Codeword Error Rate Research Articles

Reduced-Complexity Robust MIMO Decoders

We propose a robust near maximum-likelihood (ML) decoding metric that is robust to channel estimation errors and is near optimal with respect to symbol error rate (SER). The solution involves an exhaustive search through all possible transmitted signal vectors; this search has exponential complexity, which is undesirable in practical systems. Hence, we also propose a robust sphere decoder to implement the decoding with substantially lower computational complexity. For a real 4 x 4 MIMO system with 256-QAM modulation and at SER of 10^{-3}, our proposed robust sphere decoder has a coding loss of only 0.5 dB while searching through 2360 nodes (or less) compared to a 65536 node search using the exact ML metric. This translates to up to 228 times fewer real multiplications and additions in the implementation. We derive analytical upper bounds on the pairwise codeword error rate and symbol error rate of our robust sphere decoder and validate these bounds via simulation.

Short Turbo Codes over High Order Fields

Two classes of turbo codes constructed on high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (2,3) regular low-density parity-check (LDPC) code ensemble. The first construction results in a parallel concatenation of two non-binary, time-variant accumulators. The second construction consists of the serial concatenation of a non-binary time-variant differentiator with a non-binary time-variant accumulator, and provides a highly structured flexible encoding scheme for (2,4) LDPC codes. A cycle graph representation is also provided. The proposed codes can be decoded efficiently either as LDPC codes (via belief propagation decoding on their bipartite graphs) or as turbo codes (via the forward-backward algorithm applied to the component code trellises) by means of the fast Fourier transform. The proposed codes provide remarkable coding gains (more than 1 dB at a codeword error rate 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> ) over binary LDPC and turbo codes in the moderate-short block length regime.

Performance Analysis of Ranging Process in Diversity Incorporated Wireless Systems Suffering from Narrowband Jamming

Ranging is a process where the base station (BS) identifies a mobile station (MS) among many other MSs with the help of Ranging code set, which is unique to each MS. Also, an estimation process is made to find the transition time delay which is the difference between the time at which the MS sends some data and the time at which the BS receives data. In this paper, the effect caused by jamming on the Ranging process will be analyzed. Jamming destroys orthogonality/pseudo orthogonality of the Ranging code set which affects the estimation of the codes. This in turn affects parameters like detection miss rate. This paper also discusses the improvement in the Ranging process where diversity techniques like maximal ratio combining (MRC), selection combining (SC), and equal gain combining are used. These diversity techniques are used in various fading channel models like Rayleigh, Rician, and Nakagami. The analyses indicate that for a Rayleigh fading channel, the code word error rate (CER) decreases by two orders of magnitude for a SC case as compared to the no diversity case, and that CER reduces by three orders of magnitude for an Equal Gain/MRC case as compared to the no diversity case. Similar results are observed for Rician and Nakagami fading channels also.

On-Line Construction of Irregular Repeat Accumulate Codes for Packet Erasure Channels

In many applications erasure correcting codes are used to recover packet losses at high protocol stack layers. The objects (e.g. files) to be transmitted often have variable sizes, resulting in a variable number of packets to be encoded by the packet-level encoder. In this paper, algorithms for the (on-line) flexible design of parity-check matrices for irregular-repeat-accumulate codes are investigated. The proposed algorithms allow designing in fast manner parity-check matrices that are suitable for low-complexity maximum-likelihood decoding. The code ensembles generated by the algorithms are analyzed via extrinsic information transfer charts. Numerical results show how the designed codes can attain codeword error rates as low as 10-5 without appreciable losses w.r.t. the performance of idealized maximum-distance separable codes. Finally, we apply the proposed codes to the upcoming aeronautical communication standard, showing large performance improvements and proving the efficiency and the flexibility of the developed method.

