Effective Code Length Research Articles

A coded beamforming scheme for frequency-flat MIMO fading channels

In this paper, a coded beamforming scheme is considered for frequency-flat multiple-input-multiple-output (MIMO) fading channels. With channel state information (CSI) available at the transmitter, this scheme combines coded modulation (CM) with downlink transmission beamforming to exploit both diversity and coding advantages. In order to identify the appropriate code design criteria, the exact pairwise error probability and bit error rate upper bounds are derived for both frequency-flat slow and fast MIMO Rayleigh fading channels. It is shown that the minimum squared Euclidean distance of the code should be maximised in slow-fading channels, whereas the minimum effective code length and the product distances should be maximised in fast-fading scenarios. This conclusion indicates that the conventional Ungerboeck's trellis-coded modulation codes originally designed for additive white Gaussian noise channels and single-antenna Rayleigh fading channels could be directly utilised in the proposed scheme for slow and fast MIMO fading channels, respectively. This eliminates the need for complicated code design. Simulation results are provided to substantiate the theoretical analysis. For an example, it is demonstrated that a trellis-coded beamforming scheme can outperform the published space-time trellis coded beamforming schemes by up to 4 dB, although it has a simpler encoder structure and requires no specific code design. Interference free is assumed in the analysis, while the impact of the imperfect CSI and antenna correlation on the system error performance is evaluated.

Analysis and Design Criteria for Trellis-Coded Modulation With Differential Space-Time Transmit Diversity

In this letter, concatenation of trellis-coded modulation (TCM) with differential space-time block codes (DSTBC) is considered under frequency-flat Rayleigh-fading channels with and without perfect interleaver. It is shown that the design criteria of TCM concatenated with DSTBC are exactly the same as that of TCM concatenated with space-time block codes (STBC) in perfectly known channels. They are effective code length over span two symbol intervals and minimum product-sum distance over span two symbol intervals. Based on the design criteria, several new rate-2/3 systematic Ungerboeck's TCM schemes have been found by computer search. They outperform existing optimal TCM schemes designed for additive white Gaussian noise or flat fading channels.

Analysis of multidimensional trellis-coded MPSK in Rice-lognormal fading channels

The paper addresses the analysis of multidimensional trellis-coded M-ary phase shift keying (MPSK) modulation over a Rice-lognormal fading channel model, applicable to a variety of environments and to both terrestrial and satellite mobile communications. Bounds to the bit error probability are derived and applied to the analysis of a few selected trellis-coded modulation (TCM) schemes. The results, confirmed by simulation, show that on the Rice channel there exists a threshold in bit energy-to-noise density ratio above which the effective code length is the dominant parameter, while the free distance is dominating below. However, the influence of both parameters is mitigated when shadowing is present.

Multidimensional M-PSK trellis codes for fading channels

This paper investigates the code search problem for trellis-coded multidimensional phase modulation for Rayleigh fading channels. New set partitionings for multiple phase-shift keying (M-PSK) are proposed using the effective code length (ECL) and the minimum product distance (PD) as the code design criteria. By using these set-partitionings rules, new multidimensional codes which are optimum for Rayleigh fading channels are constructed. The proposed codes compare favorably with the existing multidimensional trellis codes on fading channels in terms of bit error performance. The bit error performance is evaluated by simulation.

Construction of new MPSK trellis codes for fading channels

In this paper, a new methodology for design of MPSK trellis codes on fading channels is proposed. The proposed design criteria, based on effective code length, the minimum product distance and the minimum Euclidean distance are used to construct new 8-PSK and 16-PSK trellis codes with improved bit error rate performance on fading channels. The code performance is evaluated analytically and by Monte Carlo simulation. The results show that the proposed codes achieve significant improvements relative to the best known codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance off 8-PSK trellis codes over nonlinear fading mobile satellite channels

In this paper a new analytical bound for large effective code length codes (ECL) is derived. The accuracy of the analytical bounds is validated by simulation. Based on the new bound a trellis code design procedure for fading channels is defined. A quasi-analytical technique for BER estimation on nonlinear channels is proposed. This method is used to estimate the performance degradation of nonlinear communication systems with the pilot tone.

New 16-QAM trellis codes for fading channels

Growth in communications leads to increasing requirements for high data rate transmission that can be met by band-width efficient modulation schemes. In this Letter, the TCM code design criteria based on effective code length (ECL) and product distance (PD) as well as Euclidean distance (ED) are used to construct new 16-QAM trellis codes with improved error rate. The performance of 16-QAM TCM schemes with ideal channel state information (CSI) on Rayleigh fading channels is evaluated by simulation. The results show that the proposed codes achieve significant improvements relative to the best known 16-QAM modulation codes.

Concatenated combined modulation and coding of frequency hopping multiaccess systems

A spread-spectrum system that does not have a separate state for initial code acquisition is presented. A uniform random variate selects one of several Gold codes for transmission, thus removing the notion of pseudorandom codes from spread-spectrum systems, making the effective code length infinite, and leading to acquisitionless systems. Because coding is critical to the proposed multiaccess frequency-hopping (FH) system, more powerful codes are needed. The performance of the proposed multiaccess system using the combined modulation and coding technique (trellis) concatenated with Reed-Solomon codes in partial-band jamming is investigated. The FH multiaccess performance of noncoherent soft detection of MFSK in association with trellis coding is introduced and the performance compared to that using RS outer/RS inner concatenated codes. >

Bandwidth efficient block codes for Rayleigh fading channels

It is shown that the effective code length (ECL) of a short ECL block modulation code (BCM) is the dominant factor in its performance over a Rayleigh fading channel. To demonstrate this, three new BCM codes are presented as examples. Their performances are evaluated and compared on both Gaussian and fading channels.