MAP decoding of quantized sources over soft-decision fading channels with memory

We study a joint source-channel decoding scheme that exploits the channel´s statistical memory and soft-decision information in fading channels. The channel considered is a recently introduced binary input 2^q-ary output channel with Markovian ergodic noise based on a finite queue (called NBNDC-QB). This model has been shown to effectively represent soft-decision demodulated correlated Rayleigh fading channels. The coding scheme consists of a scalar quantizer, a proper index assignment, and a sequence maximum a posteriori (MAP) decoder designed to harness the redundancy left in the quantizer´s indices, the channel´s soft-decision output, and correlation in the channel noise process. We first consider the simple case where the quantized indices form a binary symmetric Markov source and establish a necessary and sufficient condition under which the sequence MAP decoder is reduced to a simple instantaneous symbol-by-symbol decoder. We next assess the signal-to-distortion ratio (SDR) performance of our general system. Our numerical results confirm that this system can successfully take advantage of the channel memory and outperforms systems that use channel interleaving by as much as 2.6 dB in SDR. In addition, SDR gains of up to 2.8 dB are achieved using as few as 2 bits for soft-decision quantization over hard quantized output schemes. Finally, the NBNDC-QB channel model is validated in terms of SDR performance by fitting the NBNDC-QB model to a discrete correlated Rayleigh fading channel, designing a system for this matched NBNDC-QB model, and comparing this system´s performance over both the NBNDC-QB and the Rayleigh fading channels.