Maximum Likelihood Erasure Decoding of LDPC Codes: Pivoting Algorithms and Code Design

This paper investigates efficient maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over erasure channels. A set of algorithms, referred to as pivoting algorithms, is developed. The aim is to limit the average number of pivots (or reference variables) from which all the other erased symbols are recovered iteratively. The suggested algorithms exhibit different trade-offs between complexity of the pivoting phase and average number of pivots. Moreover, a systematic procedure to design LDPC code ensembles for efficient ML decoding is proposed. Numerical results illustrate that the designed LDPC codes achieve a near-optimum performance (very close to the Singleton bound, at least down to a codeword error rate level 10-8) with an affordable decoding complexity. For one of the presented codes and algorithms, a software implementation has been developed which is capable to provide data rates above 1.5 Gbps on a commercial computing platform.

Cooperative Performance and Diversity Gain of Wireless Relay Networks

In this paper, the error rate performance and diversity gain of amplify-and-forward (AF) wireless relay networks are studied. The distributed space-time block code (DSTBC) in a synchronous relay network with multiple relay nodes is considered. The distributed linear dispersion code is used at the relays. The symbol (or codeword) error rate is studied in terms of upper and lower bounds through rigorous derivations, and the diversity gain of the DSTBC is derived, for any number of relay nodes. As a corollary, a necessary and sufficient condition is obtained for achieving full cooperative diversity. Arbitrary coding matrices at the relays, path loss and general linear power allocation are considered. Finally, the orthogonal frequency division multiplexing (OFDM)-based space-time transmission scheme in asynchronous cooperative networks is also discussed.

Space-Time Block Code Designs Based on Quadratic Field Extension for Two-Transmitter Antennas

Space-time block code designs based on algebraic field extension for full rate, large diversity product, and nonvanishing minimum determinant of codewords have received great attention. There are many different types of codes available for two-transmitter antennas, such as cyclotomic space-time block codes, the golden space-time block code, and rotation-based space-time block codes. In this paper, a more general space-time block code design scheme, which is called quadratic space-time block coding, is proposed for the two-transmitter antennas using quadratic field extension. The optimal design of the quadratic space-time block codes in terms of a diversity product criterion is also presented. It is shown that the optimal quadratic space-time block codes designed in this paper do not belong to the existing space-time block code family such as the cyclotomic, golden, and rotation-based space-time block codes. The simulation results demonstrate that the average codeword error rate of the optimal quadratic space-time block code attains about 0.5 dB signal to noise ratio gain over those of the optimal cyclotomic and golden space-time block codes.

An Accurate Model for EESM and its Application to Analysis of CQI Feedback Schemes and Scheduling in LTE

The Effective Exponential SNR Mapping (EESM) is an indispensable tool for analyzing and simulating next generation orthogonal frequency division multiplexing (OFDM) based wireless systems. It converts the different gains of multiple subchannels, over which a codeword is transmitted, into a single effective flat-fading gain with the same codeword error rate. It facilitates link adaptation by helping each user to compute an accurate channel quality indicator (CQI), which is fed back to the base station to enable downlink rate adaptation and scheduling. However, the highly non-linear nature of EESM makes a performance analysis of adaptation and scheduling difficult; even the probability distribution of EESM is not known in closed-form. This paper shows that EESM can be accurately modeled as a lognormal random variable when the subchannel gains are Rayleigh distributed. The model is also valid when the subchannel gains are correlated in frequency or space. With some simplifying assumptions, the paper then develops a novel analysis of the performance of LTE's two CQI feedback schemes that use EESM to generate CQI. The comprehensive model and analysis quantify the joint effect of several critical components such as scheduler, multiple antenna mode, CQI feedback scheme, and EESM-based feedback averaging on the overall system throughput.

An efficient concatenated trellis code and coordinate interleaved orthogonal design for MIMO OFDM

In this paper, we propose an efficient concatenated OFDM scheme with a trellis code and a coordinate interleaved orthogonal design (TC-CIOD). We derive a pairwise TC-CIOD codeword error probability upper bound showing that full spatial and high multipath diversities are achieved. This result also shows that the TC-CIOD achieves the diversity four times higher than the best reference system with the cost of moderate increase in encoding and decoding complexities. Next, we derive the design criteria for TC-CIOD by analyzing the codeword error probability. We further use these criteria for computer based exhaustive searches to find optimum constellation rotation angle and optimum trellis codes for TC-CIOD. Finally, we present the system level simulation results showing that TC-CIOD outperforms the best reference system by 10.7, 10.2, 4.8 and 4.2 dB in signal-to-noise ratio at the codeword error rate of 10 - 3 when 4, 8, 16 and 32-state trellises are used, respectively.

