Combined Source/Channel Decoding: When Minimizing Bit Error Rate is Suboptimal Tim Fingscheidt, Thomas Hindelang, Richard V. Cox, Nambi Seshadri AT&T Labs – Research Florham Park, NJ 07932, USA tim,thomas,rvc,sn @research.att.com Convolutional coding as a means of error correction is widely used in mobile communi- cations, where the effects of channel noise have to be taken into account. Channel decoders usually aim at minimizing the frame, symbol or residual bit error rate of the source bits. In this contribution we show how the residual bit er- ror rate can be reduced by using a priori knowledge about the source statistics within the channel decod- ing process. This usually helps the source decoder to perform better. If the source decoder also uses a priori knowledge, however, we show that the best overall system performance is reached at a higher residual bit error rate after channel decoding. This gives new insight into optimization criteria of com- bined source/channel decoding. I. I NTRODUCTION Real world source coding usually leaves a certain amount of residual redundancy within the bit stream. This is mostly due to constraints on coding delay and complexity. In recent years an increasing interest has grown in decoding techniques that are able to make use of this residual source redundancy. Bahl et al. laid the foundations of symbol-by-symbol channel decoding that is able to exploit a priori knowl- edge about the source bits [1]. Hagenauer investigated sequence-estimating channel decoding algorithms and proposed the source-controlled channel decoding tech- nique [2]. Further work focused on channel decoding exploiting source statistics to reduce the residual path, symbol, or bit error rate is [3–5]. Alternatively, the source redundancy can of course be used in the source decoding process [6–14] often re- ferred to as soft decision or softbit decoding. In contrast to channel decoding these techniques have the advantage of an easy adaptation to arbitrary error criteria, e.g. the signal-to-noise ratio rather than the bit error rate. In this paper we investigate combined source/channel decoding in the sense that the channel decoder as well as the source decoder are able to exploit source statis- tics. Furthermore, the channel decoder yields soft deci- sions (softbits) for use in the softbit source decoder. In section II we briefly review the softbit decoding tech- nique [11,12], whereas in section III we discuss source controlled channel decoding according to [5, 15], both presented in a uniform manner. Simulation results will be presented answering the question, whether a priori knowledge can be used twice, in the channel decoder Author was on leave from Institute for Communications Engi- neering (LNT), Munich University of Technology (TUM), Germany. as well as in the source decoder. Moreover, indications will be given that in a combined source/channel decod- ing scheme, the minimization of the residual bit error rate after channel decoding is not always optimum. II. SOURCE DECODING USING SOURCE APRIORI KNOWLEDGE Let us assume a speech or an image signal being source coded. The source coder usually generates so- called codec parameters, e.g. pitch, spectral coeffi- cients, etc. In the following we focus only on a sin- gle codec parameter at time instant as depicted in Fig. 1. The parameter is scalar quan- tized and coded by the bit combination consisting of bits . When all parameters belonging to a frame are coded, their bits are multiplexed building a frame of source bits. This frame is now subject to convolutional encoding resulting in a frame of channel bits . In the following we assume the regarded parameter is generated only once per frame. Thus the parameter time instant denotes the current frame, the previous frame, etc. After transmission over an equivalent channel com- prising modulation, the physical channel, and soft- demodulation, the received frame is fed into a chan- nel decoder. To allow combined source/channel decod- ing the channel decoder is required to yield a soft out- put (softbits) [1, 11] e.g. in form of decoder proba- bilities giving a likelihood for every source bit . These probabilities are the interface to the source decoder which uses them in the form (1) Different meanings of dependent on the used type of a priori knowledge will be discussed in section III. The source decoding of a parameter can be done in sev- eral ways [11]. Applying with SD/HB (2) with being the decoded parameter at frame is equivalent to hard-output channel decoding and source decoding by table lookup. The table lookup is sym- bolized by . We call this straightforward tech- nique source decoding by hardbit decoding, abbreviated SD/HB.