General BER Expression for One-Dimensional Constellations

A novel general ready-to-use bit-error rate (BER) expression for one-dimensional constellations is developed. The BER analysis is performed for bit patterns that form a labeling. The number of patterns for equally spaced M-PAM constellations with different BER is analyzed.Comment: To appear in the Proceedings of the IEEE Global Communications Conference (GLOBECOM) 2012. Remark 3 modifie

On the Exact BER of Bit-Wise Demodulators for One-Dimensional Constellations

The optimal bit-wise demodulator for M-ary pulse amplitude modulation (PAM) over the additive white Gaussian noise channel is analyzed in terms of uncoded bit-error rate (BER). New closed-form BER expressions for 4-PAM with any labeling are developed. Moreover, closed-form BER expressions for 11 out of 23 possible bit patterns for 8-PAM are presented, which enable us to obtain the BER for 8-PAM with some of the most popular labelings, including the binary reflected Gray code and the natural binary code. Numerical results show that, regardless of the labeling, there is no difference between the optimal demodulator and the symbol-wise demodulator for any BER of practical interest (below 0.1)

On the Asymptotic Performance of Bit-Wise Decoders for Coded Modulation

Two decoder structures for coded modulation over the Gaussian and flat fading channels are studied: the maximum likelihood symbol-wise decoder, and the (suboptimal) bit-wise decoder based on the bit-interleaved coded modulation paradigm. We consider a 16-ary quadrature amplitude constellation labeled by a Gray labeling. It is shown that the asymptotic loss in terms of pairwise error probability, for any two codewords caused by the bit-wise decoder, is bounded by 1.25 dB. The analysis also shows that for the Gaussian channel the asymptotic loss is zero for a wide range of linear codes, including all rate-1/2 convolutional codes

Design and performance evaluation of bitwise retransmission schemes in wireless sensor networks

The previously proposed bitwise retransmission schemes which retransmit only selected bits to accumulate their reliability are designed and evaluated. Unlike conventional automatic repeat request (ARQ) schemes, the bitwise retransmission schemes do not require a checksum for error detection. The bitwise retransmission decisions and combining can be performed either after demodulation of the received symbols or after channel decoding. The design and analysis assume error-free feedback, however, the impact of feedback errors is also considered. The bit-error rate (BER) expressions are derived and verified by computer simulations in order to optimize the parameters of the retransmission schemes. The BER performance of coded and uncoded bitwise retransmissions is compared with a hybrid ARQ (HARQ) scheme over additive white Gaussian noise (AWGN), slow fading, and fast fading channels. It is shown that bitwise retransmissions outperform block repetition coding (BRC) over AWGN channels. In addition, the selection diversity created by the bitwise retransmissions can outperform the HARQ at large signal-to-noise ratio (SNR) over fast fading channels. Finally, the practical design of a bitwise retransmission protocol for data fusion in wireless sensor networks is presented assuming Zigbee, WiFi and Bluetooth system parameters

Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input/output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM (CCDM). Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.Comment: 11 pages, 7 figure