基于IR_HARQ系统的LDPC码改进译码方式研究
摘要
LDPC码的IR_HARQ方式,通过在重传时增加校验比特或对信息比特打孔两种方式降低码率,从而获得纠错能力更强的码。由于重传过程只需传输部分校验比特,相比其他HARQ方式,LDPC码的IR_HARQ方式能够得到更好的吞吐量性能,但它同时要求LDPC码具有码率兼容的特性。目前的研究主要集中在如何构造LDPC码方面,译码解决方案成为被忽视的问题。
本文提出了一种基于IR_HARQ系统的LDPC码的改进译码方法。3σ原理指出,在n比特的分组中出现错误比特的个数大于3σ错误区间t 3σ的概率( )P t≥t 3σ1,因此,根据译码前后的误比特率能够计算出译码前后的错误比特数。结果表明,一次译码之后,一帧中绝大部分的错误比特能够被正确译码。如何在重传译码过程中利用已纠正比特所提供的有效信息成为提高重传译码性能的关键所在。
本文对改进后译码方法的具体实现进行了研究。改进译码方法由信道的信噪比特性确定上次译码过程所能提供的信息量,从而确定加权系数以实现对上次译码结果的有效利用。由于绝大多数错误比特在一次译码过程中都可以被纠正,在重传过程中使用新的初始软信息相当于对信息传输过程中的失真进行了一定程度的弥补。同时,LDPC码采用软信息迭代译码,信道的信噪比特性是译码时必须的参数,而加权系数与上次译码结果的乘法运算和迭代译码的计算量相比微不足道,因此,改进译码方法在提高重传译码性能、减少迭代次数的同时,并不会增加译码器额外的复杂度。
本文选用802.16标准中的(2304, 1920)LDPC码和(2304, 1728)LDPC码作为纠错码,在AWGN信道下,采用BPSK调制和停等协议,对新旧译码方法的吞吐量和迭代次数进行了比较。仿真结果表明,在信噪比相对较低的范围内,新的译码方法可以使吞吐量提高2%～20%,新方法显示了在低信噪比下的性能优越性;而在信噪比相对较高的范围内,新译码方法对吞吐量的提高并不明显,但迭代次数减少了5%～20%。
A special type of LDPC codes, named structured Rate Compatible LDPC (RC_LDPC) code with flexible code rate and code sizes is proposed. Based on the essential feature of this kind of LDPC code, its Incremental Redundancy Hybrid ARQ is also presented. It reduces code rate by puncturing message bits or extending check bits. As only a part of check bits are retransmitted during retransmission, this scheme could provide better throughput performance than that of other HARQ schemes. However, this scheme requires that the FEC is Rate Compatible codes. The focus of people's research has been on how to build the RC codes, and the decoding scheme is the area to be ignored.
This paper proposes an improved decoding method based on IR_HARQ scheme that uses rate-compatible LDPC codes as the FEC codes.3σprinciple indicates that if a variable X is normally distributed, 99.7% of the observations fall within 3 standard deviations of the mean, that is, betweenμ? 3σandμ+ 3σ. So it is possible to get the numbers of error bits both before and after the decoding process with the bit-error-rate (BER) correspondingly. And the computing result shows that there are always parts of bits has been decoded correctly during a decoding process despite of whether the decoding is successful. How to make good use of the former decoding results is important to enhance the performance of retransmission decoding.
This paper proposes implementation of this improved decoding method. Instead of the initial reliabilities of the first decoding process, the final reliabilities from the previous decoding process could be selected as the initial reliabilities of the previously received bits during the latest decoding process. And the new decoding method calculates the privilege factor by the properties of the channel. Then the former decoding result could be used effectively. As most of error bits have been corrected during last decoding process, the new decoding method gives compensation to the distortion which the channel brings to. Moreover, the proposed scheme will not increase the complexity of the decoder.
Choosing both the (2304, 1920) and (2304, 1728) LDPC codes defined in the 802.16 standard as the FEC codes, this paper simulates the performance of new and traditional decoding methods under AWGN channel with BPSK modulation and stop-and-wait scheme. And the results show that nearly 2%~20% enhance of throughput efficiency could be got while SNR is comparatively lower with the new decoding method. And during the area where SNR is comparatively higher, the enhance of throughput efficiency is not apparent, however, the decrease of iterative times reaches to 5%~20%, and that means the same trend of system decoding time-delay.
