Efficient Source Decoding Over Memoryless Noisy Channels Using Higher Order Markov Models

Abstract

Abstract-Exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth-efficient way to combat noisy channel degradations. This redundancy can be employed to either assist the channel decoder for improved performance or design better source decoders. In this work, a family of solutions for the asymptotically optimum minimum mean-squared error (MMSE) reconstruction of a source over memoryless noisy channels is presented when the redundancy in the source encoder output stream is exploited in the form of a -order Markov model ( 1) and a delay of 0 is allowed in the decoding process. It is demonstrated that the proposed solutions provide a wealth of tradeoffs between computational complexity and the memory requirements. A simplified MMSE decoder which is optimized to minimize the computational complexity is also presented. Considering the same problem setup, several other maximum a posteriori probability (MAP) symbol and sequence decoders are presented as well. Numerical results are presented which demonstrate the efficiency of the proposed algorithms.Index Terms-Forward-backward recursion, joint sourcechannel coding, maximum a posteriori probability (MAP) detection, Markov sources, minimum mean-squared error (MMSE) estimation, residual redundancies, source decoding.

Vector quantisation for finite‐state Markov channels and application to wireless communications

“…We can then express Equation [22] and decoding VQ encoded Markov sources over BSCs [23]. The use of higher order Markov models for VQ decoding over memoryless channels has been considered in Reference [24].…”

“…fading gain is a constant associated with each channel state) and the continuous fading model as described in Figure 2 (in both cases, the same encoder is used). In the continuous model, the output conditional densities are estimated using (24), with m = 32 per state (note that discrete fading model simply corresponds to m = 1). The difference appearing in Figure 5 can be explained as follows.…”

Enhancing Closed-Loop Wireless Systems Through Efficient Feedback Reconstruction

“…We have assumed a Markov model and a memoryless feedback channel, so using the Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm [33], the state probabilities can be computed recursively by [31] …”

“…The sequence MAP decoder [31], [34] receives the sequence J n and determines the most probable transmitted sequence asî n = arg max P (I n |J n ) using the trellis in Section III-A1. Considering the memoryless property of the feedback channel, the following branch metric can be obtained for the respective trellis [31]: ) which is used within the well-known Viterbi algorithm to find the solution.…”

“…Considering the memoryless property of the feedback channel, the following branch metric can be obtained for the respective trellis [31]: ) which is used within the well-known Viterbi algorithm to find the solution. The estimated sequence is applied to (19).…”