Bit-Interleaved Coded Modulation

Chapter 5 - The interplay between modulation and channel coding

The IEEE 802.11a OFDM wireless local area network (WLAN) system aims to achieve code diversity in quasi-static frequency-selective fading channels by employing bit interleaved coded modulation (BICM). Since the time variation of the channel during a WLAN packet transmission is small and its frequency selectivity finite, the code diversity is limited by both the degree of the channel variation as well as by the code properties. This paper experimentally investigates the impact of channel frequency selectivity on the code-diversity performance of BICM, with and without 2/spl times/1 Alamouti transmit diversity. Using a simplified model of the finite frequency selectivity, we develop a mathematical framework to show that the code diversity is only probabilistically achieved. Our results indicate that for the frequency selectivity typically seen in indoor WLAN channels, using a channel code with larger d/sub free/ does not improve the packet error rate (PER) performance.

In this paper, we extend the iterative demapping technique to observation separation (OS), which is an iterative channel estimation and symbol detection procedure. We consider a bit interleaved coded modulation with iterative decoding (BICM-ID) on a multipath channel with coded packet oriented transmission system with 16QAM. The channels considered are the time-invariant multipath and the channel estimation corresponds to the pseudo-inverse type. We propose here to study the influence of mapping over the performance of turbo equalization. Turbo equalization is a receiving process performing iteratively equalization and channel decoding; soft information generated by each receiving function is improved through the iterations until the optimum behavior of the system reached. In the studied system the turbo equalization and the channel estimation part is based on our previous work. In the context of bit interleaved coded modulation (BICM), the iterative demapping is an iterative process between the soft demapping device and the channel decoding. We analyze here the improvement of mapping optimization for turbo equalization and we proposed an optimized binary mapping of 16-QAM constellation in order to increase coding gain, which can be used for some practically important cases. It is demonstrated that owning to a carefully designed mapping, different to the classical Gray mapping, bit error rate performance is improved.

In this paper, we analytically derive the bit error rate (BER) for bit-interleaved coded modulation (BICM) under the assumption of a temporally correlated flat Rayleigh fading channel. We assume the channel state information (CSI) to be unknown at receiver side and consider a linear minimum mean-squared error (LMMSE) channel estimator that relies on periodically inserted pilot symbols. We give asymptotic results for both non-iterative BICM and BICM with iterative decoding (BICM-ID). Furthermore, we show that the interpretation of the channel estimation error as an SNR degradation holds true in these cases.

Space-time block coded (STBC) in-phase quadrature-phase (IQ)-interleaved coded modulation (CM) schemes are proposed for orthogonal frequency division multiplexing (OFDM). Trellis coded modulation (TCM), turbo TCM (TTCM), bit-interleaved coded modulation (BICM) and iteratively decoded BICM (BICM-ID) schemes having a similar decoding complexity are employed in conjunction with 16-level quadrature amplitude modulation (16QAM) for yielding an effective throughput of 3 information bits per symbol. The IQ-diversity attained by the proposed schemes provides a significant additional coding gain. It was found that TTCM and BICM-ID assisted STBC-IQ-OFDM were the best schemes in terms of the achievable bit error ratio and frame error ratio, respectively.

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.

The paper outlines an efficient approach to evaluating the performance of bit interleaved coded modulation (BICM) systems. Most existing approaches evaluate the probability of individual pairwise error events and obtain a union bound to the bit error probability. This gives very tight bounds on performance for SNRs above the BPSK modulation cutoff rate. However, for higher order modulation systems, the number of bit errors in a symbol slot depends on the two modulated symbols involved in an error event and the linearity of the code cannot be extended to include the modulator. The performance is usually approximated by a few dominant error events which are applicable to AWGN channels. Some approaches consider infinite depth interleaving to obtain a simplified linear model. We study the evaluation and convergence of union bounds for fading channels with finite code block sizes. We develop a general approach which assumes an ideal model for the modulator and enables us to extend the linearity of the considered codes to simplify the computation. This enables us to analyze the performance of concatenated codes with an interleaver of finite length. The approach also gives greater insight into the influence of modulator parameters and the block length of the code on the diversity achieved in BICM systems. The application of our analytical model is demonstrated with examples and simulations.

Joint iterative channel estimation and decoding for 16-QAM bit-interleaved coded modulation (BICM) is considered over frequency-flat fading channels. Estimates of the complex channel gain are derived first from known pilot symbols by optimum Wiener filtering and passed to the BICM iterative decoder as initial channel state information. After each decoding iteration, the channel estimates are refined using the extrinsic information fed back from the decoder. An advanced scheme called restart is developed to effectively reduce the bit error rate floor, by restarting the decoder after several iterations with the refined channel gain estimates. Motivated by the observation of the burst errors in the transmitted sequence, the restart algorithm is extended by concatenating Reed-Solomon codes with BICM. When RS (255, 223) code is used for BICM with 16-QAM modified set partitioning labeling and a 16-state code, the BER of 10/sup -6/ can be achieved at E/sub b//N/sub 0/ of 10.5 dB for normalized fade rate f/sub d/T/sub s/ = 0.02.