本文提出了一种基于IR_HARQ系统的LDPC码的改进译码方法。3σ原理指出,在n比特的分组中出现错误比特的个数大于3σ错误区间t 3σ的概率( )P t≥t 3σ1,因此,根据译码前后的误比特率能够计算出译码前后的错误比特数。结果表明,一次译码之后,一帧中绝大部分的错误比特能够被正确译码。如何在重传译码过程中利用已纠正比特所提供的有效信息成为提高重传译码性能的关键所在。
本文对改进后译码方法的具体实现进行了研究。改进译码方法由信道的信噪比特性确定上次译码过程所能提供的信息量,从而确定加权系数以实现对上次译码结果的有效利用。由于绝大多数错误比特在一次译码过程中都可以被纠正,在重传过程中使用新的初始软信息相当于对信息传输过程中的失真进行了一定程度的弥补。同时,LDPC码采用软信息迭代译码,信道的信噪比特性是译码时必须的参数,而加权系数与上次译码结果的乘法运算和迭代译码的计算量相比微不足道,因此,改进译码方法在提高重传译码性能、减少迭代次数的同时,并不会增加译码器额外的复杂度。
本文选用802.16标准中的(2304, 1920)LDPC码和(2304, 1728)LDPC码作为纠错码,在AWGN信道下,采用BPSK调制和停等协议,对新旧译码方法的吞吐量和迭代次数进行了比较。仿真结果表明,在信噪比相对较低的范围内,新的译码方法可以使吞吐量提高2%～20%,新方法显示了在低信噪比下的性能优越性;而在信噪比相对较高的范围内,新译码方法对吞吐量的提高并不明显,但迭代次数减少了5%～20%。
A special type of LDPC codes, named structured Rate Compatible LDPC (RC_LDPC) code with flexible code rate and code sizes is proposed. Based on the essential feature of this kind of LDPC code, its Incremental Redundancy Hybrid ARQ is also presented. It reduces code rate by puncturing message bits or extending check bits. As only a part of check bits are retransmitted during retransmission, this scheme could provide better throughput performance than that of other HARQ schemes. However, this scheme requires that the FEC is Rate Compatible codes. The focus of people's research has been on how to build the RC codes, and the decoding scheme is the area to be ignored.
This paper proposes an improved decoding method based on IR_HARQ scheme that uses rate-compatible LDPC codes as the FEC codes.3σprinciple indicates that if a variable X is normally distributed, 99.7% of the observations fall within 3 standard deviations of the mean, that is, betweenμ? 3σandμ+ 3σ. So it is possible to get the numbers of error bits both before and after the decoding process with the bit-error-rate (BER) correspondingly. And the computing result shows that there are always parts of bits has been decoded correctly during a decoding process despite of whether the decoding is successful. How to make good use of the former decoding results is important to enhance the performance of retransmission decoding.
This paper proposes implementation of this improved decoding method. Instead of the initial reliabilities of the first decoding process, the final reliabilities from the previous decoding process could be selected as the initial reliabilities of the previously received bits during the latest decoding process. And the new decoding method calculates the privilege factor by the properties of the channel. Then the former decoding result could be used effectively. As most of error bits have been corrected during last decoding process, the new decoding method gives compensation to the distortion which the channel brings to. Moreover, the proposed scheme will not increase the complexity of the decoder.
Choosing both the (2304, 1920) and (2304, 1728) LDPC codes defined in the 802.16 standard as the FEC codes, this paper simulates the performance of new and traditional decoding methods under AWGN channel with BPSK modulation and stop-and-wait scheme. And the results show that nearly 2%~20% enhance of throughput efficiency could be got while SNR is comparatively lower with the new decoding method. And during the area where SNR is comparatively higher, the enhance of throughput efficiency is not apparent, however, the decrease of iterative times reaches to 5%~20%, and that means the same trend of system decoding time-delay.
