A new variant of bit interleaved coded modulation (BICM) is proposed. In the new scheme, called Parallel BICM, L identical binary codes are used in parallel using a mapper, a newly proposed finite-length interleaver and a binary dither signal. As opposed to previous approaches, the scheme does not rely on any assumptions of an ideal, infinite-length interleaver. Over a memoryless channel, the new scheme is proven to be equivalent to a binary memoryless channel. Therefore the scheme enables one to easily design coded modulation schemes using a simple binary code that was designed for that binary channel. The overall performance of the coded modulation scheme is analytically evaluated based on the performance of the binary code over the binary channel. The new scheme is analyzed from an information theoretic viewpoint, where the capacity, error exponent and channel dispersion are considered. The capacity of the scheme is identical to the BICM capacity. The error exponent of the scheme is numerically compared to a recently proposed mismatched-decoding exponent analysis of BICM.
We study quantization of log-likelihood ratios (LLR) in bit-interleaved coded modulation (BICM) systems in terms of an equivalent discrete channel. We propose to design the quantizer such that the quantizer outputs become equiprobable. We investigate semi-analytically and numerically the ergodic and outage capacity over single- and multiple-antenna channels for different quantizers. Finally, we show bit error rate simulations for BICM systems with LLR quantization using a rate 1/2 low-density parity-check code.
Caire, Taricco and Biglieri presented a detailed analysis of bit interleaved coded modulation, a simple and popular technique used to improve system performance, especially in the context of fading channels. They derived an upper bound to the probability of error, called the expurgated bound. In this correspondence, the proof of the expurgated bound is shown to be flawed. A new upper bound is also derived. It is not known whether the original expurgated bound is valid for the important special case of square QAM with Gray labeling, but the new bound is very close to, and slightly tighter than,…
In this paper, we present the diversity order analysis of bit-interleaved coded multiple beamforming (BICMB) combined with the constellation precoding scheme. Multiple beamforming is realized by singular value decomposition of the channel matrix which is assumed to be perfectly known to the transmitter as well as the receiver. Previously, BICMB is known to have a diversity order bound related with the product of the code rate and the number of parallel subchannels, losing the full diversity order in some cases. In this paper, we show that BICMB combined with the constellation precoder and maxi…
Multiple beamforming is realized by singular value decomposition of the channel matrix which is assumed to be known to both the transmitter and the receiver. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve full diversity as long as the code rate Rc and the number of employed subchannels S satisfy the condition RcS<=1. Bit-Interleaved Coded Multiple Beamforming with Constellation Precoding (BICMB-CP), on the other hand, can achieve full diversity without the condition RcS<=1. However, the decoding complexity of BICMB-CP is much higher than BICMB. In this paper, a reduced complexi…
The wideband regime of bit-interleaved coded modulation (BICM) in Gaussian channels is studied. The Taylor expansion of the coded modulation capacity for generic signal constellations at low signal-to-noise ratio (SNR) is derived and used to determine the corresponding expansion for the BICM capacity. Simple formulas for the minimum energy per bit and the wideband slope are given. BICM is found to be suboptimal in the sense that its minimum energy per bit can be larger than the corresponding value for coded modulation schemes. The minimum energy per bit using standard Gray mapping on M-PAM or …
Delayed bit-interleaved coded modulation (DBICM) generalizes bit-interleaved coded modulation (BICM) by modulating differently delayed sub-blocks of codewords onto the same signals. DBICM improves transmission reliability over BICM due to its capability of detecting undelayed sub-blocks with the extrinsic information of the decoded delayed sub-blocks. In this work, we propose a novel windowed decoding algorithm for DBICM, which uses the extrinsic information of both the decoded delayed and undelayed sub-blocks, to improve the detection on all sub-blocks. Numerical results show that the propose…
This paper investigates the design and performance of delayed bit-interleaved coded modulation (DBICM) with low-density parity-check (LDPC) codes. For Gray labeled square $M$-ary quadrature amplitude modulation (QAM) constellations, we investigate the optimal delay scheme with the largest spectrum efficiency of DBICM for a fixed maximum number of delayed time slots and a given signal-to-noise ratio. When analyzing the capacity of DBICM, we find two important properties: the capacity improvement due to delayed coded bits being mapped to the real and imaginary parts of the transmitted symbols ar…
