Teaching Convolutional Coding using MATLAB in Communication Systems Course

In this contribution we present an exhaustive treatment of various coding and decoding techniques for use in fast frequency-hopping/multiple frequency shift keying multiple-access systems. One of the main goals is to show how reliability information on each received bit can be derived to enable soft-decision decoding. Convolutional codes as well as turbo codes are considered applying soft-decision, erasure, and hard-decision decoding. Their performance is compared to that of previously proposed Reed-Solomon with either errors-only or errors-and-erasures decoding. A mobile radio environment yielding a frequency-selective fading channel is assumed. It is shown that the application of turbo codes and convolutional codes with soft decision decoding can allow for a comparable number of simultaneously transmitting users to Reed-Solomon codes with errors-and-erasures decoding. Furthermore, the advantage of soft decisions is shown, which can be applied to a widely and growing range of channel codes. The pertinent technique of calculating soft decisions is described in the paper.

End-to-end learning of a communications system using the deep learning-based autoencoder concept has drawn interest in recent research due to its simplicity, flexibility and its potential of adapting to complex channel models and practical system imperfections. In this paper, we have compared the bit error rate (BER) performance of autoencoder based systems and conventional channel coded systems with convolutional coding (CC), in order to understand the potential of deep learning-based systems as alternatives to conventional systems. From the simulations, autoencoder implementation was observed to have a better BER in 0-5 dB E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> range than its equivalent half-rate convolutional coded BPSK with hard decision decoding, and to have only less than 1 dB gap at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . Furthermore, we have also proposed a novel low complexity autoencoder architecture to implement end-to-end learning of coded systems in which we have shown better BER performance than the baseline implementation. The newly proposed low complexity autoencoder was capable of achieving a better BER performance than half-rate 16-QAM with hard decision decoding over the full 0-10 dB E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> range and a better BER performance than the soft decision decoding in 0-4 dB E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> range.

In this paper, we evaluate the performances of the Reed–Solomon (RS) and low density parity check (LDPC) codes in order to propose an efficient coding system for the outer code in high density optical recording channels. Hard decision decoding (HDD) RS code, iterative soft decision decoding (SDD) RS code or LDPC code is used as the outer code and LDPC code is used as the inner code. We compare the bit error rate (BER) performance of each coding system for various code rates, code lengths and burst errors. Simulation results show that the LDPC code has a better BER performance than the HDD RS and iterative SDD RS codes as the outer code in high density optical channels. Therefore, the LDPC code could be more attractive as the outer code than the RS code in high density optical channels.

This paper proposes a novel joint network- channel coding (JNCC) system based on improved distributed turbo coded (DTC) scheme for multiple-access relay channel, using decode-and-forward protocol. The diversity of improved DTC scheme is that the two parity streams of the two RSC encoders of UE are converted into one stream by puncturing. In addition, we adopt the punctured parity streams of Convolutional Turbo Code (CTC) at the relay and BS, which takes advantage of the feature of two inputs for the decoded information bits from two mobile stations. Here, CTC acts as a network coding as well as channel coding between relay and BS. The performance of this communication system depends on the twice decoding at the BS according to the side information and CTC punctured parity information. The simulation results show that performance of proposed scheme overperforms the reference network-coding scheme which separates channel decoding from network coding, and has 0.8dB improvement at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> in AWGN channel than the reference scheme.

With rapid growth in today’s technology, digital communication is playing a major role to provide hostile environment to meet various applications. In this communication, Coding plays a prominent role to contribute error free transmission through channel coding which improves capacity of a channel by adding some redundant bit to the original information. One way to provide a better performance of the communication system is by concatenating different types of channel coding techniques. The concatenation can be done either in parallel or serial. The primary aim of this paper is to concatenate the Reed-Solomon codes with Convolutional codes in series, which provides better results comparing with single coding techniques. The performance of the concatenation of Reed-Solomon codes with Convolutional codes can be evaluated by finding bit error rate with various values of signal-to-noise ratio over AWGN channel. The analytical result has been obtained by using MATLAB/OCTAVE.

