A method and system for power code length allocation based on expired channel under limited code length

Abstract

This invention proposes a power and code length allocation method and system based on expired channels under finite code length conditions. The method includes: in a finite code length transmission scenario based on expired channel state information in the Industrial Internet of Things (IIoT), constructing a channel time-domain evolution model based on the correlation between expired and current channel state information; deriving the expected transmission rate given expired channel state information based on the channel time-domain evolution model; constructing a joint optimization problem concerning transmit power and code length with the objective of maximizing the total expected transmission rate of the system; performing continuous relaxation and convexity analysis on the joint optimization problem, and solving it using the ellipsoidal method; rounding the code length solution to output the final joint transmit power and code length allocation strategy. This invention significantly improves the total system transmission rate of finite code length transmission based on expired channels in the IIoT and is suitable for high-dynamic communication scenarios in the IIoT.

Description

Technical Field

[0001] This application relates to the field of wireless communication, specifically a power code length allocation method and system based on expired channels under limited code length. Background Technology

[0002] The Industrial Internet of Things (IIoT), as a core support for next-generation industrial systems such as smart manufacturing and smart factories, needs to support real-time transmission of data from a large number of devices under limited spectrum resources to achieve device interconnection and control. IIoT transmission signals typically have small data volumes, and systems often employ finite-length channel coding for transmission, i.e., finite code length domain. Existing research shows that transmission performance only approaches Shannon capacity when the code length approaches infinity. Even if the transmission rate is lower than the channel capacity in the finite code length domain, transmission errors cannot be ignored. Therefore, to achieve highly reliable, low-latency transmission in IIoT, the impact of finite code length transmission must be considered.

[0003] To improve the performance of limited code length (FBL) transmission in IIoT, existing technologies have proposed solutions such as power control, block length allocation, and beamforming. However, most of these solutions are based on the ideal assumption that the transmitter can obtain perfect channel state information. In dynamic IIoT networks, the channel changes over time, and 3GPP technical specification 36.213 (TS 36.213) stipulates that Channel Quality Indicator (CQI) feedback should be reported periodically (e.g., Radio Resource Control (RRC) configuration period of 5–160ms). In IIoT, limited code length (FBL) transmission results in transmission time that is much shorter than the channel estimation time. The transmitter obtains outdated channel state information feedback, leading to a mismatch between the transmission scheme and channel changes, thus reducing system performance.

[0004] To address the performance degradation caused by expired Channel State Information (CSI) in IIoT, existing technologies have conducted research on resource allocation based on statistical CSI or expired CSI. For example, in 2023, H. Peng et al. combined HARQ with the statistical characteristics of CSI for joint power and rate allocation. Other works have considered the time-domain correlation of the average coding rate expression and designed resource allocation schemes accordingly. For instance, in 2025, Y. Wang et al., considering the time-domain correlation of CSI in downlink transmission for dynamic communication scenarios, derived a closed-form expression for the average transmission rate under RSMA-enabled FBL transmission and proposed a power optimization scheme based on this. However, these works all rely on the statistical characteristics of CSI to construct long-term average system performance and perform resource optimization, without jointly utilizing the time-domain correlation between channels and the statistical characteristics of CSI to achieve real-time adaptive adjustment of the resource allocation scheme.

[0005] Existing technologies generally do not adequately address the issue of inaccurate CSI (Code State Indicator) in IIoT scenarios, nor the contradiction between limited spectrum resources and the service demands of a large number of devices. Therefore, a joint power and code length allocation method considering the limited code length effect is needed in IIoT scenarios. This method should construct the desired coding rate model with only expired channel state information and achieve efficient solution to improve system spectrum utilization. Summary of the Invention

[0006] This invention considers the high reliability communication requirements and CSI expiration characteristics in IIoT scenarios, and proposes a joint power allocation code length allocation method based on expired channels. This method not only reveals the resource allocation strategy for FBL transmission in IIoT scenarios but also contributes to the development and application of IIoT networks. It features low latency, high reliability, and high spectral efficiency.