This paper addresses the performance of bit-interleaved coded multiple beamforming (BICMB) [1], [2] with imperfect knowledge of beamforming vectors. Most studies for limited-rate channel state information at the transmitter (CSIT) assume that the precoding matrix has an invariance property under an arbitrary unitary transform. In BICMB, this property does not hold. On the other hand, the optimum precoder and detector for BICMB are invariant under a diagonal unitary transform. In order to design a limited-rate CSIT system for BICMB, we propose a new distortion measure optimum under this invaria…
It is shown that while the mutual information curves for coded modulation (CM) and bit interleaved coded modulation (BICM) overlap in the case of a single input single output channel, the same is not true in multiple input multiple output (MIMO) channels. A method for mitigating fading in the presence of multiple transmit antennas, named coordinate interleaving (CI), is presented as a generalization of component interleaving for a single transmit antenna. The extent of any advantages of CI over BICM, relative to CM, is analyzed from a mutual information perspective; the analysis is based on an…
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders,…
When the Channel State Information (CSI) is known by both the transmitter and the receiver, beamforming techniques employing Singular Value Decomposition (SVD) are commonly used in Multiple-Input Multiple-Output (MIMO) systems. Without channel coding, there is a trade-off between full diversity and full multiplexing. When channel coding is added, both of them can be achieved as long as the code rate Rc and the number of employed subchannels S satisfy the condition RcS<=1. By adding a properly designed constellation precoder, both full diversity and full multiplexing can be achieved for both un…
This letter investigates bit-interleaved coded multiple beamforming (BICMB) with perfect coding in millimeter-wave (mm-wave) massive multiple-input multiple-output (MIMO) systems to achieve both maximum diversity gain and multiplexing gain. Using perfect coding with BICMB enables us to do this. We show that by using BICMB and perfect coding, the diversity gain becomes independent from the number of transmitted data streams and the number of antennas in each remote antenna unit (RAU) at the transmitter and the receiver. The assumption is that the perfect channel state information (CSI) is known…
For broadband wireless communication systems, Orthogonal Frequency Division Multiplexing (OFDM) has been combined with Multi-Input Multi-Output (MIMO) techniques. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be applied to achieve both spatial diversity and multipath diversity, making it an important technique. However, analyzing the diversity of BICMB-OFDM is a challenging problem. In this paper, the diversity analysis o…
This paper investigates the design of spatially coupled low-density parity-check (SC-LDPC) codes constructed from connected-chain ensembles for bit-interleaved coded modulation (BICM) schemes. For short coupling lengths, connecting multiple SC-LDPC chains can improve decoding performance over single-chains and impose structured unequal error protection (UEP). A joint design of connected-chain ensembles and bit mapping to further exploit the UEP from codes and high-order modulations is proposed. Numerical results demonstrate the superiority of the proposed design over existing connected-chain e…
This paper develops a low-complexity near-optimal non-coherent receiver for a multi-level energy-based coded modulation system. Inspired by the turbo processing principle, we incorporate the fundamentals of bit-interleaved coded modulation with iterative decoding (BICM-ID) into the proposed receiver design. The resulting system is called bit-interleaved coded energy-based modulation with iterative decoding (BICEM-ID) and its error performance is analytically studied. Specifically, we derive upper bounds on the average pairwise error probability (PEP) of the non-coherent BICEM-ID system in the …
In this paper, diversity analysis of bit-interleaved coded multiple beamforming (BICMB) is extended to the case of general spatial interleavers, removing a condition on their previously known design criteria and quantifying the resulting diversity order. The diversity order is determined by a parameter Qmax which is inherited from the convolutional code and the spatial de-multiplexer used in BICMB. We introduce a method to find this parameter by employing a transfer function approach as in finding the weight spectrum of a convolutional code. By using this method, several Qmax values are shown …
We revisit the information-theoretic analysis of bit-interleaved coded modulation (BICM) by modeling the BICM decoder as a mismatched decoder. The mismatched decoding model is well-defined for finite, yet arbitrary, block lengths, and naturally captures the channel memory among the bits belonging to the same symbol. We give two independent proofs of the achievability of the BICM capacity calculated by Caire et al. where BICM was modeled as a set of independent parallel binary-input channels whose output is the bitwise log-likelihood ratio. Our first achievability proof uses typical sequences, …
Bit-interleaved coded modulation (BICM) has attracted considerable attention from the research community in the past three decades, because it can achieve desirable error performance with relatively low implementation complexity for a large number of communication and storage systems. By exploiting the iterative demapping and decoding (ID), the BICM is able to approach capacity limits of coded modulation over various channels. In recent years, protograph low-density parity-check (PLDPC) codes and their spatially-coupled (SC) variants have emerged to be a pragmatic forward-error-correction (FEC…
