MAP Detection and Robust Lossy Coding Over Soft-Decision Correlated Fading Channels

Abstract

Abstract-The joint source-channel coding problem for softdecision demodulated time-correlated fading channels is investigated without the use of channel coding and interleaving. For the purpose of system design, the recently introduced non-binary noise discrete channel with queue based noise (NBNDC-QB) is adopted. This analytically tractable Markovian model has been shown to effectively represent correlated fading channels that are hard to handle analytically. Optimal sequence maximum a posteriori (MAP) detection of a discrete Markov source sent over the NBNDC-QB is first studied. When the Markov source is binary and symmetric, a necessary and sufficient condition under which the MAP decoder is reduced to a simple instantaneous symbol-by-symbol decoder is established. Two robust lossy source coding schemes with low-encoding delay are next proposed for the NBNDC-QB. The first scheme consists of a scalar quantizer, a proper index assignment, and a sequence MAP decoder designed to harness the redundancy left in the quantizer's indices, the channel's soft-decision output and noise correlation. The second scheme is the classical noise resilient vector quantizer known as the channel optimized vector quantizer. It is demonstrated that both systems can successfully exploit the channel's memory and soft-decision information. Signal-to-distortion (SDR) gains of more than 1.7 dB are obtained over hard-decision demodulation by using only 2 bits for soft-decision. Furthermore, gains as high as 4.4 dB can be achieved for a strongly correlated channel, in comparison with systems designed for the ideally interleaved (memoryless) channel. Finally, it is numerically observed that for low coding rates the NBNDC-QB model can accurately approximate discrete fading channels in terms of SDR performance.

MAP Decoding of Correlated Sources over Soft-Decision Orthogonal Multiple Access Fading Channels with Memory

“…It is demonstrated that the residual redundancy in the source (in the form of non-uniform distribution and/or memory) and the channel noise can be used to improve performance in terms of the signal-to-distortion ratio (SDR). It is also observed in [4] that using the channel's soft-decision information can result in significant SDR gain over hard-decision decoding, which is in line with other works showing that soft-decision decoding can increase channel capacity and system performance (e.g., see [7]- [10]). …”

“…The system description in this paper is a generalization of the single-user system presented in [4]. The output samples of the first source are encoded using a rate-n scalar quantizer (SQ).…”

“…In this paper, we extend the results of [4], where a singleuser system was considered, and study the JSCC problem of sending two correlated Gaussian sources over an orthogonal multiple access channel (MAC). A practical situation where two sensors separately measure a pair of correlated parameters, such as temperature and humidity, and sending them to a fusion center is one motivation for considering such a problem.…”

“…In [4], sequence maximum a posteriori (MAP) decoding is studied for a system with no algebraic channel coding and channel interleaving. This is one approach to design a JSCC system based on lossy coding (see also [5], [6], and other works) .…”

“…Each sub-channel is a point-to-point correlated Rayleigh discrete fading channel (DFC) used with antipodal signaling and softdecision (non-binary) output quantization. However, as the Rayleigh DFC is hard to treat analytically [4], we will instead use the recently introduced non-binary noise discrete channel with queue based noise (NBNDC-QB) which has been shown to efficiently model such DFC [11], [12]. We design a joint sequence MAP decoder (which is optimal in terms of sequence error probability) and implement it using a modified version of the Viterbi algorithm.…”