Reordered Exponential Golomb Error Correction Code for Universal Near-Capacity Joint Source-Channel Coding

Joint Source-Channel Coding (JSCC) is a powerful technique that allows for the efficient transmission of information by simultaneously considering the characteristics of both the source and the channel. The recently proposed Exponential Golomb Error Correction (ExpGEC) and Rice Error Correction (REC) codes provide generalized JSCC schemes for the near capacity coding of symbols drawn from large or infinite alphabets. Yet these require impractical decoding structures, with large buffers and inflexible system design, this was mitigated by the introduction of the Reordered Elias Gamma Error Correction (REGEC) which itself had limited flexibility with regards to source distribution. In this paper, we propose a novel Reordered Exponential Golomb Error Correction (RExpGEC) coding scheme, which is a JSCC technique designed for flexible and practical near-capacity performance. The proposed RExpGEC encoder and decoder are presented and its performance is analysed using Extrinsic Information Transfer (EXIT) charts. The flexibility of the RExpGEC is shown via the novel trellis encoder and decoder design. Finally, the Symbol Error Rate (SER) performance of RExpGEC code is compared when integrated into the novel RExpGEC-URC-QPSK scheme against other comparable JSCC and Separate Source Channel Coding (SSCC) benchmarkers. Specifically the RExpGEC-URC-QPSK scheme is compared against the REGEC-URC-QPSK scheme, and a serial concatenation of the Exponential Golomb and Convolution Code, which becomes the novel Exp-CC-URC-QPSK scheme. Our simulation results demonstrate the performance gains and flexibility of the proposed RExpGEC-URC-QPSK scheme against the benchmarkers in providing reliable and efficient communications. Specifically, the RExpGEC-URC-QPSK scheme outperforms the SSCC in a uncorrelated Rayleigh fading channel by 2 to 3.6 dB (dependent on source distribution). Furthermore, the RExpGEC-URC-QPSK scheme consistently operates within 2.5 dB of channel capacity when measuring
$E_{b}/N_{0}$
, whilst providing flexibility in SNR performance when compared to the REGEC-URC-QPSK scheme. These performance gains come at the cost of complexity, whereby the RExpGEC-URC-QPSK scheme is 3.6 times more complex than Exp-CC-URC-QPSK scheme under certain conditions. This paper highlights the unique capabilities of RExpGEC as a high performance, practical and flexible JSCC technique.