The effect of pulse-noise jamming noncoherent RAKE receiver with convolutional coding in the presence of Ricean fading is analyzed. The effect of additive white Gaussian noise (AWGN) is also included in the analysis. The maximum-likelihood RAKE receiver for the combination of pulse noise and AWGN is derived. Pulse jamming usually has a significant effect when soft decision decoding is used, however, we show that the maximum-likelihood RAKE receiver effectively mitigates pulse noise jamming. Hard decision decoding reduces the effect of pulse noise jamming, however, the maximum-likelihood RAKE with soft decision decoding performs better than hard decision decoding in the presence of pulse-noise jamming.

This paper studies the performance of ultra-wideband (UWB) radio communications systems employing phase shift keying (PSK) modulation and fully saturated power amplifiers through additive white Gaussian noise (AWGN) channel or Rayleigh fading channel. An impulse response method is provided to analyze the signal-to-noise ratio (SNR) degradation. Both convolutional code and turbo code are employed with the Viterbi decoding and the iterative decoding, respectively. The decoding algorithms are modified for the Rayleigh fading channel. Near optimal bit error rate (BER) performance is achieved when employing either convolutional code or turbo code. The simulation results match the derivation. Therefore, fully saturated power amplifiers can be employed in UWB PSK systems to significantly reduce radio cost, simplify radio circuit, and increase battery life for portable terminals.

Recently, low-density parity-check (LDPC) codes have attracted much attention especially in mobile communication system as a good simple error correcting codes achieving the data throughput near Shannon limit with lower complexity. In this paper, we design some regular LDPC codes with very low bit error rate (BER) and frame error rate (FER) according to the downlink parameters in TD-SCDMA system. We construct the downlink physical layer emulation model with matlab according to TD-SCDMA system's baseband signal disposing flow chart, and execute the link simulation with the performance analysis for some available channel codes and the designed regular LDPC codes based on the proposed emulation model. Passing the simulation, we obtain some conclusions that the regular LDPC codes are better than the convolutional codes or turbo codes in error rate performance.

The conventional soft decision decoding (SDD) methods require various hard decision decoders (HDDs) based on different codes or re-manipulate the generator matrix by the complicated Gaussian elimination technique according to the bit reliability. This paper presents a general multi-class neural network (NN)-based decoder for the short linear block codes, where no HDD and Gaussian elimination are required once the NN is constructed. This network architecture performs multi-classification to select the messages with high occurrence probabilities and chooses the best codeword on a maximum likelihood basis. Simulation results show that the developed approach outperforms the existing deep neural network (DNN)-based decoders in terms of decoding time and bit error rate (BER). The error-correcting performance is also superior to the conventional Chase-II algorithm and is close to the ordered statistics decoding (OSD) in most cases. For Bose–Chaudhuri–Hocquenghem (BCH) codes, the SNR is improved by 1dB to 4dB as the BER is 10−4. For the (23, 12) quadratic residue (QR) code, the SNR is improved by 2dB when the BER is 10−3. The developed NN-based decoder is quite general and applicable to various short linear block codes with good BER performance.

This paper presents the design and implementation of GMSK transceiver with low complexity and high performance in terms of bit error rate. The GSM systems in current user demand require to be great success for digital cellular standards which is widely used because of advance in integration solution for different terminal handsets. Through the user’s populations continually growth and handset plummeting price, the design efforts focus on effective GSM data receiver implementations. The receiver section in the GSM system is the most important part that will introduce different type errors due to the channel effect. Hence, the decoding plays a vital role in the receiver part by decode the received signals in appropriate techniques. This paper introduces efficient receiver demodulation technique based on soft decision decoder. The obtained results were compared with traditional technique and hard decision decoder to show the effectiveness of this method under noisy channel. In low and high code rate, the soft decision decoder can underestimate the bit error rate by up to 25%. The improved bit error rate after decoding is shown to give reliable estimation across diverse channels condition and modulations setup.KeywordsGMSKSoft decision decoderBER

This paper is concerned with the soft-decision decoding of error-correcting codes in the context of h.f. data transmission. The use of soft-decision information from the data modem results in an improvement in the performance of a forward-error-correction scheme, when compared with hard-decision decoding, without any further redundancy penalty. In the paper, we estimate the theoretical improvements that can be expected from soft-decision decoding of block and convolutional codes, in terms of both random and burst error-correcting power. Also, this is related to expected coding gains for the Gaussian and Rayleigh fading channels. In addition, we investigate the performance of soft-decision decoding on two types of h.f. modem: a multisubcarrier parallel transmission format (p.t.f.) type modem, and an experimental serial transmission s.m.i.d.d. type modem. We conclude that significant improvements in the performance of coded systems are obtainable through the use of soft-decision decoding.