[0007] To address the aforementioned technical problems, the present invention adopts the following technical solution:

[0008] A power code length allocation method based on expired channels under finite code length includes the following steps:

[0009] In the limited code length transmission scenario based on expired channel state information in the Industrial Internet of Things, the base station acquires the expired channel state information caused by periodic estimation and feedback delay; based on the correlation between the expired channel state information and the current channel state information, a channel time-domain evolution model is constructed.

[0010] Based on the aforementioned channel time-domain evolution model, the expected transmission rate under given expired channel state information is derived. With the goal of maximizing the total expected transmission rate of the system, a joint optimization problem concerning transmit power and code length is constructed by combining total power constraints, single-user power constraints, total code length constraints, and single-user code length constraints.

[0011] The joint optimization problem is subjected to continuous relaxation and convexity analysis, and solved using the ellipsoid method to obtain a preliminary power and code length allocation scheme. The code length values ​​in the preliminary power and code length allocation scheme are rounded to output the final joint allocation strategy for transmit power and code length.

[0012] Furthermore, the channel time-domain evolution model is a Gaussian-Markov model, specifically expressed as follows:

[0013]

[0014] in, For users Channel gain to base station For users Expired channel gain to base station The time-domain correlation coefficient, It is independent complex Gaussian noise.

[0015] Furthermore, deriving the expected transmission rate given expired channel state information includes the following sub-steps:

[0016] An instantaneous coding rate expression is constructed based on the finite code length transmission theory.

[0017] Based on the aforementioned channel time-domain evolution model, construct the conditional probability density function of the current channel power gain under the given expired channel power gain condition;

[0018] Based on the instantaneous coding rate expression and the conditional probability density function, the expected transmission rate mathematical expression conditioned on the expired channel gain is obtained by calculating the mathematical expectation.

[0019] Furthermore, the instantaneous coding rate expression is constructed based on the finite code length normal approximation, and is expressed as:

[0020]

[0021] in, Instantaneous coding rate, For users Code length, For block error rate, For users Channel dispersion, For Gauss function The inverse function, where For integration variables, x It is the lower limit of integration. For users instantaneous signal-to-noise ratio, ,in Indicates user Channel power gain, Indicates user Path loss between the base station and the base station For noise power, This refers to the transmission power.

[0022] Furthermore, the conditional probability density function of the current channel power gain under the condition of expired channel power gain is characterized by a non-central chi-square distribution as follows:

[0023]

[0024] in, Let be the conditional probability density function of the current channel power gain under the condition of the expired channel power gain. This is a modified Bessel function of the first kind. For users Expired channel power gain, ,in This indicates average large-scale fading. It is a natural exponential function.

[0025] Furthermore, the mathematical expression for the expected transmission rate, conditioned on the expired channel gain, is as follows:

[0026]

[0027] in, The desired transmission rate is conditioned on the expired channel gain.

[0028] Furthermore, the joint optimization problem for transmit power and code length is as follows:

[0029]

[0030] in, The optimization objective is to represent the sum of the transmission rates of K users given the known expired channel gain; Indicates total power constraint. This indicates the maximum total power. This represents the power limit constraint for each user, where This represents the maximum power for each user. This means for any user All constraints are satisfied; This indicates a total code length constraint. Indicates the maximum total code length; This represents the code length limit constraint for each user. This represents the maximum code length for each user; This indicates that the transmission code length allocated to each user is an integer.

[0031] Furthermore, performing continuous relaxation and convexity analysis on the joint optimization problem includes:

[0032] By relaxing the integer code length constraint to a continuous variable, the original joint optimization problem is transformed into a continuous optimization problem.

[0033] Analyze the objective function of the continuous optimization problem with respect to the variables. , The concavity and convexity, by proving when the user When the instantaneous signal-to-noise ratio and code length satisfy the preset conditions, the objective function of the continuous optimization problem is related to the transmit power. and transmission code length The joint concave function is obtained; based on this joint concavity, the ellipsoid method is used to solve the continuous optimization problem, and the preliminary continuous power vector and continuous code length vector are obtained.

[0034] Furthermore, the final output transmit power and code length joint allocation strategy includes:

[0035] The components in the initial continuous code length vector are rounded to obtain the final code length allocation vector that satisfies the integer constraint; the final code length allocation vector and the continuous power vector together constitute the final transmit power and code length joint allocation strategy.