A novel four dimensional constellation shaping with non-uniform signaling for long-haul fiber-optic communication

A new method for adjusting positions of signal points of a traditional signal constellation used in the BICM-ID (Bit-Interleaved Coded Modulation with Iterative Decoding) system is proposed. Optimal rotation angle versus SNRs (Signal-to-Noise Power ratios) in the sense of providing the system with attainable lowest BER (Bit Error Rate) are reported.

In this paper, labeling is jointly designed with the outer code by the EXIT chart based analysis to improve the performance of bit-interleaved coded modulation with iterative decoding. A systematic design methodology is proposed for regular modulation schemes which can easily obtain a set of labelings with various slopes. Given an outer code, the optimal labeling which has the steepest slope but still makes the tunnel between the decoder and demapper transfer curves open can then be chosen to optimize the BER performance. Verified by the simulation results, our design can provide remarkable SNR gain over the conventional ones.

In this paper a coded modulation method for the additive white Gaussian noise channel is presented which incorporates signal shaping. The scheme uses a modulation map to map bits to channel inputs. A modulation map is considered that has the advantage it is can easily be combined with binary error-correcting codes. The decoding strategy is a combination of bit-interleaved coded modulation and multistage decoding. The number of required decoding stages is only small compared to other multistage decoding schemes for coded modulation. It is shown that modulation maps can be designed with a constrained capacity limit very close to the capacity of the AWGN channel. When combined with low-density parity-check codes, simulation results show that a near-capacity performance is achieved for high spectral efficiencies.

We investigate link quality metrics (LQMs) based on mutual information (MI) for fast link adaptation (FLA) in IEEE 802.11n wireless local area network (WLAN) with convolutional coding and higher order modulations. The LQMs are scalar quantities that map the receiver's post-decoding behaviour in a frequency-selective channel into an equivalent behaviour in an AWGN channel. From this metric the expected packet error rate (PER) can be predicted. Two LQMs are presented that are derived from the SINRs of all sub-carriers and streams: the effective SNR and the effective mutual information. The effective mutual information is the mean mutual information including a correction factor which improves the PER estimation accuracy in various highly frequency-selective channels. The FLA algorithm dynamically selects a modulation and coding scheme (MCS) that maximizes the throughput (TP), while keeping the average PER over time below a target value. Furthermore, we present methods of searching for the most suitable MCS. Practical performance bounds are obtained by means of simulations. We show that both investigated LQMs yield accurate PER estimates and that the resulting TP of the FLA algorithm used in a 2 x 2 MIMO bit-interleaved coded modulation (BICM) OFDM system that performs channel estimation is only 1.7 dB from the performance bound of the TP.

Bit-Interleaved Coded Modulation using Iterative Decoding (BICM-ID) is amalgamated with Luby Transform (LT) coding. The resultant joint design of the physical and data link layer substantially improves the attainable Bit Error Rate (BER) performance. A Cyclic Redundancy Check (CRC) combined with a novel Log-Likelihood Ratio (LLR) based packet reliability estimation method is proposed for the sake of detecting and disposing of erroneous packets. Subsequently, bit-by-bit LT decoding is proposed, which facilitates a further BER improvement at a lower number of BICM-ID iterations. Finally, we revisit the pseudo random generator function used for designing the LT generator matrix.

Labeling-Based Recipient Identification (LABRID) brings the possibility of representing the destination station address in a Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) system by a signal labeling rule. Low-order modulations, such as BPSK or QPSK, pose a general problem for BICM-ID due to a limited convergence of iterative decoding. In the context of LABRID, they have one more drawback—a small number of different labeling rules in general; the number of the optimal ones, which exhibit the maximal asymptotic coding gain, is reduced even further. Meanwhile, LABRID needs a sizable collection of different optimal labeling rules to serve many users in large wireless networks. In this paper, the author suggests the use of hypercube BPSK or QPSK labeling to overcome all these challenges. By means of the Reactive Tabu Search (RTS) algorithm, more than 1500 equivalent optimal hypercube labeling rules are found. Analytical error bounds of the system are developed and supported by simulation experiments. Then, the focus is moved to the criterion to determine the frame destination at the LABRID receiver; a simple threshold-based method is proposed to keep the incorrect decision probability below 10−5. Finally, it is shown that LABRID outperforms a reference BICM-ID system in terms of computational complexity.