Advanced Turbo Decoding and Iterative Stopping Rule Appendix

NOTE: This section is Under-Edit if necessary: Construction began on September 20, 2015 and was finished on September 22, 2015. Update October 10, 2015.

Turbo Coded Signaling over a Coherent Memoryless Channel: Iterative Turbo Code Decoder and Cross-Entropy Stopping Rule Appendix

by Darrell A. Nolta
September 22, 2015 with October 10, 2015 Update

Figure 5. Bit Error Probability for UnCoded, Rate = 1/2 Convolutional Coded, 
          and Rate = 1/3 Turbo Coded (using a 6144-Bit QPP Interleaver) BPSK 
          Signaling over a Coherent Memoryless Channel with Additive White 
          Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed (IID) Source 
          for 10 Million, 1 Million, and 1,001,472 Information Bits for 
          UnCoded, Convolutional Coded, and Turbo Coded BPSK Signaling 
          respectively over a Vector Channel;

          Rate = 1/2, Constraint Length K = 7 (3,1,0,3,3,2,3) a Best 
          (Optimal) Non-Recursive Convolutional Code (J.P. Odenwalder) and 
          Viterbi Algorithm using a Path Memory Length of 35 bits and an 
          Unquantized Branch Metric;

          Rate (r) = 1/3, K = 3 Turbo Code based on a r = 1/2, K = 3 (G0 = 7 
          octal, G1 = 5 octal) Recursive Systematic Convolutional component 
          code and a 6144-Bit QPP Turbo Encoder Interleaver; and

          Log-MAP Iterative Turbo Decoder using Systematic Channel Output as 
          input to both component decoders and Decode Information Bit Decision
          is based on the Sum of both decoders' log-likelihood ratios 
          (L-values) and for One Iteration, Two Iterations, Four Iterations, 
          and Six Iterations Fixed Number Stopping Rule. 

Figure 6. Bit Error Probability for UnCoded, Rate = 1/2 Convolutional Coded, 
          and Rate = 1/3 Turbo Coded (using a 32768-Bit QPP Interleaver) BPSK 
          Signaling over a Coherent Memoryless Channel with Additive White 
          Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed (IID) Source 
          for 10 Million, 1 Million, and 1,001,472 Information Bits for 
          UnCoded, Convolutional Coded, and Turbo Coded BPSK Signaling 
          respectively over a Vector Channel;

          Rate = 1/2, Constraint Length K = 7 (3,1,0,3,3,2,3) a Best (Optimal)
          Non-Recursive Convolutional Code (J.P. Odenwalder) and Viterbi 
          Algorithm using a Path Memory Length of 35 bits and an Unquantized 
          Branch Metric;

          Rate (r) = 1/3, K = 3 Turbo Code based on a r = 1/2, K = 3 (G0 = 7 
          octal, G1 = 5 octal) Recursive Systematic Convolutional component 
          code and a 32768-Bit QPP Turbo Encoder Interleaver; and

          Log-MAP Iterative Turbo Decoder using Systematic Channel Output as 
          input to both component decoders and Decode Information Bit 
          Decision is based on the Sum of both decoders' log-likelihood ratios
          (L-values) and for One Iteration, Two Iterations, Four Iterations, 
          and Six Iterations Fixed Number Stopping Rule.

Figure 7. Bit Error Probability for UnCoded, Rate = 1/2 Convolutional Coded, 
          and Rate = 1/3 Turbo Coded (TC) BPSK Signaling over a Coherent 
          Memoryless Channel with Additive White Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed  (IID) Source 
          for 10 Million, 1 Million, and 1,001,472 Information Bits for 
          UnCoded, Convolutional Coded, and Turbo Coded BPSK Signaling 
          respectively over a Vector Channel;

          Rate = 1/2, Constraint Length K = 7, (3,1,0,3,3,2,3), a Best 
          (Optimal) Non-Recursive Convolutional Code (J.P. Odenwalder) and 
          Viterbi Algorithm using a Path Memory Length of 35 bits and an 
          Unquantized Branch Metric;

          Rate (r) = 1/3, K = 3 Turbo Code based on a r = 1/2, K = 3 (G0 = 7 
          octal, G1 = 5 octal) Recursive Systematic Convolutional component 
          code and a 6144-Bit QPP Turbo Encoder Interleaver; and

          Log-MAP Iterative Turbo Decoder using Systematic Channel Output as 
          input to both component decoders and Decode Information Bit Decision 
          is based on the Sum of both decoders' log-likelihood ratios (L-values) 
          and for Fixed Number (6 Iterations) and Cross-Entropy (6 Iterations 
          Maximum) Stopping Rules.

