Turbo Code Encoder

Abstract

The present application discloses a Turbo code encoder. The Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; where L = 160, N = 8, M = 20, and the interleaving table S(x) is: 156, 65, 138, 47, 86, 13, 99, 112.

Description

Technical Field

[0001] The present invention generally relates to the field of electronic communication technology, and in particular to a Turbo code encoder and a Turbo code interleaver. Background Art

[0002] The broadband power line carrier communication system does not require rewiring. PLC terminals, relays, local equipment and auxiliary devices are configured on the existing distribution network to convert the original power line network into a power line communication network. High-speed Internet is built through power lines to complete services such as video, voice and data, which is convenient and fast, and can maximize the use of existing facilities.

[0003] IEEE P1901 and State Grid HPLC (Q / GDW 11612.41—2016) series specifications are the current broadband power line carrier communication standards, which use Turbo code as the communication code for broadband power line carrier. Turbo code is also called Parallel Concatenated Convolutional Code (PCCC). It cleverly combines convolutional code and random interleaver. While realizing the idea of ​​random coding, it realizes the method of constructing long code from short code through interleaver, and uses soft output iterative decoding to approximate maximum likelihood decoding. The Turbo encoder architecture defined in the IEEE P1901 specification is as follows: Figure 1 The Turbo code is composed of two identical component encoders ENC1, component encoder ENC2 and an interleaver, each inputting a pair of information bits (u1, u2), and outputting a systematic bit (u1, u2) and a check bit (p, q).

[0004] The interleaver rearranges the symbol or bit sequence in a predetermined manner. The Turbo code interleaver is used to construct a part of the Turbo code. In the case of a Turbo code as a parallel cascade of two constituent recursive convolutional codes, the Turbo interleaver reorders the input data sequence in a pseudo-random manner before encoding the second code. Existing interleavers use separate codes generated by two constituent encoders, whose codes are uncorrelated, and whose properties make them combined by the Turbo encoder to produce a composite code with excellent error protection capabilities.

[0005] However, the interleaver in the existing technology (such as the IEEE P1901 standard) can be further improved and optimized. First, the process of the P1901 Turbo encoder will be introduced below. ENC1 and ENC2 in the P1901 Turbo encoder use 8-state encoders. The first bit of the input data stream is mapped to u1, the second bit is mapped to u2, and so on. In one ENC, each pair of bits corresponds to an output parity bit. The calculation of the parity bits (p, q) is based on Figure 2 Determined. The state of the encoder is represented as S = 4s1 + 2s2 + s3, where S(0 ≤ S ≤ 7). The tail-biting cyclic states Sc1 (ENC1) and Sc2 (ENC2) are determined by the following two steps: The first step is to determine the response S of the encoder to the information bit pairs of length L = K / 2 in the all-zero state 0,L-1 , that is, input the information bit pairs into the component encoder ENC1 (the input of ENC2 is the interleaved information bits) until the last pair of bits, record the final state S 0,L-1 at the end of the encoding, and discard the results generated during the encoding process. The second step is the actual encoding, that is, find the S 0,L-1 corresponding to S c from the following table (the following table is the tail-biting coding cyclic state lookup table (Sc)), and set the initial state of the component encoding as S0 = S c , then re-enter the input information bit pairs into the component encoder, and after another encoding, obtain the actually output Turbo coding parity bits, and the final state S L-1 of the encoder = S0, achieving the tail-biting coding effect.

[0006]

[0007] P1901 Turbo interleaving module: The Turbo interleaver is used to interleave the original data and use it as the input of the second component code. The Turbo interleaving is performed in units of double bits (bit pairs), and the length of the interleaver is equal to the number of double bits of the original data block length. Assume that the length of the interleaver is L, and it can be split into L = MN, where M and N are positive integers. The P1901 Turbo interleaver adopts a structural interleaver, and the mapping function Π(x) of the interleaver can be expressed as:

[0008]

[0009] Where is to round x, S(x) is the first N members of the interleaver mapping function, and [S(x) mod N] represents a sequence of pseudo-random permutations from 0 to N - 1. Other members of the mapping function can be obtained through the following iterative method as follows:

[0010] Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

[0011] It can be seen that such a Turbo interleaver has a simple hardware implementation, and its Turbo decoding performance is completely determined by S(x), simplifying the design of the interleaver from the design of the L parameter to the design of the N parameter.

