Applying List Output Viterbi Algorithms to a GSM-based Mobile Cellular Radio System

Digital mobile radio systems based on the pan-European standards GSM and DCS 1800 are using concatenated coding schemes consisting of an inner error correcting convolutional code and an outer error detecting block code to ensure an appropriate performance. An improvement of this performance was achieved by applying list generating algorithms supplying a list of possible convolutional decoded sequences to the block decoder which checks them for correctness. Two list generating algorithms were investigated, namely the Serial List Output Viterbi Algorithm and the Soft Output Viterbi Algorithm with a novel list generating unit. Applying these algorithms yielded a gain of 3 dB without any bandwidth expansion nor additional delay. The only supplementary cost was a slightly increased computational effort. Therefore, List Output Algorithms seem to be a wellsuited mean for improving the performance of GSM-based mobile radio systems. Concerning speech transmission, this improvement was achieved at the expense of a larger residual frame error rate because of the poor errordetecting capabilities of the used block code. 1 I nt r od uc t i on Digital mobile radio systems combine many advantages over analogue networks such as the possibility of improved signal processing and more sophisticated signaling protocols. Since the early nineties, networks based on the pan-European standard GSM Global System for Mobile Communication are working at 900 MHz [1]. The underlying specifications have later been extended to include the frequency range of 1800 MHz (called DCS 1800). After overcoming children’s diseases, these systems have become established. Nevertheless, there are still many possibilities to improve the performance of such networks without changing the standards. Especially data transmission requires a very low bit error rate to keep re-transmissions within a certain limit and therefore avoiding an unnecessary high system load. The point of departure treated in this paper is the concatenated coding scheme consisting of an inner error correcting convolutional code and an outer error detecting block code [1]. Instead of using the conventional Viterbi Algorithm (VA) [2] for decoding the convolutional code, two List Output Algorithms have been implemented, namely the Serial List Output Viterbi Algorithm (SLVA) [5], [6], [7] and the Soft Output Viterbi Algorithm (SOVA) [3], [4] in combination with a novel list generating unit [8]. This unit takes into account both single errors and burst errors without an additional interleaver. The advantage of such algorithms is based on the fact that the block decoder not only receives the most probable sequence from the VA, but also a list of the L most probable sequences. Therefore, the block decoder has the choice between L sequences within the list enlarging the probability to find the correct one. This modification does not require any bandwidth expansion nor any additional delay. The only supplementary cost is an increased computational effort. This paper is organized as follows: Chapter 2 introduces briefly the relevant GSM-specifications concerning the coding procedure. Chapter 3 first treats some implementation aspects and then gives a short description of the SLVA and the SOVA combined with the new list generating algorithm [8]. Finally, chapter 4 discusses the simulation results for speech and data channels and chapter 5 concludes the main results. 2 B r i e f d e s c r i p t i on o f s om e G S M s p e c i f i c a t i ons Services defined by GSM can be principally divided into two groups: speech and data transmission. Concerning speech transmission, there exist standards for a full-rate and a halfrate channel using encoded data rates of 22.8 kbit/s and 11.4 kbit/s, respectively. Because of severe transmission conditions, unequal error protection is applied to the data stream as depicted in Figure 1 [1]. Full Rate Speech Channel Half Rate Speech Channel Full Rate Data Channel with RLP 50 class 1a 3 CRC 132 class 1b 4 tail 78 class 2 22 class 1a 3 CRC 73 class 1b 6 tail 17 class 2 378 convolutional encoded class 1 bits 78 class 2 211 conv. encoded and punctured class 1 bits 17 class 2 16 header 200 data bits 4 tail 456 convolutional encoded and punctured bits 24 FCS Figure 1: Unequal error protection for different GSMchannels In detail, the most important bits, called class 1a bits, are first protected by a CRC (Cyclic Redundancy Check)-code adding 3 parity bits to the information data. Second, after appending the class 1b bits, a certain number of tail bits are added forcing the convolutional coder to return to the zero state at the end of each frame. In the case of a full-rate speech channel, all these bits are encoded by a half-rate convolutional code with memory M = 4 requiring 4 tail bits. The half-rate speech channel uses a convolutional code with a rate of 1/3 and a memory of M = 6 . Here, puncturing shorten the encoded sequence to a length of 211 bits as depicted in Figure 1 (codewords associated with the 3 CRC-bits remain unpunctured) [10]. The most unimportant class 2 bits remain uncoded for both speech channels. A conventional Viterbi decoder [2] performs the decoding of the convolutional code. The CRC-decoder detects bad frames which are veiled so that no re-transmission is necessary. Recently, high rate data transmission over mobile radio channels is playing a growing role. Here, the transparent and the nontransparent mode have to be distinguished. In both modes a convolutional code is applied as a forward error correction code (FEC) [1]. The two modes differ in the fact that the nontransparent mode additionally uses the radio link protocol (RLP), whereas the transparent mode is solely restricted to convolutional coding. The RLP consists of a header, the information sequence itself, and a parity check sum of it (see Figure 1). As in the case of speech transmission, the Viterbi algorithm performs the convolutional decoding. The frame check sequence (FCS)-decoder detects remaining errors. In the case of a transmission error, the frame has to be repeated. 3 L i s t O ut p ut A l g or i t hm s