Maximal Minimum Hamming Distance Codes for Embedding SI in a Data based BSLM Scheme for PAPR Reduction in OFDM

The bi-orthogonal codes for embedding Side-Information (SI) in data-based blind SLM (BSLM) proposed in Joo et al. (2012) produce better bit error rate (BER) and SI error rate (SIER) performance compared to binary codes. However, the authors do not provide details for code generation; instead, they list some codes with a length of  and a minimum Hamming distance of . The suggested bi-orthogonal code does not work for any value of the maximum iteration number  other than . Therefore, this paper proposes two algorithms for generating  codes for any value of . The proposed methods maintain the normalized minimum Hamming distance between generated codes to . However, the second proposed algorithm, which works in the case of , is also able to only consider codes with a maximum Hamming distance, allowing it to improve SIER performance. Thus, the second proposed algorithm improves SIER performance by up to 1 dB at Eb/No=3dB. Furthermore, the proposed algorithms are able to generate a multiple set of  codes that deliver same performance.

Blind SLM; OFDM; PAPR; Side Information; SLM

where  is the th sample of OFDM time domain signal , and  denotes expectation.

Many methods have been proposed to alleviate the high PAPR problem; each one has advantages and disadvantages. Examples of PAPR reduction techniques found in the literature are clipping (Juwono et al., 2013), partial transmit sequence (PTS) (Müller et al., 1997; Müller and Huber, 1997), selected mapping (SLM) (Müller et al., 1997; Sa'd and Wahab, 2019), tone injection (TI) (Wattanasuwakull and Benjapolakul, 2005), tone reservation (TR) (Park et al., 2003), interleaving (Rahmatallah and Mohan, 2013), and hybrid (Jones et al., 1994; Wang and Chen, 2014; Sa’d et al., 2016; Wahab and Sa’d, 2017; Liang et al., 2019).

SLM is a well-known distortion-less PAPR reduction technique; however, it requires sending side information (SI) for the receiver to be able to retrieve the original signal. To solve this problem, many blind SLM (BSLM) schemes have been proposed in the literature (Jayalath and Tellambura, 2002; Pezeshk and Khalaj, 2002; Baxley and Zhou, 2005; Jayalath and Tellambura, 2005; Han et al., 2006; Chen and Zhou, 2006;Alsusa and Yang, 2008; Han et al., 2008; Joo et al., 2009; Le Goff et al., 2009; Hong et al., 2010; Park et al., 2011;Li et al., 2011; Badran and El-Helw, 2011;Eom et al., 2012; Joo et al., 2012; El-Helw et al., 2012; Hong et al., 2013; Ji and Ren, 2013; Elhelw and Badran, 2015; Ji et al., 2015; Yoon et al., 2018; Goel and Sidhu, 2020). BSLM, in general, embeds SI in an OFDM signal by utilizing noise margins instead of dedicated subcarriers to eliminate data rate waste due to SI. While there are different types of BSLM, the data-based BSLM proposed in Joo et al. (2012) can maintain a similar PAPR and an almost similar BER as conventional SLM without manipulating or imposing restrictions on channel estimation methods, providing that the number of subcarriers of OFDM is not very small. SI is embedded onto the phase of data subcarriers by making a unique and distinguished phase disparity between all the possible iterations of data manipulation, and this is done over all data subcarriers. To improve SI error rate (SIER) performance, phase disparity forms are constructed using a biorthogonal vector with a code length of . However, the work in Joo et al. (2012) lacks the generalization of constructing biorthogonal codes for any  value. Therefore, in this paper, we propose a systematic way of generating  SI embedding-codes that fulfill the general and important condition of having a normalized minimum Hamming distance of at least 0.5.

        This paper is organized as follows. Section 2 explains the data?based BSLM in Joo et al. (2012). Section 3 discusses SI embedding-code generation and explains the proposed maximal Hamming distance code generation method. Finally, a conclusion is drawn in Section 4.

    Two new algorithms were proposed for generating maximal Hamming distance codes of  for embedding SI. The proposed algorithms generalize the construction of SI embedding codes for any value of . The codes produced using the algorithms proposed here and the biorthogonal codes used in Joo et al. (2012) have similar SIER performance for , since they all have a normalized minimum distance of . However, for  Algorithm 2 proposed here produces better SIER performance.

    This research was supported partially by Research University Grant, Universiti Sains Malaysia (1001/PELECT/8014160).

