使用Verilog语言完成polar码编码与SC译码仿真，并给出testbench,

以下是Verilog语言实现polar码编码的代码：

module polar_encoder(input clk, input rst, input [7:0] data_in, output reg [7:0] encoded_data);

parameter N = 8; // 符号长度
parameter K = 4; // 信息位长度
parameter L = 3; // 循环次数
parameter F = 2; // 冻结位长度

reg [7:0] u [0:N-1];
reg [7:0] x [0:N-1];
reg [7:0] y [0:N-1];

integer i, j, t, m;
integer bit_reverse_table[N];

always @(posedge clk) begin
    if (rst) begin
        for (i = 0; i < N; i = i + 1) begin
            u[i] = 0;
            x[i] = 0;
            y[i] = 0;
        end
        for (i = 0; i < N; i = i + 1) begin
            bit_reverse_table[i] = i;
        end
        for (i = 0; i < N/2; i = i + 1) begin
            bit_reverse_table[i] = bit_reverse_table[i] ^ bit_reverse_table[N-i-1];
            bit_reverse_table[N-i-1] = bit_reverse_table[i] ^ bit_reverse_table[N-i-1];
            bit_reverse_table[i] = bit_reverse_table[i] ^ bit_reverse_table[N-i-1];
        end
    end else begin
        // 构造输入信息
        for (i = 0; i < K; i = i + 1) begin
            u[i] = data_in[i];
        end
        // 构造冻结位
        for (i = K; i < N; i = i + 1) begin
            u[i] = 0;
        end
        // 构造输入序列
        for (i = 0; i < N; i = i + 1) begin
            x[bit_reverse_table[i]] = u[i];
        end
        // 构造码字
        for (t = 0; t < L; t = t + 1) begin
            m = 1 << t;
            for (i = 0; i < N; i = i + 2*m) begin
                for (j = 0; j < m; j = j + 1) begin
                    y[i+j] = x[i+j] ^ x[i+j+m];
                    y[i+j+m] = x[i+j+m];
                end
            end
            for (i = 0; i < N; i = i + 1) begin
                x[i] = y[i];
            end
        end
        // 构造输出码字
        for (i = 0; i < N; i = i + 1) begin
            encoded_data[i] = x[bit_reverse_table[i]];
        end
    end
end

endmodule

以下是Verilog语言实现SC译码的代码：

module polar_sc_decoder(input clk, input rst, input [7:0] received_data, output reg [7:0] decoded_data);

parameter N = 8; // 符号长度
parameter K = 4; // 信息位长度
parameter L = 3; // 循环次数
parameter F = 2; // 冻结位长度

reg [7:0] u_hat [0:N-1];
reg [7:0] u [0:N-1];
reg [7:0] x [0:N-1];
reg [7:0] y [0:N-1];
reg [7:0] llr [0:N-1];
reg [7:0] path_metric [0:2**(L+1)-1][0:N-1];
reg [7:0] path_history [0:2**(L+1)-1][0:L-1];
reg [1:0] path_index [0:L-1];

integer i, j, t, m, s;
integer bit_reverse_table[N];
integer min_metric_index;
integer path_index_temp;

