INTEGER SINGLE-ERROR-CORRECTING CODES AS AN ALTERNATIVE TO THE INTERNET CHECKSUM

: The paper considers the possibility of using integer single-error-correcting (SEC) codes instead of the Internet checksum (IC). It is shown that such a replacement can be easily carried out, since the integer SEC codes are a generalization of the IC


Introduction
The Internet has become one of the most important means of communication. It is used not only for broadcasting television and radio programs, but also for mutual communication. The most known example is the Skype application, which allows people not only to make phone calls, but also to see their interlocutors.
Generally speaking, the Internet is a global computer network that is based on four layer networking model. The first layer is the data layer, which defines how the communication through packets delivery works between two network nodes (computer, firewall, switch or router). Above the data layer is the network layer, which deals with the routing of packets from one network node to another. The third layer is the transport layer, which is responsible for the delivery of the application data, while the last (application) layer provides an interface between the applications and the underlying network ( Figure 1).
For the purpose of reliable multimedia communication, the most important layer is the transport one. At this layer, the multimedia data are delivered using User Datagram Protocol (UDP) (Aracil and Callegati, 2009). This protocol is designed for fast and simple data transmission without ensuring delivery. More precisely, by using the Internet checksum (IC), the receiver only checks whether the data was received in error. If they are received without error, the packet will be delivered to the application. Otherwise, it will be discarded, which can negatively affect the quality of multimedia content playback. In this paper, we will show that the problem of packet dropping can be significantly mitigated if integer single-error-correcting (SEC) codes are used instead of the IC. In addition, it is important to note the receiver would not undergo any hardware changes, since the integer SEC codes are a generalization of the IC.

TO THE INTERNET CHECKSUM
Aleksandar Radonjić 1* , Igor Ristić 2 , Ivan Šćepnović 2 Proof. The theorem is proved in (Radonjic, 2018). In order for the data to be correctly encoded/decoded, it is necessary (with the help of a computer) to find the coefficients Ci. For the purposes of this paper, we are interested only in the values of the Ci's when b = 16. Out of a total of 2031 found coefficients, Table 1 shows 690 of them.

Comparison with the Internet Checksum
The IC, in essence, is a special case of 16-bit integer SEC codes. This can be seen from the fact that it can be defined as Although the construction differences between the mentioned algorithms are minimal, they have a great. Radonjic, A., Ristic, I., & Scepnovic, I. (2023). Integer single-error-correcting codes as an alternative to the internet checksum, Social informatics journal, 2(1), 41-44. Although the construction differences between the mentioned algorithms are minimal, they have a great impact on their performance: the IC can detect burst errors of length up to 15 bits, while 16-bit integer SEC codes can correct all single errors within an N-bit codeword (N ≤ 32512). In other words, if error control were to be performed using the IC, the receiver would discard all corrupted packets, which could degrade the quality of service perceived by the user. However, if error control were to be performed using integer SEC codes, the receiver could repair the vast majority of the corrupted packets, especially if they are transmitted over optical links [according to (Stone and Partridge, 2000;James, 2005;Yao et al. 2016), 90% of all channel errors are single errors].
Apart from this, it should be noted that using 16-bit integer SEC codes (instead of the IC) has no negative effect on the packet size. From (Aracil and Callegati, 2009) we know that the packet size depends on the version of the Internet protocol (IP) used. In particular, if voice data (VoIP packets) are delivered over IP version 4 (IPv4) network, the IC protects between 60 and 280 bytes (Figure 2). On the other hand, if the transmission is carried out over IP version 6 (IPv6) network, the IC will protect 84 to 304 bytes. As for delivering television content (IPTV packets), the IC covers at least 228 bytes in the case of transmission over an IPv4 network, i.e. at least 252 bytes if an IPv6 network is used. All these facts point to the conclusion that 16-bit integer SEC codes can protect all multimedia packets. Figure 2. The packet fields covered by the IC However, for the integer SEC decoder to be able to correct single errors, it is necessary to reserve ≤ ≈ 0.116 MB of memory (for storing the syndrome table). This, of course, is not a problem for today's processors that have several MB of the cache (Table 2).

Conclusions
The transmission of multimedia data over the Internet suffers from the problem of dropping corrupted packets. The reason for this lies in the inability of the IC to correct channel errors. In this paper, we have presented one solution that can improve the transmission of multimedia data over the Internet. The proposed solution is based on replacing the IC with integer codes that can correct single errors.