Elsevier

Computer Communications

Volume 28, Issue 4, 16 March 2005, Pages 441-448
Computer Communications

Markov chain analysis of collaborative codes in random multi access communication systems

https://doi.org/10.1016/j.comcom.2004.08.015Get rights and content

Abstract

A discrete-time Markov chain analysis is developed for the performance of collaborative codes in random multi access communication systems (CCMA). Two media access schemes are proposed: asynchronous CCMA where users can start transmission at any time and synchronous CCMA where users can start transmission only at the start of a synchronizing clock. The performance of these two systems is compared with pure ALOHA and slotted ALOHA, respectively. It is shown that these well-known protocols are special case of CCMA when the number of available codes is only one. The performance of 2-, 3-, and 5-user codes is studied and it is shown that they offer significant performance enhancement in CCMA environment compared to the non-coded case in terms of throughput, efficiency, delay, and the number of retries for a successful transmission. Because of CCMA advantages, their use for voice traffic application is studied and it was found that CCMA allows more traffic than the non-coded case for all codes used, which is doubled in the case of 5-user slotted environment.

Introduction

Collaborative code multiple access (CCMA) technique allows two or more users to simultaneously share a common channel such as wireless media, where the bandwidth is a very restricted resource. The main advantage of CCMA is that transmission rate is greater than time division multiple access (TDMA) [1]. This technique is attractive for multi-user receiver implementations employing digital signal processing (DSP) dedicated hardware architecture. The signals of each user are coded before transmission where they add up in the channel. CCMA codewords are selected such that each combination of transmitted symbols is distinct. The receiver is then able to decode this combined message into its constituent codewords and deliver them to their respective users. Fig. 1 shows the situation where each receiver decodes the received codewords and extract the desired data addressed to it. The most widely published uniquely decodable CCMA codes are the two-user [2] and three-user codes [3]. More recently, a five-user collaborative code has been proposed [1]. Complex-valued collaborative codes have been proposed also for fading channels [4]. As an example, a three-code system has three allowed constituent codewords K1={00,11}, K2={10,01}, and K3={00,10}. For example, if the user chooses to use codeword K2 to send a ‘0’, then the bit pattern ‘10’ is sent. Table 1 gives the possible codewords sent by a user while transmitting ‘0’ or ‘1’.

Assume that we have three users employing a three-user CC system such that user 1 uses code K1, user 2 employs code K2, and user 3 employs code K3. Assuming all three users are active, the data transmitted on the channel is explained in Table 2.

The table shows that all three users are able to transmit their data simultaneously provided that each user uses its own assigned codeword. The value of the signal on the channel uniquely identifies the bit pattern that was sent. For example, if the decoder detects the signal values ‘31’, then we know that the bit pattern ‘101’ was sent where user 1 sent ‘1’, user 2 sent ‘0’ and user 3 sent ‘1’. The values of signals carried by the channel constitute a set of valid values that allow the decoders to detect the bit values transmitted by the different users.

In an K-user collaborative code system, each user is assigned a unique code for encoding its 0 and 1 bits. Although the problem of data collision is avoided, the total channel capacity is wasted when any of the users are idle. This is similar to the situation of TDMA where each time slot in a frame is dedicated to a certain user irrespective of that user being idle or active. Furthermore, the number of users is small and depends on the code employed. In the case of the 2-user code, for example, only two users can access the system simultaneously.

To service N users using K codes (with K<N), centralized reservation or decentralized random access media access control (MAC) techniques could be employed. Any one of the N users can access the system at the start of the next clock cycle using one of the available K codes. Therefore, the number of users accessing the channel at each clock cycle varies between 0 and N.

In a centralized reservation scheme a central controller polls all users and allocates codes to the active users based on some reservation or scheduling strategy. Collisions will not take place when a centralized reservation scheme is employed. Reservation schemes are best suited for delay- and bandwidth-critical applications where the Quality of Service (QoS) must be guaranteed based on lower bounds on performance [5].

A distributed random access or statistical multiplexing scheme does not require a central controller. In this scheme a user that has data to send does so by choosing one code from the set of K codes. Collisions can take place when a distributed random access scheme is employed. Random access schemes are best suited for data transmission applications where delay is not a critical factor or when statistical guarantees for QoS are adequate.

A collision could occur here if two or more users attempt to access the channel using the same code. In that case the combined signal generated at the channel may or may not match any of the outputs within the codebook. Collision detection in CCMA is best made at the packet rather than the bit level. The synchronization pattern (normally 01111110) is sent at the beginning of each packet by the users. At the decoder, if such patterns cannot be recovered, then a collision is declared. As an example, consider the case of a 3-code CCMA system as shown in Table 3, when the synchronization pattern is being sent by user 1, 2, and 3 utilizing the codes K3, K1, and K3, respectively. The decoded pattern for user 1 is correct, but since patterns for users 2 and 3 were not correctly extracted, a collision is declared.

Fig. 2 shows user activity versus time for a 3-code system where a random access, synchronous scheme is used. In a synchronous scheme users attempt a transmission only at the start of a frame as indicated by a global timing signal. At time step n three users attempt a transmission and each user picks a different code. No collision takes place as indicated. At time step n+1 three users attempt a transmission but two users use the same code. As a result, a collision is said to have occurred and all three packets are lost. At time step n+2 two users attempt a transmission and two different codes are chosen. No collision takes place and the two packets are transmitted.

Each user accessing the channel may randomly select one of the K codes available. A maximum of K users can utilize the channel simultaneously, if they have used different codes, otherwise collision will take place and all messages will be lost. For the case of 3-user code, for instance, up to three users can access the channel at the same clock cycle without interfering or corrupting their data, if the three messages were encoded differently.

Section 2 provides an analysis for the asynchronous collaborative code MAC system and Section 3 provides an analysis for the synchronous collaborative code MAC system.

Section snippets

Asynchronous collaborative codes multiple access (A-CCMA)

In an asynchronous collaborative code communication system a user with data to send picks a code at random from the pool of available codes and starts transmission. A collision occurs if another user transmits or is already transmitting a packet using the same code. In that case all users of the channel suffer a collision. When a collision takes place, users can start to transmit after choosing a code at random and waiting for a random amount of time.

We make the following assumptions for our

Synchronous MAC (S-CCMA) modeling

In this section we perform Markov chain analysis of the synchronous MAC (S-CCMA) protocol when it is used in a mobile environment. A user with data to send is only permitted to transmit at the start of a time slot. This synchronized access to the channel results in increased system throughput and reduced packet delay as we shall see in the following analysis.

Fig. 9 shows the transition diagram for the S-CCMA protocol. The channel can move from collided state to transmitting state in one time

Application—voice traffic example

One of the motives for using CCMA protocols is to provide support for high data rate and real-time traffic (e.g. voice). Voice traffic requires stringent delay requirements. Thus, CCMA could be used to support multiple users under a centralized reservation scheme as was discussed in Section 1. A simpler scheme to support voice traffic is to use the random access schemes studied in this paper since these schemes do not require the services of a central controller.

Random access schemes only

Conclusions

This paper presented discrete-time Markov chain analysis of collaborative codes when used in two different multiple access modes: synchronous and asynchronous. Performance figures for each protocol were developed and investigated through numerical simulations. We also compared the performance of collaborative codes with pure ALOHA and slotted ALOHA schemes. It was found that CCMA yields better performance than the corresponding non-coded case in terms of throughput, delay, speedup factor and

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