always @(posedge clk) begin
    if (rst) begin
        for (i = 0; i < N; i = i + 1) begin
            u_hat[i] = 0;
            u[i] = 0;
            x[i] = 0;
            y[i] = 0;
            llr[i] = 0;
        end
        for (i = 0; i < 2**(L+1); i = i + 1) begin
            for (j = 0; j < N; j = j + 1) begin
                path_metric[i][j] = 0;
            end
            for (j = 0; j < L; j = j + 1) begin
                path_history[i][j] = 0;
            end
        end
        for (i = 0; i < L; i = i + 1) begin
            path_index[i] = 0;
        end
        for (i = 0; i < N; i = i + 1) begin
            bit_reverse_table[i] = i;
        end
        for (i = 0; i < N/2; i = i + 1) begin
            bit_reverse_table[i] = bit_reverse_table[i] ^ bit_reverse_table[N-i-1];
            bit_reverse_table[N-i-1] = bit_reverse_table[i] ^ bit_reverse_table[N-i-1];
            bit_reverse_table[i] = bit_reverse_table[i] ^ bit_reverse_table[N-i-1];
        end
    end else begin
        // 构造输入符号
        for (i = 0; i < N; i = i + 1) begin
            u_hat[i] = received_data[i];
        end
        // 构造输入信息
        for (i = 0; i < K; i = i + 1) begin
            u[i] = u_hat[i];
        end
        // 构造冻结位
        for (i = K; i < N; i = i + 1) begin
            u[i] = 0;
        end
        // 构造输入序列
        for (i = 0; i < N; i = i + 1) begin
            x[bit_reverse_table[i]] = u_hat[i];
        end
        // 计算LLR
        for (i = 0; i < N; i = i + 1) begin
            if (u_hat[i] == 1) begin
                llr[i] = -128;
            end else begin
                llr[i] = 128;
            end
        end
        // 构造码字
        for (t = 0; t < L; t = t + 1) begin
            m = 1 << t;
            for (i = 0; i < N; i = i + 2*m) begin
                for (j = 0; j < m; j = j + 1) begin
                    y[i+j] = x[i+j] ^ x[i+j+m];
                    y[i+j+m] = x[i+j+m];
                end
            end
            for (i = 0; i < N; i = i + 1) begin
                x[i] = y[i];
            end
        end
        // 构造输出信息
        for (i = 0; i < K; i = i + 1) begin
            decoded_data[i] = x[i];
        end
        // 计算路径度量
        for (i = 0; i < N; i = i + 1) begin
            path_metric[0][i] = llr[i];
        end
        for (t = 0; t < L; t = t + 1) begin
            m = 1 << t;
            for (s = 0; s < m; s = s + 1) begin
                for (i = 0; i < 2**t; i = i + 1) begin
                    for (j = 0; j < m; j = j + 1) begin
                        path_metric[(i*(2*m))+j+s+m][i*(2*m)+j] = path_metric[(i*(2*m))+j+s][i*(2*m)+j] + path_metric[(i*(2*m))+j+s][i*(2*m)+j+m];
                        path_metric[(i*(2*m))+j+s][i*(2*m)+j+m] = path_metric[(i*(2*m))+j+s][i*(2*m)+j] - path_metric[(i*(2*m))+j+s][i*(2*m)+j+m];
                    end
                end
            end
        end
        // 选择最优路径
        for (i = 0; i < 2**L; i = i + 1) begin
            path_metric[(2**L)+i][0] = path_metric[i*(2**(L-1))][0];
            path_history[(2**L)+i][0] = i;
        end
        for (t = 1; t < L; t = t + 1) begin
            for (i = 0; i < 2**(L-t); i = i + 1) begin
                min_metric_index = 0;
                for (j = 0; j < 2; j = j + 1) begin
                    if (path_metric[(i*2+j)*(2**t)][t] < path_metric[(i*2+min_metric_index)*(2**t)][t]) begin
                        min_metric_index = j;
                    end
                end
                path_metric[(i+2**(L-t))*(2**t)][t] = path_metric[(i*2+min_metric_index)*(2**t)][t];
                for (j = 0; j < t; j = j + 1) begin
                    path_history[(i+2**(L-t))*(2**t)][j] = path_history[(i*2+min_metric_index)*(2**t)][j];
                end
                path_history[(i+2**(L-t))*(2**t)][t-1] = min_metric_index;
            end
        end
        min_metric_index = 0;
        for (i = 0; i < 2**L; i = i + 1) begin
            if (path_metric[(2**L)+i][N-1] < path_metric[(2**L)+min_metric_index][N-1]) begin
                min_metric_index = i;
            end
        end
        for (i = 0; i < L; i = i + 1) begin
            path_index[i] = path_history[(2**L)+min_metric_index][i];
        end
        // 译码
        for (i = 0; i < N; i = i + 1) begin
            u[i] = u_hat[i];
        end
        for (t = L-1; t >= 0; t = t - 1) begin
            m = 1 << t;
            for (i = 0; i < 2**t; i = i + 1) begin
                path_index_temp = path_index[t*(2**t)+i];
                for (j = 0; j < m; j = j + 1) begin
                    u[i*(2*m)+j+path_index_temp*m] = u[i*(2*m)+j] ^ u[i*(2*m)+j+m];
                    u[i*(2*m)+j+m+path_index_temp*m] = u[i*(2*m)+j+m];
                end
            end
        end
        // 构造输出序列
        for (i = 0; i < N; i = i + 1) begin
            decoded_data[i] = u[bit_reverse_table[i]];
        end
    end
end

endmodule

以下是Verilog语言实现polar码编码与SC译码的testbench代码：

module polar_testbench();

parameter N = 8; // 符号长度
parameter K = 4; // 信息位长度
parameter L = 3; // 循环次数
parameter F = 2; // 冻结位长度

reg clk;
reg rst;
reg [7:0] data_in;
wire [7:0] encoded_data;
wire [7:0] received_data;
wire [7:0] decoded_data;
integer i, j;

polar_encoder encoder(clk, rst, data_in, encoded_data);
polar_sc_decoder decoder(clk, rst, received_data, decoded_data);

initial begin
    clk = 0;
    rst = 1;
    data_in = 0;
    #100;
    rst = 0;
end

always #10 clk = ~clk;

always @(posedge clk) begin
    if (~rst) begin
        data_in = data_in + 1;
    end
end

initial begin
    #100;
    for (i = 0; i < 2**K; i = i + 1) begin
        data_in = i;
        #10;
        $display("data_in = %d, encoded_data = ", data_in);
        for (j = 0; j < N; j = j + 1) begin
            $write("%d ", encoded_data[j]);
        end
        $write(", received_data = ");
        for (j = 0; j < N; j = j + 1) begin
            if ($random % 2 == 0) begin
                received_data[j] = encoded_data[j];
            end else begin
                received_data[j] = ~encoded_data[j];
            end
            $write("%d ", received_data[j]);
        end
        $write(", decoded_data = ");
        for (j = 0; j < K; j = j + 1) begin
            $write("%d ", decoded_data[j]);
        end
        $display("");
    end
    #10;
    $finish;
end

endmodule