A Study of Source Controlled Channel Decoding for GSM AMR Vocoder

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1 A Study of Source Controlled Channel Decoding for GSM AMR Vocoder K.S.M. Phanindra Girish A Redekar David Koilpillai Department of Electrical Engineering, IIT Madras, Chennai phanindra@midascomm.com, girish@iitm.ac.in, koilpillai@tenet.res.in Abstract Error resilience is an important consideration in wireless communication systems, where effects like multipath fading and shadowing make channels error-prone. In this regard, Source Controlled Channel Decoding (SCCD), introduced by J. Hagenauer [2], is a useful method to reduce the errors induced by the channel. In the literature, this technique has been successfully applied to the GSM full rate (FR) and enhanced full rate (EFR) codecs. Adaptive Multirate (AMR) coder is a state of the art vocoder introduced into GSM standard in In this paper, we study the effect of using the wellknown SCCD algorithm for three representative modes of the GSM AMR vocoder kbps, 7.4 kbps and 4.75 kbps modes. Significant inter-frame and intra-frame correlations are observed between bits of these three modes. We exploit these correlations using an APRI-SOVA[2] algorithm and show that for the highly correlated bits, SNR gains of 1 db can be obtained as compared to the conventional approach. 1. Introduction Practical source coders do not perform complete compression due to limitations like delay, complexity, and non-stationary nature of the source, leaving some redundancy in the encoded bits. Different source-encoded bits have different significance with regard to reconstruction. In the GSM AMR vocoder, a 20 msec speech segment is encoded into a single frame. These encoded bits are not completely independent and some bear significant correlation with other bits in the same frame (intra-frame correlation); equipositioned bits in succeeding/preceding frames are also correlated (inter-frame correlation). This correlation can be exploited to combat noise and other signal impairments in order to improve the overall performance [Fig.1]. Source Controlled Channel decoding [2] exploits source redundancy at the channel decoder. We study the use of this Figure 1: Relation between source and channel (de)coding in a wireless link technique for the GSM AMR codec. A simple modification of the Viterbi Algorithm (VA) that accomodates a priori information about the source symbols and generates soft outputs was presented in [2]. The resulting A priori Soft Output Viterbi Algorithm (APRI-SOVA) was then used to obtain improved BER performance in the GSM full rate (FR) vocoder. Hindelang [1] extended Hagenauer s work on GSM-FR vocoder by exploiting intra-frame correlation in addition to inter-frame correlation. Veaux [4] exploits both inter and intra-frame correlations and presents results for GSM full rate as well as enhanced full rate speech codecs. Strauch [3] presents a low complexity approach to SCCD and gives results for both GSM full rate and enhanced full rate systems. In this paper, we explore the use of SCCD for three modes of the GSM AMR system. AMR has eight different modes, viz. 12.2, 10.2, 7.95, 7.4, 6.7, 5.9, 5.15 and 4.75 kbps. In our simulations, we investigated 12.2, 7.4 and 4.75 kbps modes for presence of inter-frame and intra-frame correlations. We have found significant amount of both types of correlations. As expected, 12.2 kbps mode has the largest correlation whereas the 4.75 kbps mode, the least. We have identified the highly correlated bits in these three modes and used an APRI-SOVA algorithm to improve BER. For the highly correlated bits in the 12.2 kbps mode, we have achieved SNR gains of around 1 db over the SOVA algorithm which does not use one or both of the inter- and intra-frame correlations. For the other two modes, the gains obtained are less but are still significant. Compared to the SOVA algorithm, 1