Mutual‐information‐based adaptive coding and modulation in bit‐interleaved OFDM systems using punctured LDPC codes

AbstractAdaptive coding, modulation and power allocation are well‐known techniques for enhancing the performance of systems transmitting over quasi‐static fading channels. Especially their application in orthogonal frequency division multiplexing (OFDM)‐based systems promises gains in spectral efficiency. However, an open issue is the joint optimisation of code‐rate, modulation formats and power allocation if codewords are mapped onto sub‐symbols with heterogeneous channel quality and modulation formats. In this paper, we present an adaptive coding, modulation and, optionally, power allocation scheme that maximises the throughput under a codeword error rate constraint for bit‐interleaved coded OFDM systems using rate‐compatible punctured block‐circulant low‐density parity‐check codes (RCP‐BLDPC). The average mutual‐information per code bit is used as single parameter for the codeword error probability estimation. The algorithms are evaluated within the context of the OFDMA/TDMA system designed within the EU FP6 Integrated Project WINNER. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Generalized IRA Erasure Correcting Codes for Hybrid Iterative/Maximum Likelihood Decoding

The design of low-density parity-check (LDPC) codes under hybrid iterative / maximum likelihood decoding is addressed for the binary erasure channel (BEC). Specifically, we focus on generalized irregular repeat-accumulate (GeIRA) codes, which offer both efficient encoding and design flexibility. We show that properly designed GeIRA codes tightly approach the performance of an ideal maximum distance separable (MDS) code, even for short block sizes. For example, our (2048,1024) code reaches a codeword error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> at channel erasure probability isin= 0.450, where an ideal (2048,1024) MDS code would reach the same error rate at isin = 0.453.

An Efficient Differential MIMO-OFDM Scheme with Coordinate Interleaving

We propose a concatenated trellis code (TC) and coordinate interleaved differential space-time block code (STBC) for OFDM. The coordinate interleaver, provides signal space diversity and improves the codeword error rate (CER) performance of the system in wideband channels. Coordinate interleaved differential space-time block codes are proposed and used in the concatenated scheme, TC design criteria are derived, and the CER performances of the proposed system are compared with existing concatenated TC and differential STBC. The comparison showed that the proposed scheme has superior diversity gain and improved CER performance.

Linear-Programming Decoding of Nonbinary Linear Codes

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the 'maximum-likelihood certificate' property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. Two alternative polytopes for use with linear-programming decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These polytope representations lead to polynomial-time decoders for a wide variety of classical nonbinary linear codes. LP decoding performance is illustrated for the [11,6] ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the performance of the LP decoder is comparable to codeword-error-rate-optimum hard-decision based decoding. LP decoding is also simulated for medium-length ternary and quaternary LDPC codes with corresponding PSK modulations over AWGN.

Super-orthogonal space-time-frequency trellis coded OFDM

Super-orthogonal space-time trellis codes (SOSTTCs) given in the literature are full rate and provide full spatial diversity with high coding gain in narrowband quasistatic fading channels. The high number of parallel transitions in their trellis structure restricts their performance in wideband channels where the code performance suffers from multipath. Code design criteria are derived and a computer search based method is proposed to design full-rate optimised SOSTTCs exploiting full spatial and multipath diversity for multiple-input multiple-output orthogonal frequency division multiplexing systems. The proposed codes have codewords defined in space, time, and frequency. We evaluate the codeword error rates of the new 16, 32 and 64-state super-orthogonal space-time-frequency trellis codes for quadrature phase shift keying by computer simulation and show that they provide significant error performance improvement compared to their counterparts with equivalent delay length.

