.

[00104] The apparatus may further include wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: generate at least one hidden bit given the fact that at least one index label has been merged, the value of the at least one hidden bit determining a transmission priority of the at least one merged index label.

[00105] The apparatus may further include wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: sum a plurality of parity bits and the at least one hidden bit to create a plurality of new parity bits; and transmit the new parity bits through the channel.

[00106] The apparatus may further include wherein the lookup table within inconstancies is probabilistic due to at least one of: a codeword appearing more than once in the lookup table being associated with a probability, wherein a codeword comprises a number of bits at the output of the distribution matcher; or the plurality of output symbols being randomly chosen for each index label out of a set of possible output symbols, wherein the number of possible output symbols is determined according to the formula wherein k is a number

of input bits of each index label, n is a number of output bits of each codeword, and m is a number of bits of each output symbol.

[00107] The apparatus may further include wherein the channel probability distribution is a Maxwell-Boltzmann (MB) distribution given by probability masses that are proportional to exp(-ʋ *|s|^Λ2), where s is a symbol and ʋ is an MB- distribution parameter.

[00108] The apparatus may further include wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: update the lookup table in response to a change in the channel probability distribution, the change being based on a change in a condition of the channel.

[00109] An apparatus is provided, the apparatus comprising: means for generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

[00110] The apparatus may further include wherein the lookup table with inconstancies is fixed-length, and a number of amplitudes generated at an output of the distribution matcher is fixed.

[00111] The apparatus may further include in response to the output probability distribution being within a threshold of closeness to the channel probability distribution: means for transmitting a plurality of parity bits through the channel; and in response to the output probability distribution not being within a threshold of closeness to the channel probability distribution: means for assigning at least one of the output labels to two or more index labels by changing at least one output symbol of the at least one output label to perform the shaping of the output probability distribution to more closely match the channel probability distribution.

[00112] The apparatus may further include means for defining an apriori probability for each index label that has been merged, wherein the apriori probability is calculated as a number of codewords that have not been changed to more closely match the channel probability distribution divided by a length of the lookup table.

[00113] The apparatus may further include means for generating at least one hidden bit given the fact that at least one index label has been merged, the value of the at least one hidden bit determining a transmission priority of the at least one merged index label.

[00114] The apparatus may further include means for summing a plurality of parity bits and the at least one hidden bit to create a plurality of new parity bits; and means for transmitting the new parity bits through the channel.

[00115] The apparatus may further include wherein the lookup table within inconstancies is probabilistic due to at least one of: a codeword appearing more than once in the lookup table being associated with a probability, wherein a codeword comprises a number of bits at the output of the distribution matcher; or the plurality of output symbols being randomly chosen for each index label out of a set of possible output symbols, wherein the number of possible output symbols is determined according to the formula wherein k is a number

of input bits of each index label, n is a number of output bits of each codeword, and m is a number of bits of each output symbol. [00116] The apparatus may further include wherein the channel probability distribution is a Maxwell-Boltzmann (MB) distribution given by probability masses that are proportional to exp(-ʋ *|s|^Λ2), where s is a symbol and ʋ is an MB- distribution parameter.

[00117] The apparatus may further include means for updating the lookup table in response to a change in the channel probability distribution, the change being based on a change in a condition of the channel.

[00118] An example method is provided, the method comprising: generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

[00119] An example non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations is provided, the operations comprising: generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

[0001] It should be understood that the foregoing description is only illustrative. Various alternatives and modifications can be devised by those skilled in the art. For example, features recited in the various dependent claims could be combined with each other in any suitable combination (s). In addition, features from different embodiments described above could be selectively combined into a new embodiment. Accordingly, the description is intended to embrace all such alternatives, modifications and variances which fall within the scope of the appended claims.

Claims

CLAIMS What is claimed is:

1. An apparatus comprising: at least one processor; and at least one non-transitory memory including computer program code; wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus at least to perform: generate an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

2. The apparatus of claim 1, wherein the lookup table with inconstancies is fixed-length, and a number of amplitudes generated at an output of the distribution matcher is fixed.

3. The apparatus of claim 1, wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: in response to the output probability distribution being within a threshold of closeness to the channel probability distribution: transmit a plurality of parity bits through the channel; and in response to the output probability distribution not being within a threshold of closeness to the channel probability distribution: assign at least one of the output labels to two or more index labels by changing at least one output symbol of the at least one output label to perform the shaping of the output probability distribution to more closely match the channel probability distribution.