Alsusa, E., Yang, L., 2008. Redundancy-Free and BER-Maintained Selective Mapping with Partial Phase-Randomising Sequences for Peak-to-Average Power Ratio Reduction in OFDM Systems. IET Communications, Volume 2, pp. 66–74

Badran, E.F., El-Helw, A.M., 2011. A Novel Semi-Blind Selected Mapping Technique for PAPR Reduction in OFDM. IEEE Signal Processing Letters, Volume 18(9), pp. 493–496

Baxley, R.J., Zhou, G.T., 2005. MAP Metric for Blind Phase Sequence Detection in Selected Mapping. IEEE Transactions on Broadcasting, Volume 51(4), pp. 565–570

Chen, N., Zhou, G.T., 2006. Peak-to-Average Power Ratio Reduction in OFDM with Blind Selected Pilot Tone Modulation. IEEE Transactions on Wireless Communications, Volume 5(8), pp. 2210–2216

El-Helw, A.M., Badran, E.F., Al-Kafrawy, H.Y., 2012. A New Sequence for Embedding Side Information in SLM for PAPR Reduction in OFDM. In: Japan-Egypt Conference on Electronics, Communications and Computers (JEC-ECC), 2012, pp. 53–56

Elhelw, A.M., Badran, E.F., 2015. Semi-Blind Error Resilient SLM for PAPR Reduction in OFDM using Spread Spectrum Codes. PloS ONE, Volume 10(5): e0127639. https://doi.org/10.1371/journal.pone.0127639

Eom, S.-S., Nam, H., Ko, Y.-C., 2012. Low-Complexity PAPR Reduction Scheme Without Side Information for OFDM Systems. IEEE Transactions on Signal Processing, Volume 60(7), pp. 3657–3669

Goel, A., Sidhu, K., 2020. PAPR Reduction in MIMO-OFDM System using SLM Without SI. Journal of Optical Communications, Volume 41(3), pp. 325–330

Han, S.H., Cioffi, J.M., Lee, J.H., 2006. Tone Injection with Hexagonal Constellation for Peak-to-Average Power Ratio Reduction in OFDM. IEEE Communications Letters, Volume 10(9), pp. 646–648

Han, S.H., Cioffi, J.M., Lee, J.H., 2008. On the Use of Hexagonal Constellation for Peak-to-Average Power Ratio Reduction of an ODFM Signal. IEEE Transactions on Wireless Communications, Volume 7(3), pp. 781–786

Han, S.H., Lee, J.H., 2005. An Overview of Peak-to-Average Power Ratio Reduction Techniques for Multicarrier Transmission. Wireless Communications, IEEE, Volume 12(2), pp. 56–65

Hong, E., Kim, H., Yang, K., Har, D., 2013. Pilot-Aided Side Information Detection in SLM-Based OFDM Systems. IEEE Transactions on Wireless Communications, Volume 12(7), pp. 3140–3147

Hong, E., Mi, S., Har, D., 2010. SLM-Based OFDM System Without Side Information for Data Recovery. Electronics Letters, Volume 46(3), 271–272

Jayalath, A., Tellambura, C., 2002. A Blind SLM Receiver for PAR-Reduced OFDM. In: Proceedings of the Vehicular Technology Conference, 2002, pp. 219–222

Jayalath, A.D.S., Tellambura, C., 2005. SLM and PTS Peak-Power Reduction of OFDM Signals Without Side Information. IEEE Transactions on Wireless Communications, Volume 4(5), 2006–2013

Ji, J., Ren, G., 2013. A New Modified SLM Scheme for Wireless OFDM Systems Without Side Information. IEEE Signal Processing Letters, Volume 20(11), pp. 1090–1093

Ji, J., Ren, G., Zhang, H., 2015. A Semi-Blind SLM Scheme for PAPR Reduction in OFDM Systems with Low-Complexity Transceiver. IEEE Transactions on Vehicular Technology, Volume 64(6), pp. 2698–2703

Jiang, T., Wu, Y., 2008. An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals. IEEE transactions on Broadcasting, Volume 54(2), p. 257–268

Jones, A.E., Wilkinson, T.A., Barton, S., 1994. Block Coding Scheme for Reduction of Peak to Mean Envelope Power Ratio of Multicarrier Transmission Schemes. Electronics letters, Volume 30(25), pp. 2098–2099

Joo, H.-S., Heo, S.-J., Jeon, H.-B., No, J.-S., Shin, D.-J., 2009. A New Blind SLM Scheme with Low Complexity of OFDM Signals. In: Vehicular Technology Conference Fall 2009, pp. 1–5

