Previous work on concatenated single parity-check codes has yielded exceptionally good performance despite, or perhaps because of, their weak algebraic structure. In this article, maximum a posteriori single parity-check decoders are applied to the decoding of systematic binary algebraic block codes. Results for a range of Hamming codes show good performance compared to soft-decision brute force (maximum-likelihood) and algebraic decoding. The decoding complexity of the proposed technique grows only linearly with increasing block length.

Single parity-check (SPC) codes are applied in both parallel and serial concatenated structures to produce high-performance coding schemes. The number of concatenations or stages, M, is increased to improve system performance at moderate-to-low bit-error rates without changing the overall code parameters (namely, code rate and code block length). Analytical bounds are presented to estimate the performance at high signal-to-noise ratios. The SPC concatenated codes are considered with binary phase-shift keying and with 16-quadrature amplitude modulation bit-interleaved coded modulation on the additive white Gaussian noise channel and the independent Rayleigh fading channel. Simulations show that the four-stage serial or parallel concatenated SPC codes can, respectively, outperform or perform as well as 16-state turbo codes. Furthermore, decoding complexity is approximately 9-10 times less complex than that of 16-state turbo codes. The convergence behavior of both serial and parallel concatenated SPC codes is also discussed.

A generalised performance bounding technique for BICM systems is presented. We show that, in the Rayleigh fading channel, it is possible to estimate accurately the error performance of coded BICM systems employing large signal constellations, by using only the error performance of a BPSK system employing the same code in the same channel. Our method generalizes the work of G. Caire et al. (see IEEE Trans. on Information Theory, vol.44, no.3, p.927-46, 1998) to all SNR values and is independent of the channel coding scheme and the code rate. The work here implies that, in the Rayleigh fading channel, analytical bounds for any coding scheme derived for the BPSK system can be easily applied to BICM systems with larger signal constellations. Simulation results are presented for the Rayleigh fading channel to verify the analysis.

In this paper, single parity check (SPC) codes are applied in a parallel concatenated structure to produce a high performance coding scheme with very low complexity. We show a simple yet elegant way of improving system performance at medium-low bit error rates (BER), without changing the overall code parameters (code rate, code block length). We compare its BER performance with other coding schemes. Multiple parallel concatenated SPC (M-PC-SPC) codes are capable of outperforming not only the best 64-state convolutional coding schemes, but also the 16-state turbo codes. For bit interleaved coded modulation (BICM) schemes, the 4 parallel concatenated SPC code is about 10 times less complex than the 16-state turbo codes, and yet with only 5 iterations, it still performs better than the turbo code iterated 6 times in the fading and AWGN channel. Combined with multilevel modulation schemes, this high performance scheme is very suitable for practical systems due to its flexible code parameters, and low complexity.

In this paper, MAP decoders for single parity check (SPC) codes are applied to the decoding of systematic binary algebraic block codes. We compare the performance of this decoding technique to hard decision syndrome decoding and soft decision brute force decoding. Simulation results are presented for the (7,4,3) and (15,11,3) Hamming codes in the AWGN and Rayleigh fading channels. Using a product (7,4,3) Hamming code, the proposed scheme is also compared to the dual code technique as described Berrou and Glavieux (see IEEE Trans. Communications, vol.44, no.10, p.1261-71, 1996). Although the BER performance is slightly inferior, the proposed scheme is much less complex to implement.

Single parity check (SPC) codes are applied in a serial concatenation structure to produce a high performance coding scheme with very low complexity. We show a simple yet elegant way of improving the system performance at low bit error rates (BER), without changing the overall code parameters (code rate, code block length). We compare its BER performance to the best 64-state convolutional codes, and the 16-state turbo codes. Comparisons show that its performance is only slightly poorer. Despite this inferior performance, the scheme is very suitable for practical implementation due to its flexible code parameters. We conclude by showing that its decoding complexity is more than 1 order of magnitude less than that of a 16-state turbo code.