Reordered Elias Gamma Error Correction Codes For The Near-Capacity Transmission Of Multimedia Information

A novel joint source and channel coding (JSCC) scheme is proposed, which we refer to as the reordered Elias gamma error correction (REGEC) code. Like the recently proposed unary error correction (UEC) code and EGEC code, the proposed code facilitates the practical near-capacity transmission of source symbol values that are randomly selected from a large or infinite alphabet. However, in contrast to the UEC code, both the EGEC and our proposed REGEC codes are universal codes, facilitating the transmission of source symbol values that are randomly selected using any monotonic probability distribution. However, the EGEC code has a complicated structure comprising two parts, where unequal error protection is required to balance the two parts with the aid of a specific parameterization that must be tailored to the source distribution, preventing its employment for unknown or non-stationary sources. By contrast, the proposed REGEC code does not need unequal error protection, and hence its parameterization does not have to be tailored to the particular source distribution, and thus the REGEC code is a more attractive scheme. More explicitly, our REGEC code has a simple structure comprising only a single part, which does not suffer from the delay and loss of synchronization that are associated with the two parts of the EGEC code. In a particular practical scenario, where the source symbols obey a specific Zeta probability distribution, our REGEC scheme is shown to offer gains of up to 0.9 dB over the best of JSCC and separate source and channel coding (SSCC) benchmarkers, when QPSK modulation is employed for transmission over an uncorrelated narrowband Rayleigh fading channel. In the scenario where the source symbols obey the distribution produced by the H. 265 video codec, our REGEC scheme is shown to offer a gain of 0.7 dB over the SSCC benchmarker. These gains are achieved for free, without increasing the required transmit-duration, transmit-bandwidth, transmit-energy, or decoding complexity.