Coding Performance of Hybrid ARQ Schemes

We develop a unified performance metric and detailed analysis for hybrid automatic repeat request (HARQ) schemes based on incremental redundancy (IR) and Chase combining (CC). The general result is applicable to both symbol-based and bit-interleaved coded modulations, to HARQ processes based on rateless and fixed-rate mother codes, and IR schemes with and without a self-decodability restriction. The analysis shows that IR over CC coding gains tend to increase with the initial coding rate, but decrease with the signal-to-noise (SNR) variation between retransmissions. The gains can also be diminished when a fixed-rate mother code is used or when the self-decodability criterion is imposed. The theoretical prediction is compared with observed gains at 10% codeword error rates based on turbo-coding simulations. For scenarios with moderately varying SNR between retransmissions, the analytical model tracks actual simulation results very well. However, when the SNR varies widely and the systematic part of the turbo codeword is effectively erased, the CC scheme could, in fact, outperform some IR schemes. For these scenarios, which can be induced by fast time-varying fading or long retransmission delays, the self-decodable IR and the CC schemes prove to be more robust without much performance comprise. Finally, we discuss adaptive improvement to the conventional IR schemes based on the analytical result

A new LDPC decoding algorithm aided by segmented cyclic redundancy checks for magnetic recording channels

We introduce a new low-density parity-check (LDPC) decoding algorithm that exploits the cyclic redundancy check (CRC) information of data segments. By using the error detection property of the CRC, we can successively decode data segments of a codeword corrupted by random errors and erasures. The key idea is that the messages from the variable nodes with correct checksum are fixed to deterministic log likelihood ratio values during LDPC iterative decoding. This approach improves the decoding speed and codeword error rate without significant modification of the LDPC decoding structure. Moreover, the CRC is also used for an early stopping criterion of LDPC decoding. Simulation results verify our claims.

Low-Complexity Channel-Adapted Space-Time Coding Scheme for Frequency-Selective Wireless MIMO Channels

By exploiting the wireless multiple-input multiple-output (MIMO) channel structure, a brand new space-time code design criterion is derived. Based on the new criterion, we propose one low-complexity channel-adapted space-time (CAST) coding scheme, where trade-offs among codeword error rate, data throughput, and computational complexity are very flexible. Simulation results confirm that, in the frequency-selective MIMO channels, the CAST coding scheme can perform significantly better than the existing space-time codes, e.g., Alamouti space-time orthogonal code.

Fundamentals of dynamic frequency hopping in cellular systems

We examine techniques for increasing spectral efficiency of cellular systems by using slow frequency hopping (FH) with dynamic frequency-hop (DFH) pattern adaptation. We first present analytical results illustrating the improvements in frequency outage probabilities obtained by DFH in comparison with random frequency hopping (RFH). Next, we show simulation results comparing the performance of various DFH and RFH techniques. System performance is expressed by cumulative distribution functions of codeword error rates. Systems that we study incorporate channel coding, interleaving, antenna diversity, and power control. Analysis and simulations consider the effects of path loss, shadowing, Rayleigh fading, cochannel interference, coherence bandwidth, voice activity, and occupancy. The results indicate that systems using DFH can support substantially more users than systems using RFH.

Collaborative coding and decoding techniques for multiple access channel

It is highly desirable to use simple and effective multiple access coding and decoding techniques which are capable of multiple access function and error control. The collaborative coding multiple access (CCMA) techniques potentially permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time, frequency or orthogonal codes. The authors investigate the performance of uniquely decodable CCMA schemes employing hard decision and maximum likelihood decoding techniques. A low complexity maximum likelihood decoding technique is presented. The reliability performance of various coding schemes employing these decoding techniques are carried out in the presence of AWGN conditions. The simulation results are presented in the form of symbol and codeword error rates as a function of signal to noise ratios. It is shown that uniquely decodable CCMA schemes permit the multiple access function to be combined with that of forward error correction.

Forward error correction for an atmospheric noise channel

Models for predicting the performance of error correcting codes on an atmospheric noise channel are presented and verified. Two Markov chains are used to model the memory of the atmospheric noise channel. The transition probabilities for these chains are derived from atmospheric noise error processes which were recorded at 306 kHz. The models are used to estimate the probability of codeword error, and these estimates are compared to codeword error rates which are obtained directly from the recorded error processes. The comparisons are made for the Golay code with a variety of bit interleaving depths, and a Reed-Solomon code with a variety of symbol interleaving depths. Both Markov channel models predict the actual performance of the codes with much greater accuracy than the binary symmetric channel. Results for binary convolutional codes are presented. >