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

以下是Polar码编码和SC译码的Verilog代码和testbench：

module polar_encoder
  #(parameter N = 8, K = 4)
  (
    input clk,
    input rst,
    input [K-1:0] data_in,
    output [N-1:0] code_out
  );
 
  wire [N-1:0] u;
  wire [N-1:0] x;
  wire [K-1:0] data;
  assign data = {data_in, {N-K{1'b0}}};
 
  // Polar transform matrix
  wire [N-1:0] G [0:N-1];
  generate
    for (genvar i = 0; i < N; i = i + 1) begin
      for (genvar j = 0; j < N; j = j + 1) begin
        if (i == j) begin
          assign G[i][j] = 1'b1;
        end else begin
          assign G[i][j] = {1'b1, 1'b0} ^ (i & j);
        end
      end
    end
  endgenerate
 
  assign u = data * G;
 
  // Encoding
  assign x = u ^ {N{1'b0}};
  assign code_out = x ^ u;
 
endmodule
 
module sc_decoder
  #(parameter N = 8, K = 4)
  (
    input clk,
    input rst,
    input [N-1:0] code_in,
    output reg [K-1:0] data_out
  );
 
  reg [N-1:0] L [0:K-1][0:N-1];
  reg [N-1:0] u [0:K-1][0:N-1];
  reg [N-1:0] x [0:K-1][0:N-1];
 
  integer i, j, k, n, m;
 
  always @(posedge clk) begin
    if (rst) begin
      for (k = 0; k < K; k = k + 1) begin
        for (n = 0; n < N; n = n + 1) begin
          L[k][n] <= {N{1'b0}};
          u[k][n] <= {N{1'b0}};
          x[k][n] <= {N{1'b0}};
        end
      end
    end else begin
      // Polar transform matrix
      wire [N-1:0] G [0:N-1];
      generate
        for (genvar i = 0; i < N; i = i + 1) begin
          for (genvar j = 0; j < N; j = j + 1) begin
            if (i == j) begin
              assign G[i][j] = 1'b1;
            end else begin
              assign G[i][j] = {1'b1, 1'b0} ^ (i & j);
            end
          end
        end
      endgenerate
 
      for (n = 0; n < N; n = n + 1) begin
        L[0][n] <= code_in[n]; // Initialize L[0][n] with code_in[n]
      end
 
      // SC decoding
      for (k = 1; k < K; k = k + 1) begin
        for (n = 0; n < N; n = n + 1) begin
          L[k][n] <= L[k-1][n] ^ L[k-1][n xor (1<<(K-k))];
        end
 
        for (n = 0; n < N; n = n + 1) begin
          u[k][n] <= u[k-1][n];
          if (n < (1<<(K-k))) begin
            x[k][n] <= x[k-1][n] ^ u[k-1][n xor (1<<(K-k))];
          end else begin
            x[k][n] <= x[k-1][n];
          end
        end
 
        for (n = 0; n < N; n = n + 1) begin
          m = G[n][k-1] ? 1 : -1;
          L[k][n] = m * L[k][n];
        end
 
        for (n = 0; n < N; n = n + 1) begin
          if (L[k][n] >= 0) begin
            u[k][n] = x[k][n];
          end else begin
            u[k][n] = x[k][n] ^ 1;
          end
        end
      end
 
      for (n = 0; n < K; n = n + 1) begin
        data_out[n] <= u[K-1][n];
      end
    end
  end
 
endmodule

module polar_tb;
  reg clk;
  reg rst;
  reg [3:0] data_in;
  wire [7:0] code_out;
  reg [3:0] data_out;
 
  polar_encoder #(.N(8), .K(4))
  encoder (
    .clk(clk),
    .rst(rst),
    .data_in(data_in),
    .code_out(code_out)
  );
 
  sc_decoder #(.N(8), .K(4))
  decoder (
    .clk(clk),
    .rst(rst),
    .code_in(code_out),
    .data_out(data_out)
  );
 
  initial begin
    clk = 0;
    rst = 1;
    data_in = 0;
    #10 rst = 0;
    #10 rst = 1;
    #10 rst = 0;
    #10 data_in = 4'h1;
    #10 data_in = 4'h2;
    #10 data_in = 4'h3;
    #10 data_in = 4'h4;
    #100 $finish;
  end
 
  always #5 clk = ~clk;
 
  always @(posedge clk) begin
    $display("data_in = %d, code_out = %b, data_out = %d", data_in, code_out, data_out);
  end
 
endmodule

在testbench中，我们对编码器和译码器进行实例化，并为输入信号提供一组测试向量。每个时钟周期，我们使用 $display() 函数来显示输入和输出信号的值。运行仿真后，我们可以观察到编码器和译码器的输出，并验证它们是否正确。

请注意，由于Verilog语言中没有内置的除法运算符，因此在上述代码中，我们使用左移运算符来计算 $2^{K-k}$。此外，我们还使用了 generate 语句来生成极化变换矩阵，以便在编码器和译码器中使用。