引文
[1] C.E.Shannon.“A Mathematical Theory of Communication,”USA Bell Systematic Technical Journal. Vol.27. pp. 379-423,623-656, July-Oct. 1948
[2]王新梅,肖国镇.“纠错码—原理与方法(修订版),”西安:西安电子科技大学出版社,2001
[3] C. Berrou, A. Glavieux, and P. Thitimajshima.“Near Shannon Limit Error-Correcting Coding and Decoding: Turbo-Codes,”Proc.ICC’93, May 1993. pp. 1064-1070
[4] R.G. Gallager.“Low Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963
[5] R.G. Gallager.“Low Density Parity-Check Codes,”IRE Trans.Inf.Theory, 1962, 8(1). pp. 21-28
[6] B. K. Classon, V. A. Desai, and M. Cudak.“Method and System for Reduced Memory Hybrid Automatic Repeat Request,”United States Patent, 6700867, Mar. 2, 2004
[7] Mantha, et al.“Hybrid Automatic Repeat Request System and Method,”United States Patent, 7000174, Feb. 14, 2006
[8] S. Sesia, G. Caire, G. Vivier.“Incremental Redundancy Hybrid ARQ Schemes Based on Low-Density Parity-Ccheck Codes,”IEEE Tran. on communication, COM-52: 1311-1322, Aug. 2004
[9]曹一卿,古建,奇琳,杨大成.“一种混和自动请求重发的方法和装置,”中国专利, 200510105204.2
[10] P. Elias.“Coding for Noisy Channels,”IRE Conv. Rec., pt. 4. pp. 37-47, Mar. 1955
[11] D. Mackay, R. Neal.“Near Shannon Limit Performance of Low Density Parity Check Codes,”IEEE Electron. Lett.,vol. 32:1645-1646, Aug. 1996
[12] M. Sipser, D. Spielman.“Expander Codes,”IEEE Trans. Inf. Theory, 42(11). pp. 1710-1722, Nov. 1996
[13] S.-Y. Chung, J. Forney., T. Richardson, R. Urbanke.“On the Design of Low-Density Parity Check Codes Within 0.0045dB of the Shannon Limit,”IEEE Comm. Lett., 5(2). pp.58-60, Feb. 2001
[14] D. Mackay.“Good Error Correcting Codes Based on Very Sparse Matrices,”IEEE Trans. Inf. Theory, vol. 45(2). pp. 399-431, Mar. 1999
[15] D. Mackay.“Gallager Codes That are Better Than Turbo Codes,”Proc. 36th Allerton Conf. Commun., Control, and Computing, Monticello, Ill., Sep. 1998
[16] D. Mackay, S. Wilson, M. Davey.“Comparison of Constructions of Irregular Gallager Codes,”IEEE Trans. Comm., 46(10). pp. 1449-1454, Oct.1998
[17] Y. Kou, S. Lin, M. Fossorier.“Low-Density Parity-Check Codes Based on Finite Geometries: A Rediscovery and New Results,”IEEE Trans. Inf. Theory, 47(7). pp. 2711-2736, 2001
[18] B. Ammar, B. Honary, Y. Kou, J. Xu, S. Lin.“Construction of Low-Density Parity-Check Codes Based on BalancedIncomplete Block Designs,”IEEE Trans. Inf. Theory, vol. 50, June 2004
[19] H. Wen, F. Hu, J. Li and F. Jin.“A New Family of Irregular LDPC Codes,”IEEE 6th CAS Symp. Proceeding of on Emerging Technologies: Mobile and Wireless Comm., Shanghai, China. pp. 285-288, May 31-Jun. 2, 2004
[20] Draft IEEE Standard for Local and Metropolitan Area Networks. Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, IEEE P802.16e/D12, Oct. 2005
[21] F. Zarkeshvari, A. Banihashemi.“On Implementation of Min-sum Algorithm for Decoding Low-Density Parity-Check Codes,”Global Telecommunications Conference vol. 2, Taiwan Taipei, pp. 17-21, 2002
[22] S. Howard, V. C. Gaudet, C. Schlegel.“Soft-bit Decoding of Regular Low-Density Parity-Check Codes,”IEEE Trans. on Circuits and Systems II. pp. 99, 2005
[23] A. Anastapoulos.“A Comparison Between the Sum-Product and the Min-Sum Iterative Detection Algorithms Based on Density Evolution,”Proc. Globecom Conf. vol.2 San Antonio, TX. pp. 25-29, 2001
