Irregular Trellis for the Near-Capacity Unary Error Correction Coding of Symbol Values From an Infinite Set

Abstract

Irregular joint source and channel coding (JSCC) scheme is proposed, which we refer to as the irregular unary error correction (IrUEC) code. This code operates on the basis of a single irregular trellis, instead of employing a set of separate regular trellises, as in previous irregular trellis-based codes. Our irregular trellis is designed with consideration of the UEC free distance, which we characterize for the first time in this paper. We conceive the serial concatenation of the proposed IrUEC code with an irregular unity rate code (IrURC) code and propose a new EXtrinsic Information Transfer (EXIT) chart matching algorithm for parametrizing these codes. This facilitates the creation of a narrow EXIT tunnel at a low $E_\text{b}/N_0$ value and provides near-capacity operation. Owing to this, our scheme is found to offer a low symbol error ratio (SER), which is within 0.4 dB of the discrete-input continuous-output memoryless channel (DCMC) capacity bound in a particular practical scenario, where gray-mapped quaternary phase shift keying (QPSK) modulation is employed for transmission over an uncorrelated narrowband Rayleigh-fading channel with an effective throughput of $0.508 \,\text{bit}\,{\text{s}}^{-1}\,{\text{Hz}}^{-1}$ . Furthermore, the proposed IrUEC–IrURC scheme offers a SER performance gain of 0.8 dB, compared to the best of several regular and irregular separate source and channel coding (SSCC) benchmarkers, which is achieved without any increase in transmission energy, bandwidth, transmit duration, or decoding complexity.