[0036] On the other hand, the present invention provides a power code length allocation system based on expired channels under finite code length, comprising:

[0037] The channel time-domain model construction module is used in the Industrial Internet of Things (IIoT) for finite code length transmission scenarios based on expired channel state information. This module enables the base station to acquire expired channel state information caused by periodic estimation and feedback delay. Based on the correlation between expired channel state information and current channel state information, a channel time-domain evolution model is constructed.

[0038] The optimization problem construction module is used to derive the expected transmission rate under given expired channel state information based on the channel time-domain evolution model; with the goal of maximizing the total expected transmission rate of the system, it constructs a joint optimization problem on transmit power and code length by combining total power constraints, single-user power constraints, total code length constraints and single-user code length constraints;

[0039] The solution and strategy generation module is used to perform continuous relaxation and convexity analysis on the joint optimization problem and solve it using the ellipsoid method to obtain a preliminary power and code length allocation scheme; the code length value in the preliminary allocation scheme is rounded to output the final transmit power and code length joint allocation strategy.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. This invention addresses the limited code length transmission scenario in IIoT networks. The constructed transmission rate optimization model is complete, comprehensively considering the limited code length transmission characteristics and CSI expiration in IIoT scenarios. By jointly allocating code length and power resources, the algorithm aims to maximize the total system transmission rate, thereby effectively improving the transmission performance in the limited code length transmission scenario of IIoT networks. The algorithm features high spectral efficiency, low latency, and high reliability.

[0042] 2. By utilizing the timing correlation between channels and the conditional probability distribution of channels, this invention derives a mathematical expression for the expected transmission rate adapting to different power and code lengths under the condition of known expired CSI. This performance expression not only improves the accuracy of performance characterization but also enhances its flexibility and applicability in practical applications, thus possessing high practical application value. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the transmission network according to an embodiment of the present invention;

[0044] Figure 2 This is a flowchart illustrating the method implemented in this invention;

[0045] Figure 3 This is a graph showing the variation of the overall transmission rate of the system in this embodiment of the invention with the block error rate and the time-domain correlation coefficient. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0047] Example 1

[0048] This invention provides a power code length allocation method based on expired channels under finite code length conditions. It aims to maximize the total expected coding rate of the system by jointly solving for user transmit power and code length under constraints of total power, code length, and single-user power and code length upper limits.

[0049] The following is combined with Figure 1-3 This invention introduces a joint power and code length allocation method based on an expired channel for finite code length transmission, as detailed below:

[0050] Figure 1 This invention considers a multi-user limited code length (CSI) transmission network, comprising one base station and K users. The base station transmits pilot signals to the users for channel estimation. The user terminal performs channel estimation based on the received pilot signals and feeds it back to the base station. Due to feedback delay, the CSI received by the base station is outdated. To improve the performance of the limited code length transmission network, it is necessary to efficiently allocate the resources of the wireless system to maximize the total transmission rate of the network. Since the optimization problem is non-convex and the objective function is mathematically complex, solving the problem is very difficult.

[0051] like Figure 2 The diagram shown is a flowchart of the method of the present invention, which includes the following steps:

[0052] Step 1: In the limited code length transmission scenario based on expired channel state information in the Industrial Internet of Things, the base station acquires the expired channel state information caused by periodic estimation and feedback delay; based on the correlation between the expired channel state information and the current channel state information, a channel time-domain evolution model is constructed.

[0053] Step 2: Based on the channel time-domain evolution model, derive the expected transmission rate under given expired channel state information; with the goal of maximizing the total expected transmission rate of the system, combine the total power constraint, single-user power constraint, total code length constraint and single-user code length constraint to construct a joint optimization problem on transmit power and code length;

[0054] Step 3: Perform continuous relaxation and convexity analysis on the joint optimization problem, and solve it using the ellipsoid method to obtain a preliminary power and code length allocation scheme; round the code length value in the preliminary power and code length allocation scheme to output the final transmit power and code length joint allocation strategy.

[0055] In step 1 of this embodiment, the base station periodically transmits pilot signals and estimates the link quality accordingly, feeding it back to the base station. Considering the feedback delay generated during this process, which leads to the expiration of channel state information, a transmission expression is constructed.

