# Low Delay Inter-Packet Coding in Vehicular Networks
## 2 Preliminaries
### Convolutional Codes for Network Applications  
Generally speaking, any error-correcting code can be used for recovering lost packets in networks. However, criteria for constructing packet erasure-correcting codes for V2R networks differ significantly from those used for evaluating codes correcting or detecting errors at the physical level. The difference stems from the difference in the acceptable decoding complexity and delay. Short lifetime of the transmitted data makes these requirements much stronger than for other networks.  
Raptor codes [14] represent an efficient low-complexity network-oriented class of codes. However, they are not the best solution for the V2R application since they are meant for correcting large number of independent erasures without restriction on delay, rather than for correcting a small number of erased large packets with strictly limited delay.  
Another class of codes which can be efficiently used for recovering packets of erasures are so-called codes with rank metric [21; 22]. They were suggested as a generalization of codes for magnetic recording [23]. These codes protect two-dimensional data against both row and column errors and erasures. In the V2R application, it is enough to correct one-dimensional erasures which can be equally well done by the Reed-Solomon (RS)-codes [24]. The approach based on convolutional version of the RS-codes [17] is studied below as one of the solutions.  
It is well known that complexity of ML decoding over the binary symmetric channel (BSC) and over the additive white Gaussian noise (AWGN) channel is, typically, an exponentially growing function of code length of block code or of constraint length of convolutional code. For this reason, usually codes with simple suboptimal decoding are preferred, e.g., concatenated codes, product codes, turbo-codes, LDPC codes, etc.  
The situation is completely different for the BEC (M-BEC), where correcting of \(\
u\) erasures can be reduced to solving a system of linear equations of order at most \(\
u\). Thus, ML-decoding complexity is a polynomial, at most cubic, function of code length. In this case, the decoding delay becomes a basic requirement when selecting codes. Convolutional codes, the decoding delay of which is determined by the encoder memory and does not depend on the length of the code, have practically no alternative in such an application. Low-delay high-rate convolutional codes are among most promising candidates for the V2R network application.  
The considered further decoding scenario is shown in Figure 2.  
Data packets from the physical layer of the network include data of different priority followed by cyclic redundancy check (CRC) and parity-check bits of error detecting code used in IEEE 802.11 standard. It is assumed that highest priority bits in the sequence of these packets are encoded by a convolutional code.  
Two classes of binary and nonbinary high-rate convolutional codes are analyzed and compared with block codes of the same rate and approximately the same decoding delay. We demonstrate the efficiency of these codes when correcting erasures in the BEC and M-BEC obtained from the wireless fading channel by using technique in [25]. Then, the chosen codes are simulated on the stream of packet losses provided by AstaZero.