[24] R. Benice, A. H. Frey, Jr.,“An Analysis of Retransmission Systems,”IEEE Trans. Comm. Technol, COM-12. pp. 135-45, Dec. 1964
[25] H. Burton, D. Sullivan.“Errors and Error Control,”Proc. IEEE, 60(11). pp. 1293-1310, Nov. 1972
[26] K. Brayer.“Error Control Techniques Using Binary Symbol Burst Codes,”IEEE Trans. Comm., COM-16. pp. 199-214, Apr. 1968
[27] D. Mandelbaum.“A Daptive-Feedback Coding Scheme Using Incremental Redundancy,”IEEE Trans. Inf. Theory, IT-20. pp. 388-39, May 1974
[28] S. Lin, J.-S. Ma.“A Hybrid ARQ System With Parity Retransmission for Error Correction,”IBM Res. Rep., 7478(#32232), Jan. 1979
[29] J. Metzner.“Improvements in Block-Retransmission Schemes,”IEEE Trans. Comm., COM-27. pp. 525-32, February 1979
[30] T. Ancheta.“Convolutional Parity Check Automatic Repeat Request,”Proc. IEEE Intl. Symp. Inform. Theory, Grignano, Italy. pp. 25-29, June 1979
[31] S. Lin, P.-S. Yu.“A Hybrid ARQ Scheme With Parity Retransmission For Error Control of Satellite Channels,”IEEE Trans. Comm., COM-30. pp. 1701-1719, July 1982
[32] D. Rowith, L. Milstein.“Rare Compatible Punctured Turbo (RCPT) Codes in A Hybrid FEC/ARQ System,”IEEE Global Telecommun Mini-Conf. Phoenix, A Z. pp. 55-59, 1997
[33] P. Li, W.-K. Leung, N. Phamdo.“Low Density Parity Check Codes with Semi-Random Parity Check Matrix”, Electron. Lett., 35(1). pp. 38-39, 1999
[34] R. Echard, S.-C. Chang.“The Rotation Low-Density Parity-Check Codes,”Proc. GLOBECOM. pp. 980-984, 2001
[35] 3GPP TSG RAN WG1 #42,R1-050840,“Comparison of Structured LDPC Codes and 3GPP Turbo Codes”, London, UK, Aug. 29th-Sept. 2nd, 2005
[36] H. Behairy, S.-C. Chang. Parallel Concatenated Gallagher Codes,”Electron. Lett., 36(24). pp. 2025-2026, 2000
[37] S. Brink, G. Kramer, A. Ashikhmin.“Design of Low-Density Parity-Check Codes for Modulation and Detection,”IEEE Trans. on Commun., vol. 52, No. 4, Apr. 2004
[38] S. Brink.“Convergence Behavior of Iteratively Decoded Parallel Concatenated Codes,”IEEE Trans. Comm., vol.49. pp. 1727-1737, Oct. 2001
[39] Madhav Chinta,Abdelsalam (Sumi) Helal,Chonhwa Lee. C—TCP: An Interlayer Collaboration Protocol for TCP Performance lm-proverment in Mobile and Wireless Environments [J]. Wireless Communications and Networking, IEEE, 2003, 2(3). pp. 1004-1010
[40] Z.-B. Yao, P. Fan, Z.-G Cao.“Cross Layer Design for Service Diferentiation in Mobile Ad Hoc Networks[C],”IEEE 2003 International Symposium on Personal, Indoor and Mobile Radio Communication Proceedings, 2003
[41] M. Alouini, A. Goldsmith.“Adaptive Modulation Over Nakagami Fading Channels,”Kluwer J. Wireless Commun., vol. 13, no.1-2. pp. 119-143, May 2000
[42] M. Assaad, D. Zeghlache.“Cross-Layer Design in HSDPA System to Reduce the TCP Effect,”IEEE J. Sel. Areas Commun., vol. 24, no. 3. pp. 614-625, Mar. 2006
[43] Q. Liu, S. Zhou, G. Giannakis.“Cross-Layer Combining of Adaptive Modulation and Coding with Truncated ARQ Over Wireless Links,”IEEE Trans. Wireless Commun., vol. 3, no.5. pp. 1746-1755, Sep. 2004
[44] Physical layer aspects of UTRA high speed downlink packet access (release 4), 3GPP TR 25.848 V4.0.0, 2001
[45] L. Le, E. Hossain, A. Alfa.“Service Differentiation in Multirate Wireless Networks with Weighted Round-Robin Scheduling and ARQ-Based Error Control,”IEEE Trans. Comm., vol. 54, No.2 pp. 208-215, Feb. 2006