[0012] The P1901 standard defines three PB lengths, namely: PB16, PB136, and PB520. The State Grid HPLC standard (Q / GDW11612.41—2016) adds two more PB modes, namely: PB72 and PB264. Their Turbo interleaving parameters are given in the following table:

[0013]

[0014] It should be noted that when the output address of the interleaver is even, the 0th and 1st bits of the corresponding interleaved information bit pair need to be swapped to further remove the correlation of double binary bits.

[0015] The design of the Turbo code interleaver is far from an exact science and can only be obtained through simulation-verified design methods. Generally, the performance of the interleaver improves as the length L of the interleaver increases. However, for common frame lengths, it is quite difficult to find (design) a good interleaving table because the search dimension increases exponentially with L. Obviously, it is completely impossible and unrealistic to find the interleaving table using the exhaustive method within a limited time and verify it through performance simulation. Therefore, a practical interleaving table design method must first make full use of the structural characteristics of the interleaver, apply appropriate index constraints, and perform performance comparison simulations for screening.

[0016] To effectively support low-power wireless meter reading applications and meet the requirements of the dual-mode communication protocol of broadband power line carrier and micro-power wireless communication, the SMI-01 standard committee of the China Smart Metering Alliance added a new PB length, PB40, but there is no effective interleaving parameter table for PB40. Summary of the Invention

[0017] The purpose of the present invention is to provide an interleaving method and a Turbo code interleaver for a data block with a length of 40 bytes, and provide an interleaving table for PB40.

[0018] In one embodiment of the present application, a Turbo code encoder is provided. The Turbo code encoder includes an interleaver, where L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N;

[0019] Among them, L = 160, N = 8, M = 20, and the interleaving table S(x) is: 156, 65, 138, 47, 86, 13, 99, 112.

[0020] In a preferred example, the Turbo code encoder is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standards.

[0021] In a preferred example, the mapping function for the interleaver to perform interleaving on the input data stream is:

[0022] where x = 0, 1, …, L - 1, and the interleaving table S(x) is the first N members of the mapping function;

[0023] The remaining members of the mapping function are calculated by the following iterative method:

[0024] Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

[0025] In another embodiment of the present application, a Turbo code encoder is provided, where the Turbo code encoder includes an interleaver, L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N;

[0026] Among them, L = 160, N = 8, M = 20, and the interleaving table S(x) is: 149, 56, 129, 106, 12, 38, 87, 67.

[0027] In a preferred example, the Turbo code encoder is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standards.

[0028] In a preferred example, the mapping function for the interleaver to perform interleaving on the input data stream is:

[0029] where x = 0, 1, …, L - 1, and the interleaving table S(x) is the first N members of the mapping function;

[0030] The remaining members of the mapping function are calculated by the following iterative method:

[0031] Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

[0032] In another embodiment of the present application, a Turbo code encoder is provided. Among them, the Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N;

[0033] Among them, L = 160, N = 10, M = 16, and the interleaving table S(x) is: 61, 46, 88, 100, 139, 12, 153, 24, 117, 65.

[0034] In a preferred example, the Turbo code encoder is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standards.

[0035] In a preferred example, the mapping function for the interleaver to perform interleaving on the input data stream is:

[0036] where x = 0, 1, …, L - 1, and the interleaving table S(x) is the first N members of the mapping function;

[0037] In another embodiment of the present application, a Turbo code interleaver is also provided. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; where L = 160, N = 8, M = 20, and the interleaving table S(x) is: 156, 65, 138, 47, 86, 13, 99, 112, or, L = 160, N = 8, M = 20, and the interleaving table S(x) is: 149, 56, 129, 106, 12, 38, 87, 67, or, L = 160, N = 10, M = 16, and the interleaving table S(x) is: 61, 46, 88, 100, 139, 12, 153, 24, 117, 65.

[0038] Compared with the prior art, the present application has at least the following beneficial effects:

[0039] The present application provides an interleaving table for an interleaver with a length of 40 bytes and has excellent performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The non-limiting and non-exhaustive embodiments of the present application are described with reference to the following drawings, in which the same reference numerals refer to the same parts in each drawing unless otherwise specified.

[0041] Figure 1 A schematic diagram of a Turbo encoder in the prior art is shown.

[0042] Figure 2 A schematic diagram of a component encoder in the prior art is shown.

[0043] Figure 3 Shows the comparison chart of the PB40 bit error rate curves of S(x) in various embodiments of the present application.

[0044] Figure 4 Shows the comparison chart of the PB40 frame error rate curves of S(x) in various embodiments of the present application.

[0045] Figure 5 Shows the comparison chart of the PB40 bit error rate curves between various embodiments of the present application and the reference S(x).