[0056] The time-domain correlation model between expired channel state information and current channel state information satisfies a Gauss-Markov model:

[0057]

[0058] in, For users in the current time slot Channel gain to base station The estimated value for the previous time slot, i.e., the user Expired channel gain to base station The time-domain correlation coefficient is used to directly quantify the quality of channel state information. It is independent complex Gaussian noise.

[0059] In step 2 of this embodiment, the instantaneous coding rate expression is constructed based on the finite code length normal approximation and is expressed as:

[0060]

[0061] in, Instantaneous coding rate, For users Code length, For block error rate, For users Channel dispersion, For Gauss function The inverse function, where For integration variables, For users instantaneous signal-to-noise ratio, ,in Indicates user Channel power gain, Indicates user Path loss between the base station and the base station For noise power, This refers to the transmission power.

[0062] The conditional probability density function of the current channel gain under the condition of expired channel gain is represented by a non-central chi-square distribution as follows:

[0063]

[0064] in, Let be the conditional probability density function of the current channel power gain under the condition of the expired channel power gain. For the first type of modified Bessel function, since there is a correlation between the instantaneous CSI and its expiration estimate, when the corresponding expiration channel gain is used... (Estimated from the previous time slot) When the condition is met, the user Instantaneous channel gain It will become a random variable; For users Expired channel power gain, ,in This indicates average large-scale fading. It is a natural exponential function. The instantaneous coding rate expression adopts a finite code-length normal approximation form, and based on this, the expected coding rate conditioned on the expired channel is constructed. for:

[0065]

[0066] Under constraints of total power and code length, as well as upper limits of power and code length for single users, a joint optimization problem concerning transmit power and code length is constructed with the objective of maximizing the overall system transmission rate by jointly allocating code length and power resources.

[0067]

[0068] in, The optimization objective is to represent the sum of the transmission rates of K users given the known expired channel gain; Indicates total power constraint. This indicates the maximum total power. This represents the power limit constraint for each user, where This represents the maximum power for each user. This means for any user All constraints are satisfied; This indicates a total code length constraint. Indicates the maximum total code length; This represents the code length limit constraint for each user. This represents the maximum code length for each user; This indicates that the transmission code length allocated to each user is an integer.

[0069] In step 3 of this embodiment, the joint optimization problem is approximated and the concave function relationship of the approximate optimization model with respect to the optimization variables is analyzed. Based on this, the optimization model is solved using the ellipsoid method to obtain an efficient joint resource allocation scheme.

[0070] Consider the constructed joint optimization problem (OP) where the code length is an integer variable and the power is a continuous variable, making the joint optimization problem (OP) a mixed integer programming problem. Therefore, we first relax the code length to a continuous variable, at which point the continuous optimization problem is expressed as:

[0071]

[0072] For the continuous optimization problem P1, we will analyze its convex function properties with respect to the optimization variables code length and power, and then solve the problem using common convex optimization algorithms. Specifically, since the constraints are all affine functions with respect to the optimization variables, we only need to analyze the convex function properties of the objective function with respect to the optimization variables code length and power, thus proving the objective function of the continuous optimization problem. The Hessian matrix is ​​positive semi-definite, and its Hessian matrix is:

[0073]

[0074] For Hessian matrix First-order principal minor Considering Conditional probability density function Determined by the current channel gain and the expired channel gain, and related to the power variable. It is irrelevant, and the upper and lower limits of the points do not change. The change allows the differentiation operation to be moved inside the integral sign. right The sign of the derivative is determined by the instantaneous coding rate. The derivative with respect to power determines this. Because... and The relationship is linear, so the analysis... right The derivative can be transformed into analysis right The derivative of . By proving about To prove the joint convexity about The joint concavity. For ease of derivation, let the intermediate variable... get:

[0075]

[0076] First, analyze them separately. about and The convexity of, where about The convexity can be analyzed about The convexity is obtained. about The second derivative is:

[0077]

[0078] Based on the above formula, it can be seen that when hour, Combining and It can be seen that there is a linear relationship. .