[46] S. Allpress, C. Luschi, S. Felix.“Exact and Approximated Expressions of the Log-Likelihood Ratio for 16-QAM Signals,”Icera Inc IEEE 2004
[2]王新梅,肖国镇.“纠错码—原理与方法(修订版),”西安:西安电子科技大学出版社,2001
[3] C. Berrou, A. Glavieux, and P. Thitimajshima.“Near Shannon Limit Error-Correcting Coding and Decoding: Turbo-Codes,”Proc.ICC’93, May 1993. pp. 1064-1070
[4] R.G. Gallager.“Low Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963
[5] R.G. Gallager.“Low Density Parity-Check Codes,”IRE Trans.Inf.Theory, 1962, 8(1). pp. 21-28
[6] B. K. Classon, V. A. Desai, and M. Cudak.“Method and System for Reduced Memory Hybrid Automatic Repeat Request,”United States Patent, 6700867, Mar. 2, 2004
[7] Mantha, et al.“Hybrid Automatic Repeat Request System and Method,”United States Patent, 7000174, Feb. 14, 2006
[8] S. Sesia, G. Caire, G. Vivier.“Incremental Redundancy Hybrid ARQ Schemes Based on Low-Density Parity-Ccheck Codes,”IEEE Tran. on communication, COM-52: 1311-1322, Aug. 2004
[9]曹一卿,古建,奇琳,杨大成.“一种混和自动请求重发的方法和装置,”中国专利, 200510105204.2
[10] P. Elias.“Coding for Noisy Channels,”IRE Conv. Rec., pt. 4. pp. 37-47, Mar. 1955
[11] D. Mackay, R. Neal.“Near Shannon Limit Performance of Low Density Parity Check Codes,”IEEE Electron. Lett.,vol. 32:1645-1646, Aug. 1996
[12] M. Sipser, D. Spielman.“Expander Codes,”IEEE Trans. Inf. Theory, 42(11). pp. 1710-1722, Nov. 1996
[13] S.-Y. Chung, J. Forney., T. Richardson, R. Urbanke.“On the Design of Low-Density Parity Check Codes Within 0.0045dB of the Shannon Limit,”IEEE Comm. Lett., 5(2). pp.58-60, Feb. 2001
[14] D. Mackay.“Good Error Correcting Codes Based on Very Sparse Matrices,”IEEE Trans. Inf. Theory, vol. 45(2). pp. 399-431, Mar. 1999
[15] D. Mackay.“Gallager Codes That are Better Than Turbo Codes,”Proc. 36th Allerton Conf. Commun., Control, and Computing, Monticello, Ill., Sep. 1998
[16] D. Mackay, S. Wilson, M. Davey.“Comparison of Constructions of Irregular Gallager Codes,”IEEE Trans. Comm., 46(10). pp. 1449-1454, Oct.1998
[17] Y. Kou, S. Lin, M. Fossorier.“Low-Density Parity-Check Codes Based on Finite Geometries: A Rediscovery and New Results,”IEEE Trans. Inf. Theory, 47(7). pp. 2711-2736, 2001
[18] B. Ammar, B. Honary, Y. Kou, J. Xu, S. Lin.“Construction of Low-Density Parity-Check Codes Based on BalancedIncomplete Block Designs,”IEEE Trans. Inf. Theory, vol. 50, June 2004
[19] H. Wen, F. Hu, J. Li and F. Jin.“A New Family of Irregular LDPC Codes,”IEEE 6th CAS Symp. Proceeding of on Emerging Technologies: Mobile and Wireless Comm., Shanghai, China. pp. 285-288, May 31-Jun. 2, 2004
[20] Draft IEEE Standard for Local and Metropolitan Area Networks. Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, IEEE P802.16e/D12, Oct. 2005
[21] F. Zarkeshvari, A. Banihashemi.“On Implementation of Min-sum Algorithm for Decoding Low-Density Parity-Check Codes,”Global Telecommunications Conference vol. 2, Taiwan Taipei, pp. 17-21, 2002
[22] S. Howard, V. C. Gaudet, C. Schlegel.“Soft-bit Decoding of Regular Low-Density Parity-Check Codes,”IEEE Trans. on Circuits and Systems II. pp. 99, 2005
[23] A. Anastapoulos.“A Comparison Between the Sum-Product and the Min-Sum Iterative Detection Algorithms Based on Density Evolution,”Proc. Globecom Conf. vol.2 San Antonio, TX. pp. 25-29, 2001
[24] R. Benice, A. H. Frey, Jr.,“An Analysis of Retransmission Systems,”IEEE Trans. Comm. Technol, COM-12. pp. 135-45, Dec. 1964
