Title :
Serial concatenated TCM with an inner accumulate code - part II: density-evolution analysis
Author :
Tullberg, Hugo M. ; Siegel, Paul H.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of California, La Jolla, CA, USA
Abstract :
In a companion paper, we showed the existence of decoding thresholds for maximum-likelihood (ML) decoding of a serial concatenated trellis-coded modulation (SCTCM) system with one or more inner accumulate codes. In this paper, we compute the decoding thresholds for an iterative, non-ML decoder by density evolution (DE), assuming infinite blocklengths. We also derive a stability condition for the particular case of an outer parity-check code and a single inner accumulate code. We show that, for equiprobable signaling, the bit-wise log-likelihood ratio densities for higher order constellations are symmetric. Furthermore, when used in DE, these densities can be averaged without significantly affecting the resulting threshold values. For an outer single parity-check code, the lowest decoding thresholds are achieved with two inner accumulate codes. For an outer repeat code, a single inner accumulate code gives the lowest thresholds. At code rates rc>2/3, the decoding thresholds for the SCTCM system are within 1 dB of the constellation-constrained channel capacity for additive white Gaussian noise channels, and within 1.5 dB for independent, identically distributed Rayleigh channels. Simulation results verify the computed thresholds.
Keywords :
AWGN channels; Rayleigh channels; channel capacity; concatenated codes; iterative decoding; maximum likelihood decoding; parity check codes; stability; telecommunication signalling; trellis coded modulation; additive white Gaussian noise channel; bit-wise log-likelihood ratio density; channel capacity; density-evolution analysis; distributed Rayleigh channel; fading channel; inner accumulate code; iterative decoding; maximum-likelihood decoding; parity-check code; serial concatenated TCM; trellis-coded modulation; Additive white noise; Channel capacity; Concatenated codes; Constellation diagram; Iterative decoding; Maximum likelihood decoding; Modulation coding; Parity check codes; Rayleigh channels; Stability; Accumulate codes; density evolution (DE); fading channels; iterative decoding; serial concatenation; stability condition; trellis-coded modulation (TCM);
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2004.841986