2 the bit-errors of the highly correlated bits reduced significantly by the use of APRI-SOVA algorithm. These highly correlated bits also represent the most important bits for signal reconstruction at the source decoder and hence the reconstucted speech quality can be expected to be better. The paper is organized as follows. We present the observed inter-frame and intra-frame correlations in the next section. The APRI-SOVA model used for exploiting the correlations is described in section 3. Finally, simulation results are presented for the three modes of AMR that we have studied. 2. Inter-frame and Intra-frame correlations in GSM AMR In order to study inter and intra-frame correlations in GSM- AMR encoded bits, we took several noise-free speech test vectors, encoded them using the AMR encoder, and then observed the output frames for the presence of inter-frame and intra-frame correlations. To quantify the amount of correlation, we estimated the probability of change (P c ). Let u k,b {1, 1} represent the bit at position b in frame k. Inter-frame correlation for bits in position b is estimated over N frames by finding the probability of change as P c = P (u k,b u k 1,b ) = P (u k,b u k 1,b = 1) = no. of times u k,b u k 1,b = 1 (1) N 1 Intra-frame correlation between bits at position m and n of the frame k is estimated over N frames by finding probability of change as P c = P (u k,m u k,n ) = P (u k,m u k,n = 1) = no. of times u k,m u k,n = 1 N Given a bit pair, P c indicates the probability with which one of the correlated bit will be different from the other. If P c is close to zero, the bits will be very highly correlated. To identify highly correlated bits, we chose a P c value of 0.35 as the thresold. All bit pairs which have a probability of change less than or equal to this thresold are identified as highly correlated bits Inter-frame correlation The bit-positions (in an AMR encoded frame) of the highly correlated bits for the 12.2 kbps, 7.4 kbps and 4.75 kbps modes of AMR are listed below. (2) 12.2 kbps mode : 1, 8, 9, 10, 25, 39, 40, 41, 48, 87, 88, 98, 137, 138, 142, 143, 144, 151, 190, 201, 240, kbps mode : 1, 27, 28, 29, 52, 55, 81, 84, 88, 89, 90, 113, 116, 142, kbps mode : 1, 24, 25, 26, 48, 82 The 12.2 kbps mode has the highest inter-frame correlation with 22 highly correlated bits whereas the 7.4 kbps mode has 15 higly correlated bits. The inter-frame correlations exhibited by 4.75 kbps mode are somewhat inconsistent for different test vectors. Also, the amount of correlation is not as significant as in the 12.2 kbps and 7.4 kbps modes Intra-frame correlation We give below the bit-numbers of the intra-frame correlated bit pairs in the frame output by the AMR encoder kbps mode : , , , 48-98, , , kbps mode : 27-88, 28-89, 29-90, 52-81, 55-84, , kbps mode : 48-82, Only the first two modes have significant intra-frame correlations. In the 4.75 kbps mode, only two highly correlated bit pairs are found, and these are again incostitent over several test-vectors Observations Most of the bits that exhibit inter-frame correlation also exhibit intra-frame correlation. All the bits that exhibit significant correlations are class 1a bits and hence very important for signal reconstruction at the source decoder. The correlated bits mostly represent the MSBs of the line spectral frequencies, adaptive code-book index, and fixed code-book gain. 3. Correlation model to generate a priori information A complete GSM AMR link as shown in Fig.2 was used for our simulations. We used a soft-output equalizer and an APRI-SOVA channel decoder. Hagenauer has shown in his paper [2] that the Viterbi metric for the APRI-VA can be derived as M m k = M m k 1 + N x m k,nl ck,n y k,n + u m k L(u k ) (3) n=1 2