Figure 8. Bit Error Probability for UnCoded, Rate = 1/2 Convolutional Coded, 
          and Rate = 1/2 Punctured Turbo Coded (PTC) BPSK Signaling over a 
          Coherent Memoryless Channel with Additive White Gaussian Noise 
          (AWGN):

          Equal probable Independent and Identical Distributed (IID) Source 
          for 10 Million, 1 Million, and 1,001,472 Information Bits for UnCoded, 
          Convolutional Coded and PTC BPSK Signaling respectively over a Vector
          Channel;

          Rate = 1/2, Constraint Length K = 7, (3,1,0,3,3,2,3), a Best 
          (Optimal)Non-Recursive Convolutional Code (J.P. Odenwalder) and 
          Viterbi Algorithm using a Path Memory Length of 35 bits and an 
          Unquantized Branch Metric;

          Rate (r) = 1/5, K = 4 Parent Turbo Code based on a r = 1/3, K = 4 
          (G0 = 13 octal, G1 = 15 octal, G2 = 17 octal) Recursive Systematic 
          Convolutional component code (Optimum-weight Spectrum) and a 
          6144-Bit QPP Turbo Encoder Interleaver;

          Punctured Turbo Code Rate = 1/2 for Puncturing Period of 2 and 
          Puncturing Matrix = [[1,1],[1,0],[0,0][0,1],[0,0]]; and 

          Log-MAP Iterative Turbo Decoder using Systematic Channel Output as 
          input to both component decoders and Decoder Information Bit Decision 
          is based on the Sum of both decoders' log-likelihood ratios (L-values) 
          and for Fixed Number (3 Iterations) and Cross-Entropy (3 Iterations 
          Maximum) Stopping Rules.

Figure 9. Bit Error Probability for UnCoded, Rate = 1/3 Convolutional Coded, 
          and Rate = 1/3 Turbo Coded (TC) Non-Rectangular 8-QAM Signaling over a 
          Coherent Memoryless Channel with Additive White Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed (IID) Source
          for 10,000,002, 1 Million, and 1,001,472 Information Bits for 
          UnCoded, Convolutional Coded, and Turbo Coded Non-Rectangular (NR) 
          8-QAM Signaling respectively over a Vector Channel;

          Rate = 1/3, Constraint Length K = 4, (7,5,6,7), a Best (Optimal) 
          Non-Recursive Convolutional Code (J.P. Odenwalder) and Viterbi 
          Algorithm using a Path Memory Length of 20 bits and an Unquantized 
          Branch Metric;

          Rate (r) = 1/3, K = 4 Turbo Code based on a r = 1/2, K = 4 
          (G0 = 13 octal, G1 = 17 octal) Recursive Systematic Convolutional 
          component code (Optimum-weight Spectrum) and a 6144-Bit QPP Turbo 
          Encoder Interleaver;

          NR 8-QAM Demodulation Constellation DeMapper Algorithm: Max-Log Bit 
          Metrics; and

          Max-Log-MAP Iterative Turbo Decoder using Systematic Channel Output
          as input to both component decoders and Decode Information Bit Decision
          is based on the Sum of both decoders' log-likelihood ratios (L-values)
          and for Fixed Number (5 Iterations) and Cross-Entropy (5 Iterations 
          Maximum) Stopping Rules.

Figure 10. Bit Error Probability for UnCoded, Rate = 1/2 Convolutional Coded, 
          and Rate = 1/2 Punctured Turbo Coded (PTC) Gray Coded QPSK Signaling 
          over a Coherent Memoryless Channel with Additive White Gaussian Noise
          (AWGN):

          Equal probable Independent and Identical Distributed (IID) 
          Source for 10 Million, 1 Million, and 1,001,472 Information Bits for 
          UnCoded, Convolutional Coded, and PTC Gray Coded (GC) QPSK Signaling 
          respectively over a Vector Channel;

          Rate = 1/2, Constraint Length K = 4, (3,2,3,3), a Best (Optimal) 
          Non-Recursive Convolutional Code (J.P. Odenwalder) and Viterbi 
          Algorithm using a Path Memory Length of 20 bits and an Unquantized 
          Branch Metric;

          Rate (r) = 1/3, K = 4 Parent Turbo Code based on a r = 1/2, K = 4 
          (G0 = 13 octal, G1 = 17 octal) Recursive Systematic Convolutional 
          component code (Optimum-weight Spectrum) and a 6144-Bit QPP Turbo 
          Encoder Interleaver;

          Punctured Turbo Code Rate = 1/2 for Puncturing Period of 2 and 
          Puncturing Matrix = [[1,1],[1,0],[0,1]];

          GC QPSK Demodulation Constellation DeMapper Algorithm: Max-Log 
          Bit Metrics; and

          Max-Log-MAP Iterative Turbo Decoder using Systematic Channel Output 
          as input to both component decoders and Decoder Information Bit 
          Decision is based on the Sum of both decoders' log-likelihood ratios 
          (L-values) and for Fixed Number (4 Iterations) and Cross-Entropy 
          (4 Iterations Maximum) Stopping Rules.