[0079] Furthermore, the second-order principal minors of the Hessian matrix for:

[0080]

[0081] Similar to first-order principal minors, right The sign of the derivative is determined by the instantaneous coding rate. The derivative with respect to the code length determines this. about The second derivative is:

[0082]

[0083] Based on this further analysis about The joint convexity is obtained about The joint convexity. about The determinant of the Hessian matrix is ​​given by the following formula:

[0084]

[0085] Among them, let the intermediate variable Further analysis Analyzing positive and negative values about The sign of the determinant of the Hessian matrix. Obviously... about Monotonically increasing; while about The second derivative is:

[0086]

[0087] We can obtain, about Monotonically increasing.

[0088] Therefore when Right now Sometimes,

[0089]

[0090] when hour, ,Right now about Monotonically increasing, therefore we have

[0091]

[0092] when hour, .therefore about The determinant of the Hessian matrix is ​​greater than or equal to 0, that is... about Joint convexity. In summary, when sufficient conditions are met...

[0093] hour, about Joint convexity, thus about Therefore, the optimization problem (P1) is a joint concave problem concerning transmit power and code length, and can be solved using the ellipsoid method to obtain the optimal transmit power and code length allocation scheme.

[0094] Figure 3 The figure shows the variation of the overall system transmission rate with block error rate and time-domain correlation coefficient in an embodiment of the present invention. As can be seen from the figure, the overall system transmission rate increases with the increase of the block error rate, indicating that a higher block error rate significantly improves the transmission rate. Simultaneously, the overall system transmission rate increases with the increase of the time-domain correlation coefficient. This is because a larger time-domain correlation coefficient indicates stronger inter-channel correlation, resulting in a smaller difference between the expired CSI and the true CSI values, i.e., reduced CSI uncertainty.

[0095] Example 2

[0096] This embodiment provides a power code length allocation system based on expired channels under finite code length, including:

[0097] The channel time-domain model construction module is used in the Industrial Internet of Things (IIoT) for finite code length transmission scenarios based on expired channel state information. This module enables the base station to acquire expired channel state information caused by periodic estimation and feedback delay. Based on the correlation between expired channel state information and current channel state information, a channel time-domain evolution model is constructed.

[0098] The optimization problem construction module is used to derive the expected transmission rate under given expired channel state information based on the channel time-domain evolution model; with the goal of maximizing the total expected transmission rate of the system, it constructs a joint optimization problem on transmit power and code length by combining total power constraints, single-user power constraints, total code length constraints and single-user code length constraints;

[0099] The solution and strategy generation module performs continuous relaxation and convexity analysis on the joint optimization problem and solves it using the ellipsoid method to obtain a preliminary power and code length allocation scheme. The code length values ​​in the preliminary allocation scheme are rounded to output the final transmit power and code length joint allocation strategy.

[0100] Although preferred embodiments of the invention have been described, those skilled in the art, once they have learned the basic inventive concept, can make other changes and modifications to these embodiments.

[0101] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations to the embodiments of the present invention fall within the scope of equivalent technology of the present invention, the present invention also intends to include these modifications and variations.

[0102] All other parts not described in detail are existing technologies.

Claims

1. A power code length allocation method based on an expired channel under finite code length, characterized in that, Includes the following steps: In a limited code-length transmission scenario based on expired channel state information in the Industrial Internet of Things (IIoT), the base station acquires expired channel state information caused by periodic estimation and feedback delay. Based on the correlation between the expired channel state information and the current channel state information, a channel time-domain evolution model is constructed. This channel time-domain evolution model is a Gaussian-Markov model, specifically expressed as follows: in, For users Channel gain to base station For users Expired channel gain to base station The time-domain correlation coefficient, It is independent complex Gaussian noise; Based on the aforementioned channel time-domain evolution model, the expected transmission rate under given expired channel state information is derived. With the goal of maximizing the overall expected transmission rate of the system, a joint optimization problem concerning transmit power and code length is constructed by combining total power constraints, single-user power constraints, total code length constraints, and single-user code length constraints. The derivation of the expected transmission rate under given expired channel state information includes the following sub-steps: An instantaneous coding rate expression is constructed based on the finite code length transmission theory. Based on the aforementioned channel time-domain evolution model, construct the conditional probability density function of the current channel power gain under the given expired channel power gain condition; Based on the instantaneous coding rate expression and the conditional probability density function, the expected transmission rate mathematical expression conditioned on the expired channel gain is obtained by calculating the mathematical expectation. The joint optimization problem is subjected to continuous relaxation and convexity analysis, and solved using the ellipsoid method to obtain a preliminary power and code length allocation scheme. The code length value in the preliminary power and code length allocation scheme is rounded down to output the final transmit power and code length joint allocation strategy.