[0046] Figure 6 Shows the comparison chart of the PB40 frame error rate curves between various embodiments of the present application and the reference S(x). Detailed implementation manners

[0047] Now, various aspects and examples of the present application will be described. The following description provides specific details for thoroughly understanding and implementing the description of these examples. However, those skilled in the art will understand that the present application can be practiced without many of these details.

[0048] In addition, some well-known structures or functions may not be shown or described in detail so as to be concise and avoid unnecessarily obscuring the relevant description.

[0049] The terms used in the following description are intended to be interpreted in the broadest reasonable manner, even when used in conjunction with the detailed description of certain specific examples of the present application. Even the following may emphasize certain terms. However, any term intended to be interpreted in any restricted manner will be clearly and specifically defined in this detailed description section.

[0050] Embodiment 1

[0051] In an embodiment of the present application, a Turbo code encoder is provided. In this embodiment, the data block label is PB40_1. The Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; where L = 160, N = 8, M = 20, and the interleaving table S(x) is: 156, 65, 138, 47, 86, 13, 99, 112. Among them, the Turbo code encoder in this embodiment is applicable to the IEEE P1901 and / or the State Grid HPLC Q / GDW 11612.41—2016 standard.

[0052] Among them, the mapping function of the interleaver for interleaving the input data bit stream is:

[0053] where \(x = 0, 1, \ldots, L - 1\), and the interleaving table \(S(x)\) is the first \(N\) members of the mapping function. \(\lfloor x\rfloor\) is the integer part of \(x\), and \([S(x)\bmod N]\) represents a sequence of pseudo - random permutations from \(0\) to \(N - 1\).

[0054] The remaining members of the mapping function are calculated by the following iterative method:

[0055] \(\Pi(x + mN)=[S(x)-mN + L]\bmod L\), for \(0\leq x\lt N\) and \(m = 0, 1, \ldots, M - 1\).

[0056] In a preferred example, it further includes calculating the distance spectrum \((d free .N free ,w free ) of the Turbo code, and judging whether the performance of the interleaver meets the specified requirements according to the distance spectrum, where \(d free represents the free distance, \(N free represents the multiplicity factor of the free distance, and \(w free represents the code weight of the free distance.

[0057] Among them, under the condition of a relatively high signal - to - noise ratio (\(SNR = E b / N_0\)), the performance of the Turbo code is evaluated by the following formula:

[0058]

[0059]

[0060] where \(PER\) (packet error rate) represents the packet error rate, \(BER\) (bit error rate) represents the bit error rate, \(k\) represents the length of the information bits, \(n\) represents the length of the Turbo code, \(E b represents the energy per bit, \(N_0\) represents the power spectral density of Gaussian white noise, and \(erfc(x)\) represents the Gaussian error function.

[0061] In the medium - to - high signal - to - noise ratio case, the larger \(d free is, the better the error - code performance of the Turbo code; under the condition of the same free distance, the smaller the value of \(N free is required to be. In addition, the size of \(w free only affects the bit error rate (\(BER\)), while the packet error rate (\(PER\)) only depends on the values of \(d free and \(N free .

[0062] Among them, when the interleaving table \(S(x)\) is: 156, 65, 138, 47, 86, 13, 99, 112, the distance spectrum \((d free .N free,w free ) The values are 17, 20, 140, or 18, 120, 600, or 19, 160, 1060 respectively.

[0063] Embodiment Two

[0064] In another embodiment of the present application, a Turbo code encoder is provided. Herein, in this embodiment, the data block label is PB40_1a. The Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N;

[0065] Where L = 160, N = 8, M = 20, and the interleaving table S(x) is: 149, 56, 129, 106, 12, 38, 87, 67. Herein, the Turbo code encoder in this embodiment is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW11612.41—2016 standards.

[0066] Wherein, the mapping function for the interleaver to perform interleaving on the input data code stream is:

[0067] Where x = 0, 1, …, L - 1, and the interleaving table S(x) is the first N members of the mapping function. For taking the integer part of x, [S(x) mod N] represents a sequence of pseudo-random permutations from 0 to N - 1;

[0068] The remaining members of the mapping function are calculated by the following iterative method:

[0069] Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

[0070] In a preferred example, it further includes calculating the distance spectrum (d free .N free ,w free ) of the Turbo code, and judging whether the performance of the interleaver meets the specified requirements according to the distance spectrum, where d free represents the free distance, N free represents the multiplicity factor of the free distance, w free represents the code weight of the free distance.