3 P prio (u q = +1 u r = 1) = P (c) P (c) + P (a) (5) We can similarly find the a priori conditional probabilities of bit u r. Once these are found, taking the log-likelihood ratio gives the a priori soft values used in Eq.(3). Figure 2: GSM AMR link level block diagram where the subscript k indicates time, Mk m denotes the path metric of the m th state sequence through the trellis, 1/N is the rate of the convolutional code, x k,n is the n th bit of the output of the convolutional encoder, L ck,n y k,n denotes the received soft output from the channel corresponding to x k,n, and L(u k ) denotes the a priori soft values of the source. From equation (3), it can be seen that we need a model to generate the a priori soft values L(u k ). The model uses the soft-values of the already decoded frames coupled with correlation data to generate this a priori information. Several simple models are proposed in the literature to estimate the a priori information, notably Hagenauer s HUK model [2], Veaux s model [4] and Hindelang s intra-frame model [1]. We extended Hindelang s model and used it both for interframe and intra-frame correlations. We describe it below. Assume that bits u q and u r are correlated with each other and we want to estimate the a priori probability of bit u q. Now, from probability arguments, we can write P prio (u q = +1) = P prio (u q = +1 u r = +1).Ppost(u r = +1) + P prio (u q = +1 u r = 1).Ppost(u r = 1) (4) where P prio and Ppost refer to the a priori and a posteriori probabilities respectively. The model estimates the conditional probabilities in the above equations based on the available statistics. As frames are received, the values of u q and u r are stored as the set (u q, u r ). The 4 possible sets are a = ( 1, 1), b = ( 1, +1), c = (+1, 1) and d = (+1, +1). The probabilities of each of these sets can be estimated dynamically using a sliding window that stores the N recent sets. For example, P (a) = of times a occurs in sliding window N Once the probabilities of the symbols are calculated, the a priori conditional probabilities of bit u q can be found from P prio (u q = +1 u r = +1) = P (d) P (d) + P (b) Note that this model uses Ppost(u q ) to estimate P prio (u r ). In the case of inter-frame correlation, u q is the bit in the previous frame and hence Ppost(u q ) is available. But for intra-frame correlation, u q is a bit in the current frame and hence Ppost(u q ) is not available at the time of decoding u r. To obtain this information, the channel decoder needs to be run twice in intra-frame correlation case. We first run a SOVA decoder without a priori information. Then from the obtained soft outputs, we can get L post (u q ) and from that Ppost(u q ). Then we run the APRI SOVA channel decoder with the obtained a priori information just obtained. 4. Simulation results In this section, simulation results obtained using a two-path block-rayleigh fading channel are presented. The results are for a clean speech test vector that has 10,000 frames. In the following sections, the word gain refers to the gain in SNR obtained by using APRI SOVA compared with SOVA, and the word relative bit errors (RBE) refers to the bit errors made by APRI SOVA per 100 bit errors of SOVA. In the tables, the bit numbers presented are the bit numbers after subjective re-ordering at the channel encoder Results for inter-frame correlation A maximum gain of 1 db is achieved for the highly correlated bits in the 12.2 kbps mode, (see Fig. 3). Table 1 gives the relative bit errors for these correlated bits. Note that for some very highly correlated bits, the relative bit-errors are reduced by a factor of 4 5. A gain of 0.8 db is achieved for the highly correlated bits in the 7.4 kbps mode (see Fig. 4). The 4.75 kbps mode has the least correlation and a gain of only 0.25 db is obtained for the highly correlated bits as shown in Fig Results for intra-frame correlation Results for intra-frame correlation are similar to their interframe counterparts, in terms of the gains achieved. Gain of 1 db is achieved for the highly correlated bits of 12.2 kbps Bit RBE

4 Bit RBE Table 1: Relative bit errors using inter-frame correlation for 12.2 kbps mode mode. Fig. 6 shows the gain for the highly correlated bits. Table 2 summarizes the relative bit error performance. Bit RBE Figure 3: Gain using inter-frame correlation for correlated bits of 12.2 kbps mode Bit RBE Table 2: Relative bit errors using intra-frame correlation for 12.2 kbps mode Gain of 0.5 db is obtained for the highly correlated bits of 7.4 kbps mode. Fig. 7 shows the gain for the highly correlated bits. Finally, for 4.75 kbps mode, a gain of only 0.2 db is obtained for the highly correlated bits as shown in Fig Conclusions Figure 4: Gain using inter-frame correlation for correlated bits of 7.4 kbps mode We have shown that using SCCD for GSM AMR can result in significant SNR gains. AMR codec has significant inter-frame and intra-frame correlations which can be exploited. SCCD is particularly useful for the 12.2 kbps mode and its effectiveness successively decreases for the 7.4 and 4.75 kbps modes. Exploiting inter-frame and intra-frame correlations gave similar gains showing that both these correlations are present to the same extent. Also, since bits which are highly correlated are also most important in signal reconstruction, error resilience for these bits would lead to better perceptual speech quality at the decoder output. A future direction would be an improved method for exploiting both the inter and intra frame correlations. Another interesting problem is exploring the use of using correlations across different modes when there is mode switching, i.e., the vocoder rate of AMR is dynamically switched. Figure 5: Gain using inter-frame correlation for correlated bits of 4.75 kbps mode 4

5 References [1] A.Ruscitto and T.Hindelang. Channel decoding using residual intra frame correlation in GSM system,. IEEE Electronic Letters, pages , Oct [2] J.Hagenauer. Source Controlled Channel Decoding. IEEE Transactions on Communications, pages , Sept [3] P. Strauch, C. Lusci, M. Sandel, and R. Yan. Low complexity source controlled channel decoding in a GSM system. IEEE transactions on communications, Figure 6: Gain using intra-frame correlation for correlated bits of 12.2 kbps mode [4] C. Veaux, P. Scalart, and A. Gilloire. Channel decoding using inter and intra-correlation of source encoded frames. Data compression conference, DCC 00, March Figure 7: Gain using intra-frame correlation for correlated bits of 7.4 kbps mode Figure 8: Gain using intra-frame correlation for correlated bits of 4.75 kbps mode 5