An energy-efficient approach is presented for shaping a bit-interleaved low-density parity-check (LDPC) coded amplitude phase-shift keying (APSK) system. A subset of the interleaved bits output by a binary LDPC encoder are passed through a nonlinear shaping encoder whose output is more likely to be a zero than a one. The "shaping" bits are used to select from among a plurality of subconstellations, while the unshaped bits are used to select the symbol within the subconstellation. Because the shaping bits are biased, symbols from lower-energy subconstellations are selected more frequently than …
The capacity of the AWGN broadcast channel is achieved by superposition coding, but superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Coded modulation over a broadcast channel subject to a specific channel-input modulation constraint remains an important open problem. Some progress has been made in the related area of unequal-error protection modulations which can be considered single-user broadcast transmission, but it does not approach all points on the boundary of the capacity region. This paper studies broadcast coded modulation u…
In this paper we carry out the asymptotic diversity analysis for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems by using bit interleaved coded multiple beamforming (BICMB). First, a single-user mmWave system which employs $M_t$ antenna subarrays at the transmitter and $M_r$ antenna subarrays at the receiver is studied. Each antenna subarray in the transmitter and the receiver has $N_r$ and $N_t$ antennas, respectively. We establish a theorem for the diversity gain when the number of antennas in each remote antenna unit (RAU) goes to infinity. Based on the theore…
Multi-Input Multi-Output (MIMO) techniques have been incorporated with Orthogonal Frequency Division Multiplexing (OFDM) for broadband wireless communication systems. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be employed to provide both spatial diversity and multipath diversity, making it an important technique. In our previous work, the subcarrier grouping technique was applied to combat the negative effect of subcar…
An analysis of the diversity gain for bit-interleaved coded multiple beamforming (BICMB) method in millimeter-wave (mm-Wave) massive multiple-input multiple-output (MIMO) systems is carried out for both the single-user and multi-user scenario. We show that the diversity gain is independent of the number of data streams and full spatial multiplexing order can be achieved in both scenarios. Also, we show that the diversity gain in the multi-user scenario is independent of the number of users in the system and only depends on the number of the remote antenna units (RAUs) at the transmitter side, …
A practical $2^m$-ary polar coded modulation (PCM) scheme with optimal constellation labeling is proposed. To efficiently find the optimal labeling rule, the search space is reduced by exploiting the symmetry properties of the channels. Simulation results show that the proposed PCM scheme can outperform the bit-interleaved turbo coded modulation scheme used in the WCDMA (Wideband Code Division Multiple Access) mobile communication systems by up to 1.5dB.
$2^m$-ary modulation creates $m$ bit channels which are neither independent nor identical, and this causes problems when applying polar coding because polar codes are designed for independent identical channels. Different from the existing multi-level coding (MLC) and bit-interleaved coded modulation (BICM) schemes, this paper provides a convolutional polar coded modulation (CPCM) method that preserves the low-complexity nature of BICM while offering improved spectral efficiency. Numerical results are given to show the good performance of the proposed method.
A commonly assumed drawback of multi-level coding, compared to a bit-interleaved coded modulation, is its high latency: Indeed, the levels must be decoded sequentially. In this paper, we consider polar codes to code each level. We show that the decoding time complexity of the multi-level scheme, using successive-cancellation list decoding for each polar code, is only 1.5 times the one of a single polar code, regardless of the signal-to-noise ratio and the number of levels.
A framework is proposed that allows for a joint description and optimization of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation (PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded modulation (BICM). The conceptual equivalence of polar coding and multilevel coding is pointed out in detail. Based on a novel characterization of the channel polarization phenomenon, rules for the optimal choice of the labeling in coded modulation schemes employing polar codes are developed. Simulation results regarding the error performance of the proposed schemes on th…
We consider the joint design of polar coding and higher-order modulation schemes for ever increased spectral efficiency. The close connection between the polar code construction and the multi-level coding approach is described in detail. Relations between different modulation schemes such as bit-interleaved coded modulation (BICM) and multi-level coding (MLC) in case of polar-coded modulation as well as the influence of the applied labeling rule and the selection of frozen channels are demonstrated.