[0071] Wherein, under the condition of a relatively high signal-to-noise ratio (SNR = E b / N0), the performance of the Turbo code is evaluated by the following formula:

[0072]

[0073]

[0074] Among them, PER (packet error rate) represents the frame error rate, BER (bit error rate) represents the bit error rate, k represents the information bit length, n represents the Turbo code length, E b represents the energy per unit bit, N0 represents the power spectral density of Gaussian white noise, and erfc(x) represents the Gaussian error function.

[0075] In the medium to high signal-to-noise ratio case, d free the larger it is, the better the bit error performance of the Turbo code; under the condition of the same free distance, it is required that N free the smaller the value is, the better. In addition, w free only affects the bit error rate (BER), while the frame error rate (PER) only depends on d free and N free values.

[0076] Among them, when the interleaving table S(x) is: 149, 56, 129, 106, 12, 38, 87, 67, the distance spectrum (d free .N free ,w free ) takes values of 17, 60, 300, or 18, 90, 420, or 19, 140, 780 respectively.

[0077] Embodiment 3

[0078] In another embodiment of the present application, a Turbo code encoder is provided. Among them, in this embodiment, the data block label is PB40_1b. The Turbo code encoder includes an interleaver, L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M×N;

[0079] Among them, L = 160, N = 10, M = 16, and the interleaving table S(x) is: 61, 46, 88, 100, 139, 12, 153, 24, 117, 65. Among them, the Turbo code encoder in this embodiment is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standards.

[0080] Among them, the mapping function of the interleaver for interleaving the input data stream is:

[0081] where x = 0, 1,..., L - 1, and the interleaving table S(x) is the first N members of the mapping function, To round x, [S(x) mod N] represents a sequence of pseudo-random permutations from 0 to N - 1;

[0082] The remaining members of the mapping function are calculated by the following iterative method:

[0083] Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

[0084] In a preferred example, it further includes calculating the distance spectrum (d free .N free , w free ) of the Turbo code, and judging whether the performance of the interleaver meets the specified requirements according to the distance spectrum, where d free represents the free distance, N free represents the multiplicity factor of the free distance, and w free represents the code weight of the free distance.

[0085] Among them, under the condition of a relatively high signal-to-noise ratio (SNR = E b / N0), the performance of the Turbo code is evaluated by the following formula:

[0086]

[0087]

[0088] Among them, PER (packet error rate) represents the packet error rate, BER (bit error rate) represents the bit error rate, k represents the information bit length, n represents the Turbo code length, E b represents the energy per unit bit, N0 represents the power spectral density of Gaussian white noise, and erfc(x) represents the Gaussian error function.

[0089] In the medium to high signal-to-noise ratio case, the larger d free , the better the bit error performance of the Turbo code; under the condition of the same free distance, it is required that the value of N free is as small as possible. In addition, the size of w free only affects the bit error rate (BER), while the packet error rate (PER) only depends on the values of d free and N free .

[0090] Among them, when the interleaving table S(x) is: 61, 46, 88, 100, 139, 12, 153, 24, 117, 65, the distance spectrum (d free .N free , w free)The values are 17, 64, 432, or 18, 128, 592, or 19, 208, 1136 respectively.

[0091] The following Table 1 shows the interleaving table of PB40 and the results of its free distance spectrum at a 1 / 2 code rate in each embodiment of the present application.

[0092]

[0093]

[0094] Table 1

[0095] In the present application Figure 3 and Figure 4 disclosed is the comparison of the frame error rate and bit error rate corresponding to the PB40 (R = 1 / 2) interleaver in the interleaving table S(x) in Embodiment 1, Embodiment 2, and Embodiment 3. It can be seen from Figure 3 and Figure 4 that the performance corresponding to the interleaver using the interleaving tables in each embodiment of the present application is excellent and not much different.

[0096] The following Table 2 shows the interleaving table of PB40 for reference and the results of its corresponding free distance spectrum at a 1 / 2 code rate.

[0097]

[0098] Table 2

[0099] In the present application Figure 5 and Figure 6 disclosed is the comparison of the frame error rate and bit error rate corresponding to the PB40 (R = 1 / 2) interleaver in the interleaving table S(x) in Embodiment 1, Embodiment 2, and Embodiment 3 and other interleaving tables (shown in Table 2). It can be seen from Figure 5 and Figure 6 that in terms of both the free distance spectrum and the error (frame) bit rate performance, the simulation of the interleaving tables in each embodiment of the present application is better than or not lower than other reference interleaving tables.

