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Because of their algebraic structure and simple hardware implementation, linear codes as class of errorcorrecting codes, are used in a multitude of situations such as Compact disk, backland bar code, satellite and wireless communication, storage systems, ISBN numbers and so more. Nevertheless, the design of linear codes with high minimum Hamming distance to a given dimension and length of the code, remains an open challenge in coding theory. In this work, we propose a code construction method for constructing good binary linear codes from popular ones, while using the Hadamard matrix. The proposed method takes advantage of the MacWilliams identity for computing the weight distribution, to overcome the problem of computing the minimum Hamming distance for larger dimensions.

Orthogonal frequency division multiplexing (OFDM) is the key technology used in high-speed communication systems. One of the major drawbacks of OFDM systems is the high peak-to-average power ratio (PAPR) of the transmitted signal. The transmitted signal with a high PAPR requires a very large linear range of the Power Amplifier (PA) on the transmitter side. In this paper, we propose and study a new clipping method named Palm Clipping (Palm date leaf) based on hyperbolic cosine. To evaluate and analyze its performance in terms of the PAPR and Bit Error Rate (BER), we performed some computer simulations by varying the Clipping Ratio (CR) and modulation schemes. The obtained results show that it is possible to achieve a gain of between 7 and 9 dB in terms of PAPR reduction depending on the type of modulation. In addition, comparison with several techniques in terms of PAPR and BER shows that our method is a strong alternative that can be adopted as a PAPR reduction technique for OFDM-based communication systems.

This paper aims to take advantage of the performances of polar decoding techniques for the benefit of binary linear block codes (BLBCs) with the main objective is to study the performances of the SSCL decoding for short-length BLBCs. Polar codes are one of the most recent error-correcting codes to be invented, and they have been mathematically demonstrated to be able to correct all errors under a specific situation, using the successive-cancellation decoder. However, their performances for real-time wireless communications at short block lengths remain less attractive. To take advantage of the performance of these codes in favor of error correction codes of short block length, an adaptation of the simplified successive-cancellation list as a decoder for polar codes for the benefit of short block length binary linear block codes is presented in this paper. This adaptation makes it possible to take advantage of the performances of less complex decoding methods for polar codes for BLBCs with latency and complexity optimization of the standard successive-cancellation list decoder. The experiment shows that the method can achieve the performances of the most famous order statistic decoder for binary linear block codes, which can achieve the performances of maximum-likelihood decoding with computational complexity and memory constraints.

Channel coding is commonly based on protecting information to be communicated across an unreliable medium, by adding patterns of redundancy into the transmission path. Also referred to as forward error control coding (FECC), the technique is widely used to enable correcting or at least detecting bit errors in digital communication systems. In this paper we study an original FECC known as polar coding which has proven to meet the typical use cases of the next generation mobile standard. This work is motivated by the suitability of polar codes for the new coming wireless era. Hence, we investigate the performance of polar codes in terms of bit error rate (BER) for several codeword lengths and code rates. We first perform a discrete search to find the best operating signal-to-noise ratio (SNR) at two different code rates, while varying the blocklength. We find in our extensive simulations that the BER becomes more sensitive to operating SNR (OSNR) as long as we increase the blocklength and code rate. Finally, we note that increasing blocklength achieves an SNR gain, while increasing code rate changes the OSNR domain. This trade-off sorted out must be taken into consideration while designing polar codes for high-throughput application.

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One challenge of a sensing technique is reducing sensing time while ensuring good effective data rate. In fact, once compressive sensing based on sub-Nyquist sampling is adopted, sensing time can be reduced by saving number of samples. This increases the probability of missed detection which causes collisions with primary service and worsens channel imperfections. In such case erasures occur in addition to errors. In this chapter, the authors propose a new technique to correct erasures while keeping sensing time at a desired level. Based on polar code and low complexity decoding algorithm, the proposed technique exhibits for high code rates better performance in terms of bit error rate (BER) compared to two existing techniques based on other codes, namely low-density parity check (LDPC) and BCH.