Due to the growing interest in mobile data applications, the Global System for Mobile communications (GSM) has been extended by the General Packet Radio Service (GPRS). It allows the transmission of packet data at moderate bit rates using random access channels within the existing GSM infrastructure. This paper analyses the impact of using multiple channels in a GSM system for GPRS packet transmission. Different combinations of frequency reuse and channel coding are evaluated for 1, 4 and 8 packet data channels (PDCH) per cell. A tight frequency reuse of 1, together with a strong error coding scheme was found to provide the highest capacity. The increased trunking efficiency for a system with 8 PDCH yields a capacity gain of about 64% over a system with only 1 channel. The results indicate that mixing circuit and packet switched traffic causes inefficient use of system resources. Since GSM voice services usually require a frequency reuse of 3 or 7, a separate overlaying network for GPRS provides better resource utilization and maximizes the number of users fulfilling the specified quality of service (QoS) requirements.

The performance of two direct sequence ultra wideband (DS-UWB) communication systems is investigated. The first system is the classic DS-UWB system. The second is obtained by adding a forward error control codes (FEC), convolutional code. For the two systems, binary pulse amplitude modulation is applied. The performance of these two systems is analyzed in detail under AWGN channel. In our proposed coded scheme, we use soft output Viterbi algorithm (SOVA). The analysis shows that the coded DS-UWB system outperforms the DS-UWB system significantly, or more importantly, at a given bit error rate, the coding scheme increases the number of users by a factor which is logarithmic in the number of pulses used in DS UWB systems. Simulation results on the bit error rate of the proposed system indicates that the system is capable to work in lower SNR's and therefore supports higher data transmission rates compared to the previously proposed UWB communication systems.

Benefiting from strong decoding capabilities, soft-decision decoding has been used to replace hard-decision decoding in various communication systems, and NAND flash memory systems are no exception. However, soft-decision decoding relies heavily on accurate soft information. Owing to the incremental step pulse programming (ISPP), program errors (PEs) in multi-level cell (MLC) NAND flash memory have different characteristics compared to other types of errors, which is very difficult to obtain such accurate soft information. Therefore, the characteristics of the log-likelihood ratio (LLR) of PEs are investigated first in this paper. Accordingly, a PE-aware statistical method is proposed to determine the usage of PE mitigation schemes. In order to reduce the PE estimating workload of the controller, an adaptive blind clipping (ABC) scheme is proposed subsequently to approximate the PEs contaminated LLR with different decoding trials. Finally, simulation results demonstrate that (1) the proposed PE-aware statistical method is effective in practice, and (2) ABC scheme is able to provide satisfactory bit error rate (BER) and frame error rate (FER) performance in a penalty of negligible increasing of decoding latency.

In this paper, the performance comparison of serially concatenated Recursive systematic convolutional (RSC) code system with Non-systematic convolutional (NSC) code system is conduct. The two models of serially concatenated convolutional code is tested over Additive White Gaussian (AWGN) channel, Binary Phase-Shift Keying (BPSK) modulation and Viterbi decoder using MATLAB simulation. In first model of serially concatenated convolutional code uses Recursive systematic convolutional (RSC) as outer and inner encoder. In second model of serially concatenated convolutional code uses Non-systematic convolutional (NSC) as outer and inner encoder. The outer and inner encoders are concatenated with the help of interleaver. For decoding a non-iterative Viterbi decoding scheme is performed with two Viterbi decoder are concatenated by de-interleaver. The MATLAB simulation results shows that the performance of RSC-RSC concatenated code gives the better bit error rate (BER) than the NSC-NSC concatenated code.