[25] H. Burton, D. Sullivan.“Errors and Error Control,”Proc. IEEE, 60(11). pp. 1293-1310, Nov. 1972
[26] K. Brayer.“Error Control Techniques Using Binary Symbol Burst Codes,”IEEE Trans. Comm., COM-16. pp. 199-214, Apr. 1968
[27] D. Mandelbaum.“A Daptive-Feedback Coding Scheme Using Incremental Redundancy,”IEEE Trans. Inf. Theory, IT-20. pp. 388-39, May 1974
[28] S. Lin, J.-S. Ma.“A Hybrid ARQ System With Parity Retransmission for Error Correction,”IBM Res. Rep., 7478(#32232), Jan. 1979
[29] J. Metzner.“Improvements in Block-Retransmission Schemes,”IEEE Trans. Comm., COM-27. pp. 525-32, February 1979
[30] T. Ancheta.“Convolutional Parity Check Automatic Repeat Request,”Proc. IEEE Intl. Symp. Inform. Theory, Grignano, Italy. pp. 25-29, June 1979
[31] S. Lin, P.-S. Yu.“A Hybrid ARQ Scheme With Parity Retransmission For Error Control of Satellite Channels,”IEEE Trans. Comm., COM-30. pp. 1701-1719, July 1982
[32] D. Rowith, L. Milstein.“Rare Compatible Punctured Turbo (RCPT) Codes in A Hybrid FEC/ARQ System,”IEEE Global Telecommun Mini-Conf. Phoenix, A Z. pp. 55-59, 1997
[33] P. Li, W.-K. Leung, N. Phamdo.“Low Density Parity Check Codes with Semi-Random Parity Check Matrix”, Electron. Lett., 35(1). pp. 38-39, 1999
[34] R. Echard, S.-C. Chang.“The Rotation Low-Density Parity-Check Codes,”Proc. GLOBECOM. pp. 980-984, 2001
[35] 3GPP TSG RAN WG1 #42,R1-050840,“Comparison of Structured LDPC Codes and 3GPP Turbo Codes”, London, UK, Aug. 29th-Sept. 2nd, 2005
[36] H. Behairy, S.-C. Chang. Parallel Concatenated Gallagher Codes,”Electron. Lett., 36(24). pp. 2025-2026, 2000
[37] S. Brink, G. Kramer, A. Ashikhmin.“Design of Low-Density Parity-Check Codes for Modulation and Detection,”IEEE Trans. on Commun., vol. 52, No. 4, Apr. 2004
[38] S. Brink.“Convergence Behavior of Iteratively Decoded Parallel Concatenated Codes,”IEEE Trans. Comm., vol.49. pp. 1727-1737, Oct. 2001
[39] Madhav Chinta,Abdelsalam (Sumi) Helal,Chonhwa Lee. C—TCP: An Interlayer Collaboration Protocol for TCP Performance lm-proverment in Mobile and Wireless Environments [J]. Wireless Communications and Networking, IEEE, 2003, 2(3). pp. 1004-1010
[40] Z.-B. Yao, P. Fan, Z.-G Cao.“Cross Layer Design for Service Diferentiation in Mobile Ad Hoc Networks[C],”IEEE 2003 International Symposium on Personal, Indoor and Mobile Radio Communication Proceedings, 2003
[41] M. Alouini, A. Goldsmith.“Adaptive Modulation Over Nakagami Fading Channels,”Kluwer J. Wireless Commun., vol. 13, no.1-2. pp. 119-143, May 2000
[42] M. Assaad, D. Zeghlache.“Cross-Layer Design in HSDPA System to Reduce the TCP Effect,”IEEE J. Sel. Areas Commun., vol. 24, no. 3. pp. 614-625, Mar. 2006
[43] Q. Liu, S. Zhou, G. Giannakis.“Cross-Layer Combining of Adaptive Modulation and Coding with Truncated ARQ Over Wireless Links,”IEEE Trans. Wireless Commun., vol. 3, no.5. pp. 1746-1755, Sep. 2004
[44] Physical layer aspects of UTRA high speed downlink packet access (release 4), 3GPP TR 25.848 V4.0.0, 2001
[45] L. Le, E. Hossain, A. Alfa.“Service Differentiation in Multirate Wireless Networks with Weighted Round-Robin Scheduling and ARQ-Based Error Control,”IEEE Trans. Comm., vol. 54, No.2 pp. 208-215, Feb. 2006
[46] S. Allpress, C. Luschi, S. Felix.“Exact and Approximated Expressions of the Log-Likelihood Ratio for 16-QAM Signals,”Icera Inc IEEE 2004