Several recent standards such as IEEE 802.11a/g, IEEE 802.16, and ECMA Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) for high data-rate Ultra-Wideband (UWB), employ bit-interleaved convolutionally-coded multicarrier modulation over quasi-static fading channels. Motivated by the lack of appropriate error rate analysis techniques for this popular type of system and channel model, we present two novel analytical methods for bit error rate (BER) estimation of coded multicarrier systems operating over frequency-selective quasi-static channels with non-ideal interleaving. In the fir…
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, includin…
Bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLC) are commonly used to combine polar codes with high order modulation. While BICM benefits from simple design and the separation of coding and modulation, MLC shows better performance under successive-cancellation decoding. In this paper we propose a hybrid polar coded modulation scheme that lies between BICM and MLC, wherein a fraction of bits are assigned to set-partition (SP) labeling and the remaining bits are assigned for Gray labeling. The SP labeled bits undergo sequential demodulation, using iterative demodulat…
Linear precoded discrete multitone modulation (LP-DMT) system has been already proved advantageous with adaptive resource allocation algorithm in a power line communication (PLC) context. In this paper, we investigate the bit and energy allocation algorithm of an adaptive LP-DMT system taking into account the channel coding scheme. A coded adaptive LP-DMT system is presented in the PLC context with a loading algorithm which ccommodates the channel coding gains in bit and energy calculations. The performance of a concatenated channel coding scheme, consisting of an inner Wei's 4-dimensional 16-…
We consider the problem of using polar codes with higher order modulation over AWGN channels. Unlike prior work, we focus on using modulation independent polar codes. That is, the polar codes are not re-designed based on the modulation used. Instead, we propose bit-permuted coded modulation (BPCM): a technique for using the multilevel coding (MLC) approach for an arbitrary polar code. The BPCM technique exploits a natural connection between MLC and polar codes. It involves applying bit permutations prior to mapping the polar code to a higher order modulation. The bit permutations are designed,…
The performance of bit-interleaved coded modulation (BICM) with bit shaping (i.e., non-equiprobable bit probabilities in the underlying binary code) is studied. For the Gaussian channel, the rates achievable with BICM and bit shaping are practically identical to those of coded modulation or multilevel coding. This identity holds for the whole range of values of signal-to-noise ratio. Moreover, the random coding error exponent of BICM significantly exceeds that of multilevel coding and is very close to that of coded modulation.
Coded modulation is a key technique to increase the spectral efficiency of coherent optical communication systems. Two popular strategies for coded modulation are turbo trellis-coded modulation (TTCM) and bit-interleaved coded modulation (BICM) based on low-density parity-check (LDPC) codes. Although BICM LDPC is suboptimal, its simplicity makes it very popular in practice. In this work, we compare the performance of TTCM and BICM LDPC using information-theoretic measures. Our information-theoretic results show that for the same overhead and modulation format only a very small penalty (less th…
In this letter we determine the derivative of the mutual information corresponding to bit-interleaved coded modulation systems. The derivative follows as a linear combination of minimum-mean-squared error functions of coded modulation sets. The result finds applications to the analysis of communications systems in the wideband regime and to the design of power allocation over parallel channels.
This paper presents two methods for approximating the performance of coded multicarrier systems operating over frequency-selective, quasi-static fading channels with non-ideal interleaving. The first method is based on approximating the performance of the system over each realization of the channel, and is suitable for obtaining the outage performance of this type of system. The second method is based on knowledge of the correlation matrix of the frequency-domain channel gains and can be used to directly obtain the average performance. Both of the methods are applicable for convolutionally-cod…
Multilevel coding (MLC) is a coded modulation technique which can achieve excellent performance over a range of communication channels. Polar codes have been shown to be quite compatible with communication systems using MLC, as the rate allocation of the component polar codes follows the natural polarization inherent in polar codes. MLC based techniques have not yet been studied in systems that use spatial modulation (SM). SM makes the polar code design difficult as the spatial bits actually select a channel index for transmission. To solve this problem, we propose a Monte Carlo based evaluati…
Although BICM can significantly improves the BER performance by iteration processing between the demapping and the decoding in a traditional receiver, its design and performance in PNC system has fewer studied. This paper investigates a bit interleaved coded modulation (BICM) scheme in a Gaussian two-way relay channel operated with physical layer network coding (PNC). In particular, we first present an iterative demapping and decoding framework specially designed for PNC. After that, we compare different constellation mapping schemes in this framework, with the convergence analysis by using th…
A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels are constructed and used for code design. The constructed codes perform as good as multi-edge type codes of Zhang and Kschischang (2013). For 64-ASK with probabilistic shaping, a blocklength 64800 code…
Coded modulation with probabilistic amplitude shaping (PAS) is considered for intensity modulation/direct detection channels with a transmitter peak-power constraint. PAS is used to map bits to a uniform PAM-6 distribution and outperforms PAM-8 for rates up to around 2.3 bits per channel use. PAM-6 with PAS also outperforms a cross-shaped QAM-32 constellation by up to 1 dB and 0.65 dB after bit-metric soft- and hard decoding, respectively. An alternative PAM-6 scheme based on a framed cross-shaped QAM-32 constellation is proposed that shows similar gains.
