Adaptive Channel Coding for Mobile Channels — Or Why Wasting Bandwidth for Error Detection? C. Weiß, T. Stockhammer, J. Hagenauer
A. Donner
Institute for Communications Eng. (LNT) Munich University of Technology chris,tom,hag @lnt.ei.tum.de
German Aerospace Center (DLR) Institute of Communications and Navigation
[email protected]
Abstract We present a new channel coding system which combines error detection and error correction using a single high-memory convolutional code, i.e., no dedicated error detection code is required. Since the state complexity of high-memory convolutional codes makes maximum-likelihood decoding impractical, a modified sequential decoder –the Far End Error Decoder (FEED)– is proposed. FEED adds to the conventional sequential decoding procedure a post processing operation which allows to compute the path reliability of the decoded path. With this path reliability the first error in the decoded frame can be localized, thus, enabling combined error correction and detection with a single code. The advantage of the proposed scheme over applying a dedicated error detection code is demonstrated at the example of the GSM Fullrate Speech Codec. Although the Fullrate Speech Codec is by far not the most suited source coding scheme for our new approach, a gain of up to dB in SegSNR or dB in channel SNR can be achieved with a peak complexity equal to the standard GSM system. However, in average FEED uses a significantly lower number of operations. Moreover, FEED has a scalable complexity and is self-adaptive to varying channel conditions.
1 Introduction In many communication systems channel coding is inevitable to reliably communicate over the error-prone transmission channel. Usually, the design of these channel coding systems is based on the achievable (average) bit or word error probability which inherently assumes that the reconstructed source quality is insensitive to the position of the (channel) decoding error in the source data block. However, recent investigations on still image coding [1] and speech coding [2] have shown that the reconstruction quality of efficient source coding schemes is severely affected by residual errors in the most significant source data. In these most significant parts it is of advantage, if one does not reconstruct corrupted data but rather relies only on the correctly decoded information of lower layers in image coding or uses appropriate concealment techniques [2]. Thus, it is vital for these source decoders to be supplied only with the error-free part in the most sensitive parts. Hence, the error protection scheme has to detect errors, or even better to localize errors in order to decide if at least parts of the received data can be used in the reconstruction process. To meet this requirement, recently a channel coding system for SPIHT (set partitioning in hierarchical trees, [3]) coded images has been proposed where in a change of paradigm the system was designed such that the length of the error-free decoded subblock (where a subblock begins with the first symbol of the data block) was maximized rather than to exclusively minimize the (average) bit or word error probability [4, 5]. This was achieved by a novel channel decoder that in contrast to conventional decod-
ing algorithms allows to combine error correction and localization based on a single convolutional code, i.e., no additional redundancy (bandwidth) is spent for a dedicated error detection code. In this work we use the Fullrate Speech Codec of the GSM (Global System for Mobile communications) system [6] as an example to demonstrate that the benefits of the new approach to channel coding are not restricted to image transmission but generally apply to any source coding scheme where different parts of the source data frame have different significance for the reconstruction quality. It also serves to prove that the system which was initially presented in combination with progressively coded sources can also be used with source coders which are not designed explicitly in a progressive manner, but have an inherent progressive or at least hierarchical property. In Section 2 we give a brief system overview and outline which parts of the channel coding system of the GSM Fullrate Codec are changed by our new approach to channel coding which is based on the FEED algorithm. Since the FEED algorithm is an extension of sequential decoding to the computation of path reliabilities, Section 3 gives an introduction into these topics. Finally, in Section 4 we present simulation results that indicate the improvement potential offered by the FEED principle.