2. The power code length allocation method based on an expired channel under finite code length as described in claim 1, characterized in that, The instantaneous coding rate expression is constructed based on the finite code length normal approximation and is expressed as follows: in, Instantaneous coding rate, For users Code length, For block error rate, For users Channel dispersion, For Gauss function The inverse function, where For integration variables, x It is the lower limit of integration. For users Instantaneous signal-to-noise ratio, ,in Indicates user Channel power gain, Indicates user Path loss between the base station and the base station For noise power, This refers to the transmission power.

3. The power code length allocation method based on an expired channel under finite code length as described in claim 2, characterized in that, The conditional probability density function of the current channel power gain under the condition of expired channel power gain is characterized by a non-central chi-square distribution as follows: in, Let be the conditional probability density function of the current channel power gain under the condition of the expired channel power gain. This is a modified Bessel function of the first kind. For users Expired channel power gain, ,in This indicates average large-scale fading. It is a natural exponential function.

4. The power code length allocation method based on an expired channel under finite code length as described in claim 3, characterized in that, The mathematical expression for the expected transmission rate, conditioned on the expired channel gain, is as follows: in, The desired transmission rate is conditioned on the expired channel gain.

5. The power code length allocation method based on an expired channel under finite code length as described in claim 4, characterized in that, The joint optimization problem for transmit power and code length is as follows: in, The optimization objective is to represent the sum of the transmission rates of K users given the known expired channel gain; Indicates total power constraint. This indicates the maximum total power. This represents the power limit constraint for each user, where This represents the maximum power for each user. This means for any user All constraints are satisfied; This indicates a total code length constraint. Indicates the maximum total code length; This represents the code length limit constraint for each user. This represents the maximum code length for each user; This indicates that the transmission code length allocated to each user is an integer.

6. The power code length allocation method based on an expired channel under finite code length as described in claim 5, characterized in that, Continuous relaxation and convexity analysis of the joint optimization problem include: By relaxing the integer code length constraint to a continuous variable, the original joint optimization problem is transformed into a continuous optimization problem. Analyze the objective function of the continuous optimization problem with respect to the variables. , The concavity and convexity, by proving when the user When the instantaneous signal-to-noise ratio and code length satisfy the preset conditions, the objective function of the continuous optimization problem is related to the transmit power. and transmission code length The joint concave function is obtained; based on this joint concavity, the ellipsoid method is used to solve the continuous optimization problem, and the preliminary continuous power vector and continuous code length vector are obtained.

7. The power code length allocation method based on an expired channel under finite code length as described in claim 6, characterized in that, The final output transmit power and code length joint allocation strategy includes: The components in the initial continuous code length vector are rounded to obtain the final code length allocation vector that satisfies the integer constraint; the final code length allocation vector and the continuous power vector together constitute the final transmit power and code length joint allocation strategy.

8. A power code length allocation system based on an expired channel under finite code length, characterized in that, include: The channel time-domain model construction module is used in the Industrial Internet of Things (IIoT) for finite code length transmission scenarios based on expired channel state information. This module enables the base station to acquire expired channel state information caused by periodic estimation and feedback delay. Based on the correlation between expired channel state information and current channel state information, a channel time-domain evolution model is constructed. The optimization problem construction module is used to derive the expected transmission rate under given expired channel state information based on the channel time-domain evolution model; with the goal of maximizing the total expected transmission rate of the system, it constructs a joint optimization problem on transmit power and code length by combining total power constraints, single-user power constraints, total code length constraints and single-user code length constraints; The solution and strategy generation module is used to perform continuous relaxation and convexity analysis on the joint optimization problem and solve it using the ellipsoid method to obtain a preliminary power and code length allocation scheme. The code length value in the preliminary allocation scheme is rounded down to output the final joint allocation strategy of transmit power and code length. The power code length allocation system based on expired channels under finite code length is used to perform the steps in the power code length allocation method based on expired channels under finite code length as described in any one of claims 1-7.

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