4. The apparatus of claim 1, wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: define an apriori probability for each index label that has been merged, wherein the apriori probability is calculated as a number of codewords that have not been changed to more closely match the channel probability distribution divided by a length of the lookup table.

5. The apparatus of claim 1, wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: generate at least one hidden bit given the fact that at least one index label has been merged, the value of the at least one hidden bit determining a transmission priority of the at least one merged index label.

6. The apparatus of claim 1, wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: sum a plurality of parity bits and the at least one hidden bit to create a plurality of new parity bits; and transmit the new parity bits through the channel.

7. The apparatus of claim 1, wherein the lookup table within inconstancies is probabilistic due to at least one of: a codeword appearing more than once in the lookup table being associated with a probability, wherein a codeword comprises a number of bits at the output of the distribution matcher; or the plurality of output symbols being randomly chosen for each index label out of a set of possible output symbols, wherein the number of possible output symbols is determined according to the formula wherein k

is a number of input bits of each index label, n is a number of output bits of each codeword, and m is a number of bits of each output symbol.

8. The apparatus of claim 1, wherein the channel probability distribution is a Maxwell-Boltzmann (MB) distribution given by probability masses that are proportional to exp(-ʋ *|s|^Λ2), where s is a symbol and ʋ is an MB-distribution parameter.

9. The apparatus of claim 1, wherein the at least one memory and computer program code are further configured, with the at least one processor, to cause the apparatus at least to: update the lookup table in response to a change in the channel probability distribution, the change being based on a change in a condition of the channel.

10. An apparatus comprising: means for generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

11. The apparatus of claim 1, wherein the lookup table with inconstancies is fixed-length, and a number of amplitudes generated at an output of the distribution matcher is fixed.

12. The apparatus of claim 1, further comprising: in response to the output probability distribution being within a threshold of closeness to the channel probability distribution: means for transmitting a plurality of parity bits through the channel; and in response to the output probability distribution not being within a threshold of closeness to the channel probability distribution: means for assigning at least one of the output labels to two or more index labels by changing at least one output symbol of the at least one output label to perform the shaping of the output probability distribution to more closely match the channel probability distribution.

13. The apparatus of claim 1, further comprising: means for defining an apriori probability for each index label that has been merged, wherein the apriori probability is calculated as a number of codewords that have not been changed to more closely match the channel probability distribution divided by a length of the lookup table.

14. The apparatus of claim 1, further comprising: means for generating at least one hidden bit given the fact that at least one index label has been merged, the value of the at least one hidden bit determining a transmission priority of the at least one merged index label.

15. The apparatus of claim 1, further comprising: means for summing a plurality of parity bits and the at least one hidden bit to create a plurality of new parity bits; and means for transmitting the new parity bits through the channel.

16. The apparatus of claim 1, wherein the lookup table within inconstancies is probabilistic due to at least one of: a codeword appearing more than once in the lookup table being associated with a probability, wherein a codeword comprises a number of bits at the output of the distribution matcher; or the plurality of output symbols being randomly chosen for each index label out of a set of possible output symbols, wherein the number of possible output symbols is determined according to the formula wherein k

is a number of input bits of each index label, n is a number of output bits of each codeword, and m is a number of bits of each output symbol.

17. The apparatus of claim 1, wherein the channel probability distribution is a Maxwell-Boltzmann (MB) distribution given by probability masses that are proportional to exp(-ʋ *|s|^Λ2), where s is a symbol and ʋ is an MB-distribution parameter.

18. The apparatus of claim 1, further comprising: means for updating the lookup table in response to a change in the channel probability distribution, the change being based on a change in a condition of the channel.

19. A method comprising: generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.

20. A non-transitory program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine for performing operations, the operations comprising: generating an initialization of a lookup table with inconstancies by assigning a plurality of index labels, the index labels representing an input to a distribution matcher, to a plurality of output labels of the distribution matcher, the output labels comprising a plurality of output symbols; wherein each of the plurality of output labels are capable of being assigned to two or more of the index labels, to merge the two or more index labels together, and further to shape an output probability distribution of the plurality of output symbols to be closer to a channel probability distribution associated with an error of a channel used for transmission or reception; wherein at least one of an encoding or decoding operation is performed using the lookup table with inconstancies to encode the input to the distribution matcher or to decode the plurality of output symbols.