Joo, H.-S., Heo, S.-J., Jeon, H.-B., No, J.-S., Shin, D.-J., 2012. A New Blind SLM Scheme with Low Decoding Complexity for OFDM Systems. IEEE transactions on broadcasting, Volume 58(4), pp. 669–676

Juwono, F.H., Triprasetyo, Y., Gunawan, D., 2013. Exploiting LDPC Codes for Improving the Performance of Clipped-OFDM System. International Journal of Technology, Volume 4(1), pp. 93–99

Le Goff, S.Y., Al-Samahi, S.S., Khoo, B.K., Tsimenidis, C.C., Sharif, B.S., 2009. Selected Mapping Without Side Information for PAPR Reduction in OFDM. In: IEEE Transactions on Wireless Communications, Volume 8(7), pp. 3320–3325

Li, C., Jiang, T., Zhou, Y., Li, H., 2011. A Novel Constellation Reshaping Method for PAPR Reduction of OFDM Signals. IEEE Transactions on Signal Processing, Volume 59(6), pp. 2710–2719

Liang, L.Y., Wahab, A.A.A., Alhady, S.S.N., Othman, W.A.F.W., 2019. Discrete Wavelet Transform with Discrete Cosine Transform (DCT) for Peak-to-Average Power Ratio (PAPR) Reduction in OFDM System. International Journal of Advanced Trends in Computer Science and Engineering, Volume 8(5), pp. 2260–2264

Müller, S.H., Bäuml, R.W., Fischer, R.F., Huber, J.B., 1997. OFDM with Reduced Peak-to-Average Power Ratio by Multiple Signal Representation. Annales des télécommunications. Volume 52, pp. 58–67

Muller, S.H., Huber, J.B., 1997. A Novel Peak Power Reduction Scheme for OFDM. In: Personal, Indoor and Mobile Radio Communications, 1997, pp. 1090–1094

Müller, S.H., Huber, J.B., 1997. OFDM with Reduced Peak-to-Average Power Ratio by Optimum Combination of Partial Transmit Sequences. Electronics letters, Volume 33, pp. 368–369

Park, J., Hong, E., Har, D., 2011. Low Complexity Data Decoding for SLM-Based OFDM Systems Without Side Information. IEEE Communications Letters, Volume 15(6), pp. 611–613

Park, S.-E., Yun, S., Kim, J.Y., Park, D.S., Joo, P., 2003. Tone Reservation Method for PAPR Reduction Scheme. In: Project IEEE, p. 802

Pezeshk, A., Khalaj, B.H., 2002. Extended Hexagonal Constellations as a Means of Multicarrier PAPR Reduction. In: Eurasian Conference on Information and Communication Technology, 2002, pp. 926–936

Rahmatallah, Y., Mohan, S., 2013. Peak-to-Average Power Ratio Reduction in OFDM Systems: A Survey and Taxonomy. Communications Surveys & Tutorials, IEEE, Volume 15(4), pp. 1567–1592

Sa'd, A.H.Y., Wahab, A.A.A., 2019. Novel Technique for PAPR and Average Power Reduction in OFDM Scheme. International Journal of Advanced Trends in Computer Science and Engineering, Volume 8(6), pp. 3632–3634

Sa’d, A.H.Y., Wahab, A.A.A., Sa’ad, H.H.Y., 2016. A New Precoded Partial Transit Sequence Method using the Discrete Cosine Transform for Peak-to-Average Power Ratio Reduction in an Orthogonal Frequency Division Multiplexing System. SCIENCEASIA, Volume 42(6), pp. 423–426

Wahab, A., Sa’d, A.H.Y., 2017. An Improved IDCT-OFDM with Partial Transmit Sequence. In: 9^th International Conference on Robotic, Vision, Signal Processing and Power Applications, Springer, 2017, pp. 535–546

Wang, Z., Chen, S., 2014. Reduction PAPR of OFDM Signals by Combining Grouped DCT Precoding with PTS. Journal of Signal and Information Processing, Volume 5(4), pp. 135–142

Wattanasuwakull, T., Benjapolakul, W., 2005. PAPR Reduction for OFDM Transmission by using a Method of Tone Reservation and Tone Injection.  In: Information, Communications and Signal Processing, 2005 Fifth International Conference on, IEEE, pp. 273–277

Yoon, E., Hwang, D., Jang, C., Kim, J., Yun, U., 2018. Blind Selected Mapping with Side Information Estimation based on the Received Pilot Signal. In: Wireless Communications and Mobile Computing, 2018