Alfonso Martinez

Bit-Interleaved Coded Modulation

The principle of coding in the signal space follows directly from Shannons analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal with errors introduced at the demodulator of the underlying waveform channel. The correct perspective of signal-space coding, although never out of sight of information theorists, was brought back into the focus of coding theorists and system designers by Imais and Ungerbocks pioneering works on coded modulation. More recently, powerful families of binary codes with a good tradeoff between performance and decoding complexity have been (re-)discovered. Bit-Interleaved Coded Modulation (BICM) is a pragmatic approach combining the best out of both worlds: it takes advantage of the signal-space coding perspective, whilst allowing for the use of powerful families of binary codes with virtually any modulation format. BICM avoids the need for the complicated and somewhat less flexible design typical of coded modulation. As a matter of fact, most of todays systems that achieve high spectral efficiency such as DSL, Wireless LANs, WiMax and evolutions thereof, as well as systems based on low spectral efficiency orthogonal modulation, feature BICM, making BICM the de-facto general coding technique for waveform channels. The theoretical characterization of BICM is at the basis of efficient coding design techniques and also of improved BICM decoders, e.g., those based on the belief propagation iterative algorithm and approximations thereof. In this text, we review the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. This framework allows an accurate analysis without any particular assumptions on the length of the interleaver or independence between the multiple bits in a symbol. We further consider the sensitivity of the BICM capacity with respect to the signal-to-noise ratio (SNR), and obtain a wideband regime (or low-SNR regime) characterization. We review efficient tools for the error probability analysis of BICM that go beyond the standard approach of considering infinite interleaving and take into consideration the dependency of the coded bit observations introduced by the modulation. We also present bounds that improve upon the union bound in the region beyond the cutoff rate, and are essential to characterize the performance of modern randomlike codes used in concatenation with BICM. Finally, we turn our attention to BICM with iterative decoding, we review extrinsic information transfer charts, the area theorem and code design via curve fitting. We conclude with an overview of some applications of BICM beyond the classical coherent Gaussian channel.

Performance analysis of turbo-coded APSK modulations over nonlinear satellite channels

This paper investigates the performance of M-ary amplitude-phase shift keying (APSK) digital modulation over typical nonlinear satellite channels. The effect of the satellite nonlinearity is studied, and distortion pre- and post-compensation techniques for coded APSK are presented. Moreover, clock timing, signal amplitude and carrier phase recovery schemes are discussed. For the latter, a new class of non turbo decoder-aided closed-loop phase synchronizers featuring good performance and low complexity is studied. Finally, an end-to-end coded APSK system simulator inclusive of the satellite channel model and synchronization sub-systems is discussed and its performance compared to standard trellis-coded QAM concatenated with Reed-Solomon codes, showing a remarkable gain in both power and spectral efficiency. Coded APSK, recently selected for the new standard -DVB-S2- for digital video broadcasting and interactive broadband satellite services, is shown to represent a powerand spectral-efficient solution for satellite nonlinear channels

Error probability analysis of bit-interleaved coded modulation

This correspondence presents a simple method to accurately compute the error probability of bit-interleaved coded modulation (BICM). Thanks to the binary-input output-symmetric (BIOS) nature of the channel, the pairwise error probability (PEP) is equal to the tail probability of a sum of random variables with a particular distribution. This probability is in turn computed with a saddlepoint approximation. Its precision is numerically validated for coded transmission over standard Gaussian noise and fully interleaved fading channels for both convolutional and turbo-like codes.

Design Considerations for a Transparent Mode Group Diversity Multiplexing Link

Mode group diversity multiplexing (MGDM) is an optical multiple-input-multiple-output technique that aims at creating independent communication channels over a multimode fiber, using subsets of propagating modes. This letter deals with the analysis of an MGDM point-to-point link, transparent to the transmission format. The geometry of a mode-group selective multi/demultiplexer is optimized in order to minimize the crosstalk among the channels. The power penalty is calculated when a zero-forcing algorithm is used to mitigate the crosstalk

Bit-Interleaved Coded Modulation in the Wideband Regime

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 M 2 -QAM is given by a simple formula and shown to approach - 0.34 dB as M increases. Using the low SNR expansion, a general tradeoff between power and bandwidth in the wideband regime is used to show how a power loss can be traded off against a bandwidth gain.

Mismatched Decoding: Error Exponents, Second-Order Rates and Saddlepoint Approximations

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-order rates of constant-composition coding is studied, and is shown to be at most two. For independent identically distributed random coding, asymptotic estimates of two well-known non-asymptotic bounds are given using saddlepoint approximations. Each expression is shown to characterize the asymptotic behavior of the corresponding random-coding bound at both fixed and varying rates, thus unifying the regimes characterized by error exponents, second-order rates, and moderate deviations. For fixed rates, novel exact asymptotics expressions are obtained to within a multiplicative 1+o(1) term. Using numerical examples, it is shown that the saddlepoint approximations are highly accurate even at short block lengths.

Spectral efficiency of optical direct detection

The spectral efficiency (channel capacity) of the optical direct-detection channel is studied. The modeling of the optical direct-detection channel as a discrete-time Poisson channel is reviewed. Closed-form integral representations for the entropy of random variables with Poisson and negative binomial distributions are derived. The spectral efficiency achievable with an arbitrary input gamma density is expressed in closed integral form. Simple, nonasymptotic upper and lower bounds to the channel capacity are computed. Numerical results are presented and compared with previous bounds and approximations.

Bit-interleaved coded modulation with shaping

The performance of bit-interleaved coded modulation (BICM) with shaping (i.e., non-equiprobable bit probabilities) is studied. For the AWGN channel, the rates achievable with BICM and shaping are practically identical to those of coded modulation or multilevel coding, virtually closing the gap that made BICM suboptimal in terms of information rates.

Bit-interleaved coded modulation revisited: A mismatched decoding perspective

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, and shows that due to the random coding construction, the interleaver is not required. The second proof is based on the random coding error exponents with mismatched decoding, where the largest achievable rate is the generalized mutual information. Moreover, the generalized mutual information of the mismatched decoder coincides with the infinite-interleaver BICM capacity. We show that the error exponent-and hence the cutoff rate-of the BICM mismatched decoder is upper-bounded by that of coded modulation and may thus be lower than in the infinite-interleaved model; for binary reflected Gray mapping in Gaussian channels the loss in error exponent is small. We also consider the mutual information appearing in the analysis of iterative decoding of BICM with extrinsic information transfer (EXIT) charts: if the symbol metric has knowledge of the transmitted symbol, EXIT mutual information admits a representation as a pseudo-generalized mutual information, which is in general not achievable. A different symbol decoding metric, for which the extrinsic side information refers to the hypothesized symbol, induces a generalized mutual information lower than the coded modulation capacity. In this case, perfect extrinsic side information turns the mismatched-decoder error exponent into that of coded modulation.

Temporal Stability of a Transparent Mode Group Diversity Multiplexing Link

The temporal behavior of a mode group diversity multiplexing (MGDM) link is examined. MGDM has been proposed as a way of creating parallel, independent communication channels over multimode fiber (MMF) links using different groups of modes. When the effect of dispersion can be neglected, the output electrical signals of an MGDM link are related to the input ones via a real-valued transmission matrix. The transmission matrix is vulnerable to changes in the modal spectrum of the propagating mode groups as well as to the coupling of light at the input and output of the MMF. Measurements of the transmission matrix of a two-input two-output system over 12.7 h show that an MGDM link can be very stable