In this letter, we propose a novel LDPC coding scheme to transmit extra bits aided by rotated signal constellations without any additional cost in transmission power or bandwidth. In the proposed scheme, the LDPC coded data are modulated by a rotated two-dimensional signal constellation, in which the rotation angle is specified by the given extra bits. At the receiver, the rotation angle is estimated with the aid of the statistical learning of the syndrome of the LDPC code. After recovering the rotation angle, the coded payload data can be decoded by the LDPC decoder. The simulation results sh…
The problem of private information retrieval gets renewed attentions in recent years due to its information-theoretic reformulation and applications in distributed storage systems. PIR capacity is the maximal number of bits privately retrieved per one bit of downloaded bit. The capacity has been fully solved for some degenerating cases. For a general case where the database is both coded and colluded, the exact capacity remains unknown. We build a general private information retrieval scheme for MDS coded databases with colluding servers. Our scheme achieves the rate $(1+R+R^2+\cdots+R^{M-1})$…
Use of multiple light emitting diodes (LED) is an attractive way to increase spectral efficiency in visible light communications (VLC). A non-DC-biased OFDM (NDC OFDM) scheme that uses two LEDs has been proposed in the literature recently. NDC OFDM has been shown to perform better than other OFDM schemes for VLC like DC-biased OFDM (DCO OFDM) and asymmetrically clipped OFDM (ACO OFDM) in multiple LEDs settings. In this paper, we propose an efficient multiple LED OFDM scheme for VLC which uses {\em coded index modulation}. The proposed scheme uses two transmitter blocks, each having a pair of L…
In this paper, we formulate a new problem to cope with the transmission of extra bits over an existing coded transmission link (referred to as coded payload link) without any cost of extra transmission energy or extra bandwidth. This is possible since a gap to the channel capacity typically exists for a practical code. A new concept, termed as accessible capacity, is introduced to specify the maximum rate at which the superposition transmission of extra bits is reliable and has a negligible effect on the performance of the coded payload link. For a binary-input output-symmetric (BIOS) memoryle…
A hybrid ARQ (HARQ) scheme for polar code, which is called active-bit relocation under masks (ARUM), is proposed. In each transmission, the data bits are encoded and bit-wisely XOR-masked using a binary vector before being transmitted through the channel. The masking process combines multiple transmissions together which forms another step of inter-transmission channel transform. The reliabilities are updated after every transmission, and the less reliable bits in earlier ones are relocated to the more reliable positions at the latest transmitted block. ARUM is a very flexible HARQ scheme whic…
A pragmatic coded modulation system is presented that incorporates signal shaping and exploits the excellent performance and efficient high-speed decoding architecture of staircase codes. Reliable communication within 0.62 bits/s/Hz of the estimated capacity (per polarization) of a system with L=2000 km is provided by the proposed system, with an error floor below 1E-20. Also, it is shown that digital backpropagation increases the achievable spectral efficiencies---relative to linear equalization---by 0.55 to 0.75 bits/s/Hz per polarization.
In this paper, we design and compare multilevel polar coding (MLPC) and bit-interleaved polar coded modulation (BIPCM) for uplink sparse code multiple access (SCMA) systems that operate over fast and block fading channels. Both successive cancellation (SC) and successive cancellation list (SCL) decoding algorithms are considered. Simulation results show that, with either decoder, BIPCM performs better than its MLPC counterpart. Also, both BIPCM and MLPC exhibit a performance advantage over LTE turbo-coded and WiMAX LDPC SCMA systems when the SCL technique is used for decoding.
A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, cod…
A centralized coded caching system, consisting of a server delivering N popular files, each of size F bits, to K users through an error-free shared link, is considered. It is assumed that each user is equipped with a local cache memory with capacity MF bits, and contents can be proactively cached into these caches over a low traffic period; however, without the knowledge of the user demands. During the peak traffic period each user requests a single file from the server. The goal is to minimize the number of bits delivered by the server over the shared link, known as the delivery rate, over al…
