Experimental Results

Computer simulations were conducted to evaluate three MAP-based error mitigation schemes for DSR over burst error channels. First a bit-level trellis MAP decoding scheme BMAP is considered that uses the standard BCJR algorithm to decode the index-bits. The decoders SMAP1 and SMPA2 exploit the symbol-level source redun-dancy by using a modified BCJR algorithm based on a sectionalized trellis structure.

The SMAP1 is designed for a memoryless binary symmetric channel, whereas the SMAP2 exploits the channel memory though the Gilbert channel characterization.

The channel transition probabilities to be used for the SMAP1 is p(et) in (3.11), and p(et|e_t−1) in (3.12) for the SMAP2. For purpose of comparison, we also investigated an error mitigation scheme [15] which applied the concept of softbit speech decoding (SBSD) and achieved good recognition performance for AWGN and burst channels. A preliminary experiment was first performed to evaluate various decoders for reconstruc-tion of the feature pair (C₀, logE) encoded with the DSR front-end. A rate R = 1/2 convolutional code with memory order M = 6 and the octal generator (46, 72)8 is cho-sen as the channel code. Table 3.2 precho-sents the signal-to-noise ratio (SNR) obtained from transmission of the index-bits over Gilbert channel with BER ranging from 10⁻³ to 10⁻¹. The results of these experiments clearly demonstrate the improved perfor-mance achievable using the SMAP1 and SMAP2 in comparison to those of BMAP and SBSD. Furthermore, the improvement has a tendency to increase for noisy channels with higher BER. This indicates that the residual redundancy of quantizer indexes is better to be exploited at the symbol level to achieve more performance improvement.

A comparison of the SMAP1 and SMAP2 also revealed the importance of matching the real error characteristics to the channel model on which the MAP symbol decoder design is based. The better performance of SMAP2 can be attributed to its ability to compute the symbol APP taking interframe and intraframe memory of the channel into consideration, as opposed to the memoryless channel assumption made in the SMAP1.

We further validate the proposed decoding algorithms for the case where error

se-Table 3.2: SNR(dB) performance for various decoders on a Gilbert channel.

quences were generated using a complete GSM simulation. The simulator is based on the CoCentric GSM library [29] with TCH/F4.8 data and channel coding, interleaving, modulation, a channel model, and equalization. The channel model represents a typical case of a rural area with 6 propagation paths and a user speed of 50 km/h. Further, cochannel interference was simulated at various carrier-to-interference ratios (CIR). In using the SMAP1 and SMAP2 schemes, the channel transition probabilities have to be combined with a priori knowledge of Gilbert model parameters which can be estimated once in advance using the gradient iterative method [30]. For each of simulated error sequences, we first measured the error-gap distribution by computing the probability that at least l successive error-free bits will be encountered next on the condition that an error bit has just occurred. The optimal identification of Gilbert model parame-ters was then formulated as the least square approximation of the measured error-gap distribution by exponential curve fitting. Table 3.3 gives estimated Gilbert model pa-rameters for the GSM TCH/F4.8 data channels operating at CIR = 1, 4, 7, 10 dB. The next step in the present investigation concerned the performance degradation that may result from using the SMAP2 scheme under channel mismatch conditions. In Table 3.4, CIRd refers to the CIR value assumed in the design process, and CIRa refers to the true CIR used for the evaluation. The best results are in the main diagonal of the table, where channel-matched Gilbert model parameters are used for the channel

tran-Table 3.3: Estimated Gilbert model parameters for GSM TCH/F4.8 data channels.

Table 3.4: SNR performance of the SMAP2 over the GSM data channel under channel mismatch conditions.

sition probability computation of (3.13). The performance decreases in each column below the main diagonal when the CIRdis increased. The investigation further showed that the SMAP2 is not very sensitive to a channel mismatch between the design and evaluation assumptions.

We next considered the speaker-independent recognition of Mandarin digit strings as the task without restricting the string length. A Mandarin digit string database recorded by 50 male and 50 female speakers was used in our experiments. Each speaker pronounced 10 utterances and 1-9 digits in each utterance. The speech of 90 speakers (45 male and 45 female) was used as the training data, and the other 10 as test data.

The total numbers of digits included in the training and test data were 6796 and 642, respectively. The DSR results obtained by various error mitigation algorithms for the

Figure 3.4: Recognition performances for DSR transmission over a Gilbert channel.

Gilbert channel are shown in Figure 3.4. It can be seen that employing the source a priori information, sectionalized trellis MAP decoding, and channel memory constantly improves the recognition accuracy. The SMAP2 scheme performs the best in all cases, showing the importance of combining the a priori knowledge of source and channel by means of a sectionalized code trellis and Gilbert channel characterization.

3.5 Summary

A JSCD scheme which exploits the combined source and channel statistics as an a priori information is proposed and applied to the channel error mitigation in DSR applica-tions. We first investigate the residual redundancies existing in the DSR features and find ways to exploit these redundancies in the MAP symbol decoding process. Also proposed is a modified BCJR algorithm based on sectionalized code trellises which

uses Gilbert channel characterization for better decoding in addition to source a priori knowledge. Experiments on Mandarin digit string recognition indicate that the pro-posed decoder achieved significant improvements in recognition accuracy for DSR over burst error channels.

Chapter 4