A Comprehensive Survey of Recent Advancements in Molecular Communication <s> C. Error Correction Codes <s> Preface. List of Program Files. List of Laboratory Exercises. List of Algorithms. List of Figures. List of Tables. List of Boxes. PART I: INTRODUCTION AND FOUNDATIONS. 1. A Context for Error Correcting Coding. PART II: BLOCK CODES. 2. Groups and Vector Spaces. 3. Linear Block Codes. 4. Cyclic Codes, Rings, and Polynomials. 5. Rudiments of Number Theory and Algebra. 6. BCH and Reed-Solomon Codes: Designer Cyclic Codes. 7. Alternate Decoding Algorithms for Reed-Solomon Codes. 8. Other Important Block Codes. 9. Bounds on Codes. 10. Bursty Channels, Interleavers, and Concatenation. 11. Soft-Decision Decoding Algorithms. PART III: CODES ON GRAPHS. 12. Convolution Codes. 13. Trefils Coded Modulation. PART IV: INTERATIVELY DECODED CODES. 14. Turbo Codes. 15. Low-Density Parity-Check Codes. 16. Decoding Algorithms on Graphs. PART V: SPACE-TIME CODING. 17. Fading Channels and Space-Time Coding. References. Index. <s> BIB001 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> C. Error Correction Codes <s> Communication between nanoscale devices is an area of considerable importance as it is essential that future devices be able to form nanonetworks and realise their full potential. Molecular communication is a method based on diffusion, inspired by biological systems and useful over transmission distances in the nm to m range. The propagation of messenger molecules via diffusion implies that there is thus a probability that they can either arrive outside of their required time slot or ultimately, not arrive at all. Therefore, in this paper, the use of a error correcting codes is considered as a method of enhancing the performance of future nanonetworks. Using a simple block code, it is shown that it is possible to deliver a coding gain of ∼ 1.7dB at transmission distances of 1 m. Nevertheless, energy is required for the coding and decoding and as such this paper also considers the code in this context. It is shown that these simple error correction codes can deliver a benefit in terms of energy usage for transmission distances of upwards of 25 m for receivers of a 5 m radius. <s> BIB002 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> C. Error Correction Codes <s> In this paper, we investigate the performance of convolutional coding techniques in an ideal diffusion-based concentration-encoded molecular communication (CEMC) channel with pulse amplitude modulation (PAM) transmission scheme. Convolutional codes have shown to provide a significant amount of gain in the signal-to-interference strength (energy) ratio between a pair of communicating nanomachines and thus help increase the communication range and improve the end-to-end system performance. We have also determined the impact of convolutional codes for several key performance factors, e.g. transmission data rate, communication range, and the constraint length of the convolutional code in the context of diffusion-based CEMC. In addition, we have compared the PAM system with the impulse modulation system in CEMC. We have found that the use of a multilevel (M-ary) signalling scheme in the CEMC system provides a degraded bit error rate performance even in short communication ranges. Therefore, a convolutional coded scheme with larger alphabet size should not be recommended for a CEMC system because of the stronger intersymbol interference produced within symbols. As an alternative, a convolutional coded scheme with binary alphabet and higher symbol rate was evaluated and found to provide a gain in the signal-to-interference energy ratio of the system and is therefore recommended for short- to medium-range CEMC. For long communication ranges, an uncoded system can rather be preferred to convolutional coded schemes. <s> BIB003 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> C. Error Correction Codes <s> Molecular communications emerges as a promising scheme for communications between nanoscale devices. In diffusion-based molecular communications, molecules as information symbols diffusing in the fluid environments suffer from molecule crossovers, i.e., the arriving order of molecules is different from their transmission order, leading to intersymbol interference (ISI). In this paper, we introduce a new family of channel codes, called ISI-free codes, which improve the communication reliability while keeping the decoding complexity fairly low in the diffusion environment modeled by the Brownian motion. We propose general encoding/decoding schemes for the ISI-free codes, working upon the modulation schemes of transmitting a fixed number of identical molecules at a time. In addition, the bit error rate (BER) approximation function of the ISI-free codes is derived mathematically as an analytical tool to decide key factors in the BER performance. Compared with the uncoded systems, the proposed ISI-free codes offer good performance with reasonably low complexity for diffusion-based molecular communication systems. <s> BIB004
In traditional communication systems, channel codes are used to mitigate the effects of noise and fading that is introduced into the system by the channel and electronic components. In essence channel coding introduces redundancy which can then be used to detect and correct errors. For example, in a simple reputation code, a binary bit-0 is encoded as 000, and a binary bit-1 is encoded as 111. At the receiver the majority number of bits are used to decode the bit. For example, 011 is decoded as bit-1, and 010 is decoded as bit-0. It is fairly trivial that such a simple repetition code can correct one bit errors. Capacity achieving codes are codes that allow information transmission rates that are very close to the maximum theoretical limits of the channel (i.e., channel capacity). Many different capacity achieving codes such as low density parity check (LDPC) codes and turbo codes have been developed for the traditional communication systems BIB001 . However, the encoder and the decoder for these channel codes are computationally complex, and as such they may not be practical for many molecular communication systems, specially at microscales. Furthermore, because the nature of the noise is different in molecular communication channels, it is not clear if better error correcting codes exist for these channels. For example, molecular communication channels typically have memory. Only a limited amount of work has been done on channel codes for molecular communication, and there are still many open problems in this area. In BIB002 , Hamming codes were proposed as simple error correcting codes for on-off-keying in diffusion based molecular communication. First, it was shown that these error correcting codes can improve the probability of bit error rate when a large number of information particles were used for representing each bit. Uncoded transmission outperformed coded transmission, however, when smaller number of molecules were used to represent each bit. This occurs because of the extra inter-symbol interference introduced by the extra parity bits. The authors then modeled the extra energy needed for transmitting the extra parity bits and showed that coding was not energy-efficient when the separation distance between the transmitter and the receiver was small. In BIB003 , convolutional coding schemes were applied to a very simplified diffusion based channel model employing on-off-keying modulation. It was shown that convolutional codes could improve the bit error rate of these molecular communication channels. In BIB004 , a new code family called ISI-free code family was introduced for diffusions based molecular communication channels with drift. It was assumed that the type of the information particles is used to encode information. In this coding scheme, the crossovers up to level-between consecutive codewords and within the current codeword were eliminated. It was shown that these code families can improve the biterror rate performance of molecular communication channels compared to uncoded transmission, under similar throughputs.