2
System Overview
As already outlined in the introduction our main goal is not to provide a new channel coding system for the GSM system but to show the potentials of the FEED algorithm for speech transmission over wireless channels. For this reason we specify a well-defined system environment which models mobile speech transmission appropriately and, furthermore, allows for a simple setup which can easily be rebuilt for comparison purposes. The relevant components, source and channel coder, and the corresponding decoders are used according to the GSM system. Let us briefly define and justify our transmission system. GSM as well as most other 2G systems use a TDMA approach to separate different users within one cell. For GSM Fullrate transmission a total of radio slots are accessible for each speech frame, each consisting of channel symbols to be used for the channel coded speech frame. As two speech frames share one radio burst we obtain a total of channel symbols per speech frame. For slow to moderate user mobility it can be assumed that the channel encounters slowly time-varying frequencyflat Rayleigh fading. In addition, as most 2G systems have introduced the capacity increasing feature of frequency hopping, the assumption of statistical independent Rayleigh fading within two radio bursts is appropriate. Rayleigh fading is used as it serves as a worst-case assumption without any direct signal path component between base station and mobile. Although GSM uses a partial response GMSK modulation scheme with appropriate equaliza-
tion techniques at the receiver to combat intersymbol interference and multi-path fading, in general, BPSK with Nyquist signaling excluding intersymbol interference and equalization results in an accurate model [7]. Therefore, assuming a soft-decision detector and additive white Gaussian noise, we adopt the following timediscrete signal model. Let us define the speech frame as vector where the components are binary random variables that represent the output samples of the speech encoder. This convolutional encoder that speech frame is the input to a rate maps a bit to a binary -tuple of code bits , i.e., the encoder outputs at time in response to the inis a binary random variable also put symbol . Clearly, since the components are binary random variables. In channel decoding it has proven to be useful to define the loglikelihood ratio of a binary random variable as
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describing the transmission channel. We now continue to describe the transmission system and will afterwards define the mapping of channel code symbols to transtransmitted symbols. In our model the user has access to mission radio slots to transmit the speech frame. Slots are denoted by their index . Let , and be the received signal, the transmitted signal and the noise encountered in slot , respectively. The average transmission energy is given as and noise is assumed Gaussian and i.i.d. with variance . The propagation channel is assumed slowly time-varying and frequency-flat for each time slot. In particular, the channel gain over slot is assumed to be constant over the entire slot. The received signal of slot is then given by . We assume that the receiver has perfect knowledge of the channel gain and of the signal-to-noise ratio (SNR) for all where denotes the channel power gain. Without loss of generality we assume for the remainder of this work that and, therefore, the average SNR is . Estimation of the channel gain and of the SNR is achieved in practice by evaluating the inserted training symbols in each radio slot. Finally, we define the mapping of the channel symbols to the transmission frames as a bijective mapping of the index pair , with and , to the index pair , with and . With this mapping, we define the log-likelihood value
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Speech Codec [8, 6]. Bad frame handling is implemented according to the GSM specification [9]. The channel coding part of GSM is shown in Fig. 1. The first class 1a bits in the speech frame are protected by a bit error detection sequence. The class 1a bits, the error detection bits and the residual class 1b bits are reordered in such a way that the more important bits are inherently more protected by placing them in the beginning and the end of the channel coded frame. These class 1 bits are then protected by an inner convolutional code . Termination bits are appended. Overof memory and rate all, this results in channel coded symbols. The residual class 2 bits are inserted uncoded in the frame. At the decoder we apply soft-decision Viterbi decoding. A bad frame is signaled to the speech decoder, if either the bit CRC fails or if reencoding of the decoded data block differs in more than positions compared to the hard decision of the received vector.
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Fig. 1. GSM Fullrate Channel Coding
According to Fig. 2 we only replace this channel coding and decoding part including the reordering of the GSM system where the reordering relates only to the output of the speech encoder and is not to be confused with the interleaving of channel symbols described above. While interleaving serves to spread channel burst errors, the reordering arranges the speech samples such that the information which is most significant for reconstruction is placed in that positions of the speech frame that are best protected by the channel code. Since this is clearly dependent on the channel coding method, it is obvious that we have to adapt the speech frame reordering in our new error correction scheme. This scheme consists of the following components. A high-memory rate systematic convolutional code is used to obtain parity symbols. Subsequently, a puncturing unit allows to adjust the rate appropriately over the frame. Unequal error protection might be applied to different source components. At the receiver side decoding with a sequential decoding algorithm with a certain complexity per speech frame is applied. This sequential decoding provides a method to determine the virtual error-free part of the decoded path and will be explained in more detail in the next section
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3 The Far End Error Decoder A distinctive feature of FEED is that it allows to combine error correction and localization based on a single convolutional code, i.e., no additional redundancy (bandwidth) has to be spent for a dedicated error detection code. The FEED algorithm employs highmemory (e.g., ) convolutional codes which due to their large number of states cannot be decoded using a Viterbi decoder; instead a modified sequential decoder has to be used. In the following, we first discuss some basic properties of sequential decoding. Then we extend the sequential decoding procedure such that it can provide path reliabilities for the partially decoded frame which can be used to localize the first decoding error.
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3.1 Principles of Sequential Decoding The basic idea behind any sequential decoding algorithm is to extend at any time instant only the most promising path where each path of the code tree corresponds to a (partial) code word. Hence, during the decoding process only a subtree of the entire code tree is explored. As a consequence a metric is required that enables us to compare paths of different lengths. The well known Fano metric [10] (written in -values [11])
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