Iterative Source-Channel Decoding
Soft Decision Source Decoding
The principle of iterative source-channel decoding is based on the technique of Soft Decision Source Decoding (SDSD). This technique consists in the inverse operation of the quantization and the index assignment. In traditional systems, the channel decoder outputs hard bits (0 or 1) which are transformed into pseudo-analog values using a table-lookup. Modern channel decoders however are able to deliver soft-information, i.e., reliabilities of each decoded bit. Together with the residual redundancy of the source parameters (unequal distribution and correlation), this soft information can be exploited to perform an MMSE estimation of the source parameters.
Iterative Source-Channel Decoding
The soft decision source decoding receiver can be extended such that it is able to generate additional information (expressed in terms of probabilities) on the bits at its input using the source symbol distrution and the correlation properties. It is then possible to generate extrinsic information which can be utilized again by a channel decoder to improve the channel decoding step. In the following diagram the receiver of a system employing iterative source-channel decoding is depicted.
The channel decoder (usually a maximum a posteriori (MAP) decoder) and the soft decision source decoder exchange extrinsic information in an iterative process until the system converges and a quality improvement of the reconstructed source symboles has been achieved. The convergence of the system can best be analyzed using so-called EXIT charts. The EXIT characteristic of a receiver component plots the mutual information between extrinsic output and data bits against the mutual information between a priori input and data bits. The characteristic can be recorded separately for both components of the iterative receiver. The figure on the right depicts the characteristics of a channel decoder (red) and a source decoder (green). The characteristic of the source decoder is mirrored such that the mutual information of a priori input (corresponding to the extrinsic output of the channel decoder!) is plotted over the mutual information of the extrinsic output (which is fed back to the a priori input of the channel decoder!). The iterative exchange of extrinsic information can now be visualized as a staircase-like curve in the EXIT chart. The intersection point of both characteristics characterized the convergence point. In this example, 5-6 iterations can be exploited until system convergence has been reached.
Key element of the optimization of systems employing iterative source-channel decoding (ISCD) at the reciver is the index assignment, the choice of the channel encoder and the quantizer. The optimization is usually done using the aforementioned EXIT charts. The picture on the left depicts the advantages of ISCD. The transmission of correlated parameters over an AWGN channel has been simulated. The utilized channel code is a rate 1/2 RNSC convolutional code with constraint length 4. The index assignment has been optimized specifically for this system. The quantizer is a Lloyd-Max quantizer with 8 quantization levels. The figure plots the signal-to-noise ratio of the transmitted parameters over the channel quality. Both black curves show the simulation results for the non-iterative case. The bottom curve depicts the performance for the traditional case, i.e., the channel decoder delivers hard bits and a table operation is performed to reconstruct the parameter. The utilization of soft decision source decoding already permits considerable gains (approximately 2 dB channel quality at a constant parameter SNR). If a parameter SNR of for instance 13 dB is the target during the system design stage, the utilization of iterative source-channel decoding permits an additional gain of approximately 2.8 dB (red curve)