Length-compatible polar codes are a class of polar codes which can support a wide range of lengths with a single pair of encoder and decoder. In this paper we propose a method to construct length-compatible polar codes by employing the reduction of the 2n× 2npolarizing matrix proposed by Arikan. The conditions under which a reduced matrix becomes a polarizing matrix supporting a polar code of a given length are first analyzed. Based on these conditions, length-compatible polar codes are constructed in a suboptimal way by codeword-puncturing and information-refreezing processes. They have low encoding and decoding complexity since they can be encoded and decoded in a similar way as a polar code of length 2n. Numerical results show that length-compatible polar codes designed by the proposed method provide a performance gain of about 1.0 - 5.0 dB over those obtained by random puncturing when successive cancellation decoding is employed.

The diversity-multiplexing tradeoff (DMT) of a multiple-input multiple-output (MIMO) multiple-access system is analyzed, where a successive cancellation (SC) receiver is employed. In order to analyze the asymptotic performance of each user in a practical MIMO multiple-access system, we derive the per-user DMT considering error propagation due to imperfect cancellation of the SC process. The diversity gain of each user is shown to be expressed as a simple function of the multiplexing gains of the previously detected users as well as its own multiplexing gain. Also, we show that the diversity gain of each user who suffers from error propagation is strictly smaller than that under the assumption of perfect cancellation in a range of multiplexing gains of the users. Numerical results show that our DMT analysis matches well with the performance of practical multiple-access systems.

Bounds on the diversity-multiplexing tradeoff (DMT) curves of the Bell labs layered space-time (BLAST) architecture are analyzed, where zero-forcing successive interference cancellation (ZF-SIC) receivers are employed. The DMT curve in the presence of error propagation caused by SIC process is derived under the assumption that each transmit antenna employs Gaussian random coding and the interference caused by detection errors has Gaussian distribution. This result can provide a lower bound on that of the ZF-SIC receiver with error propagation.

In this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in Bell labs layered space-time (BLAST) architectures employing successive decoding and interference cancellation. We then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of BLAST architectures. Since the methods are developed by using ergodic capacity and outage capacity functions of the layers, the allocated rates and powers depend only on a given channel statistic. Finally, we prove that the rate allocation yields a better asymptotic performance than the power allocation. Numerical results show that BLAST architectures with the rate and power allocation perform better by 4 dB and 3 dB, respectively, than a BLAST architecture with the same rate and power in all layers.

Group layered multi-antenna architectures (GLAs) employing orthogonal space-time block codes and spatial multiplexing techniques may simultaneously exploit diversity and multiplexing gains with simple decoding algorithms based on successive interference cancellation (SIC). In this paper we first describe a decoding method of a SIC receiver based on QR decomposition in a GLA using LDPC codes, and then find a combination of code rate and modulation order which optimizes the asymptotic performance of the GLA. Simulation results show that the performance of the GLA using code rates and modulation orders found by our method is better by 2 dB than that of a GLA using the same code rate and modulation order in all layers. Our optimization method can be applied to adaptive modulation and coding schemes for GLAs.

In this paper we derive the symbol error rate (SER) of the vertical Bell laboratories layered space-time (V-BLAST) detection algorithm based on zero-forcing successive interference cancellation (ZF-SIC) over an independent and identically distributed Rayleigh flat fading channel. By introducing the concepts of "event" and "state" related to error propagation, we evaluate the effect of error propagation and calculate the exact SER of each layer in a simple way. Compared with the pre-existing results, our approach can offer the closed-form expression of the SER of arbitrary quadrature-amplitude modulation (QAM) for an arbitrary number of transmit and receiver antennas. Furthermore, our analysis matches very well with Monte Carlo simulation results.