[0100] In another embodiment of the present application, a Turbo code interleaver is further provided, which is used for interleaving data blocks with a length of 40 bytes. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; the interleaver adopts the above-mentioned interleaving table, that is, L = 160, N = 8, M = 20, and the interleaving table S(x) is: 156, 65, 138, 47, 86, 13, 99, 112, or, L = 160, N = 8, M = 20, and the interleaving table S(x) is: 149, 56, 129, 106, 12, 38, 87, 67, or, L = 160, N = 10, M = 16, and the interleaving table S(x) is: 61, 46, 88, 100, 139, 12, 153, 24, 117, 65.

[0101] It should be noted that in the application documents of this patent, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including one" does not exclude the existence of another identical element in the process, method, article or device including the element. In the application documents of this patent, if it is mentioned that an act is performed according to a certain element, it means at least performing the act according to the element, including two cases: performing the act only according to the element, and performing the act according to the element and other elements. Expressions such as multiple, multiple times, multiple types, etc. include 2, 2 times, 2 types, and more than 2, more than 2 times, more than 2 types.

[0102] All documents mentioned in this specification are considered to be integrally included in the disclosure content of this application so that they can be used as a basis for modification when necessary. In addition, it should be understood that the above are only preferred embodiments of this specification and are not used to limit the protection scope of this specification. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of one or more embodiments of this specification shall be included in the protection scope of one or more embodiments of this specification.

[0103] In some cases, the acts or steps recited in the claims may be performed in a different order than in the embodiments and still achieve the desired result. Additionally, the processes depicted in the figures do not necessarily require the particular order shown or sequential order to achieve the desired result. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

Claims

1. A Turbo code encoder, characterized in that, The Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; where L = 160, N = 8, M = 20, and the interleaving table S(x) is: 156, 65, 138, 47, 86, 13, 99, 112; where the interleaving table supports the PB40 mode; where the mapping function for the interleaver to perform interleaving on the input data stream is: where x = 0, 1, …, L-1, and the interleaving table S(x) is the first N members of the mapping function; The remaining members of the mapping function are calculated by the following iterative method: Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

2. The Turbo code encoder according to claim 1, characterized in that, The Turbo code encoder is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standard.

3. A Turbo code encoder, characterized in that, The Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; where L = 160, N = 8, M = 20, and the interleaving table S(x) is: 149, 56, 129, 106, 12, 38, 87, 67; where the interleaving table supports the PB40 mode; where the mapping function for the interleaver to perform interleaving on the input data stream is: where x = 0, 1, …, L−1, and where the interleaving table S(x) is the first N members of the mapping function; The remaining members of the mapping function are calculated by the following iterative method: Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

4. The Turbo code encoder according to claim 3, wherein, The Turbo code encoder is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standard.

5. A Turbo code encoder, characterized in that, The Turbo code encoder includes an interleaver. L represents the length of the interleaver, S(x) represents the interleaving table of the interleaver, N represents the length of the interleaving table, and L = M × N; where L = 160, N = 10, M = 16, and the interleaving table S(x) is: 61, 46, 88, 100, 139, 12, 153, 24, 117, 65; where the interleaving table supports the PB40 mode; where the mapping function for the interleaver to perform interleaving on the input data stream is: where x = 0, 1, …, L−1, and where the interleaving table S(x) is the first N members of the mapping function; The remaining members of the mapping function are calculated by the following iterative method: Π(x + mN) = [S(x) - mN + L] mod L, 0 ≤ x < N, m = 0, 1, …, M - 1.

6. The Turbo code encoder according to claim 5, characterized in that, The Turbo code encoder is applicable to the IEEE P1901 and / or State Grid HPLC Q / GDW 11612.41—2016 standard.

7. A Turbo code interleaver, characterized in that, Let \(L\) denote the length of the interleaver, \(S(x)\) denote the interleaving table of the interleaver, \(N\) denote the length of the interleaving table, and \(L = M\times N\); where \(L = 160\), \(N = 8\), \(M = 20\), and the interleaving table \(S(x)\) is: \(156, 65, 138, 47, 86, 13, 99, 112\), or, \(L = 160\), \(N = 8\), \(M = 20\), and the interleaving table \(S(x)\) is: \(149, 56, 129, 106, 12, 38, 87, 67\), or, \(L = 160\), \(N = 10\), \(M = 16\), and the interleaving table \(S(x)\) is: \(61, 46, 88, 100, 139, 12, 153, 24, 117, 65\); where the interleaving table supports the PB40 mode; where the mapping function for the interleaver to perform interleaving on the input data stream is: where x = 0, 1, …, L-1, and the interleaving table S(x) is the first N members of the mapping function; The remaining members of the mapping function are calculated by the following iterative method: \(\Pi(x + mN)=[S(x)-mN + L]\bmod L, 0\leq x\lt N, m = 0, 1,\cdots,M - 1\).

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