Figure 11. Bit Error Probability for UnCoded, Rate Matching (RM) Punctured 
          Convolutional Coded (PCC), and RM Punctured Turbo Coded PTC) 
          'Impure' Gray Coded Non-Rectangular (NR) 16-QAM Signaling over a 
          Coherent Memoryless Channel with Additive White Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed (IID) 
          Source for 10 Million, 1 Million, and 1,001,472 Information Bits 
          for UnCoded, RM PCC, and RM PTC Gray Coded NR 16-QAM Signaling 
          respectively over a Vector Channel;

          Parent Code Rate = 1/3, K = 4, (7,5,6,7) a Non-Recursive 
          Convolutional Code and Viterbi Algorithm Decoder using a Path Memory 
          Length of 48 bits and a squared Euclidean distance Branch Metric;

          Punctured Code (Rp = 2/4) derived from this 1/3 rate parent code 
          for Puncturing Period of 2 using the Puncturing Matrix 
          P = [[1,0],[1,1],[0,1]];

          Rate (r) = 1/3, K = 4 Parent Turbo Code based on a r = 1/2, K = 4 
          (G0 = 13 octal, G1 = 17 octal) Recursive Systematic Convolutional
          component code (Optimum-weight Spectrum) and a 6144-Bit QPP Turbo 
          Encoder Interleaver;

          Punctured Turbo Code Rate = 1/2 for Puncturing Period of 2 and 
          Puncturing Matrix P = [[1,1],[1,0],[0,1]];

          'Impure' Gray Code NR 16-QAM Demodulation Constellation DeMapper 
          Algorithm: Max-Log Bit Metrics; and

          Max-Log-MAP Iterative Turbo Decoder using Systematic Channel Output 
          as input to both component decoders and Decoder Information Bit 
          Decision is based on the Sum of both decoders' log-likelihood ratios 
          (L-values) and for Fixed Number (4 Iterations) and Cross-Entropy 
          (4 Iterations Maximum) Stopping Rules.

Figure 12. Bit Error Probability for UnCoded and Rate = 1/3 Turbo Coded (TC) 
          BPSK Signaling over a Coherent Memoryless Channel with Additive White 
          Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed  (IID) Source
          for 10 Million and 1,001,472 Information Bits for UnCoded and 
          Turbo Coded BPSK Signaling over a Vector Channel, respectively;

          Rate (r) = 1/3, K = 3 Turbo Code based on a r = 1/2, K = 3 (G0 = 7 
          octal, G1 = 5 octal) Recursive Systematic Convolutional component 
          code and a 6144-Bit QPP Turbo Encoder Interleaver; and

          Log-MAP Iterative Turbo Decoder using Systematic Channel Output as 
          input to both component decoders and Decode Information Bit Decision 
          is based on the Sum of both decoders' log-likelihood ratios (L-values) 
          and for Cross-Entropy (6 Iterations Maximum) Stopping Rule.

Figure 13. Bit Error Probability for UnCoded and Rate = 1/2 Punctured Turbo 
          Coded (PTC) BPSK Signaling over a Coherent Memoryless Channel 
          with Additive White Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed (IID) Source 
          for 10 Million and 1,001,472 Information Bits for UnCoded and PTC BPSK 
          Signaling over a Vector Channel, respectively;

          Rate (r) = 1/5, K = 4 Parent Turbo Code based on a r = 1/3, K = 4 
          (G0 = 13 octal, G1 = 15 octal, G2 = 17 octal) Recursive Systematic 
          Convolutional component code (Optimum-weight Spectrum) and a 
          6144-Bit QPP Turbo Encoder Interleaver;

          Punctured Turbo Code Rate = 1/2 for Puncturing Period of 2 and 
          Puncturing Matrix = [[1,1],[1,0],[0,0][0,1],[0,0]]; and 

          Log-MAP Iterative Turbo Decoder using Systematic Channel Output as 
          input to both component decoders and Decoder Information Bit Decision 
          is based on the Sum of both decoders' log-likelihood ratios (L-values) 
          and Cross-Entropy (3 Iterations Maximum) Stopping Rule.

Figure 14. Bit Error Probability for UnCoded and Rate = 1/2 Punctured Turbo 
          Coded (PTC) Gray Coded QPSK Signaling over a Coherent Memoryless 
          Channel with Additive White Gaussian Noise (AWGN):

          Equal probable Independent and Identical Distributed (IID) Source 
          for 10 Million and 1,001,472 Information Bits for UnCoded and PTC 
          Gray Coded (GC) QPSK Signaling over a Vector Channel, respectively;

          Rate (r) = 1/3, K = 4 Parent Turbo Code based on a r = 1/2, K = 4 
          (G0 = 13 octal, G1 = 17 octal) Recursive Systematic Convolutional 
          component code (Optimum-weight Spectrum) and a 6144-Bit QPP Turbo 
          Encoder Interleaver;

          Punctured Turbo Code Rate = 1/2 for Puncturing Period of 2 and 
          Puncturing Matrix = [[1,1],[1,0],[0,1]];

          GC QPSK Demodulation Constellation DeMapper Algorithm: Max-Log 
          Bit Metrics; and

          Max-Log-MAP Iterative Turbo Decoder using Systematic Channel Output 
          as input to both component decoders and Decoder Information Bit 
          Decision is based on the Sum of both decoders' log-likelihood ratios 
          (L-values) and for Cross-Entropy (4 Iterations Maximum) Stopping Rule.

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