Axel Huebner

Irregular turbo codes and unequal error protection

Turbo codes (TC) with unequal error protection (UEP) are introduced. We consider a serial cascade of an array of repetition codes, an interleaver, and a TC. Such a coding scheme was introduced by B.J. Frey and D.J.C. MacKay (1999) as an irregular turbo code (ITC). A lower bound on the protection level of the ITC is presented. Additionally, simulation results are shown.

On Space-Frequency Coding Using Cyclic Delay Diversity for OFDM Based Transmission Systems

We present a space-frequency coding scheme using cyclic delay diversity (CDD) for an orthogonal frequency division multiplexing (OFDM)-based transmission system. CDD is a simple multiple transmit antenna approach for increasing the frequency selectivity of the channel seen at a single antenna receiver. This is due to the insertion of virtual echoes caused by antenna specific cyclic delays in the time domain at the transmitter. On each antenna a shifted version of the signal is sent, with these shifts being performed in the frequency domain. This allows the receiver to apply optimum demodulation, and thus exploit the diversity introduced by CDD. We optimize the selection of the time domain cyclic delays in the CDD so as to get full spatial diversity with the proposed space-frequency codes with CDD (SFC-CDDs) scheme. Moreover, we show simulation results for SFC-CDD, which confirm theoretical results with respect to the achieved spatial diversity, and present a comparison with the well-known Alamouti scheme implemented as SFC.

On permutor designs based on cycles for serially concatenated convolutional codes

A new permutor design for serially concatenated convolutional codes is presented. It is based on the construction of a permutation matrix without short cycles of special types. For such a permutor, we give a lower bound on the minimum distance of the overall code that is significantly larger than that achievable with first-order separation (spreading factors). Additionally, the minimum distance can be attuned to the permutation length. This property may be useful for the construction of codes with moderate block lengths.

On the design of woven convolutional encoders with outer warp row permutors

In this paper, permutor design aspects for woven convolutional encoders (WCEs) with outer warp (OW) are discussed. We show how the minimum distance of the overall code can be increased by considering all warp permutors together. A bound on the minimum distance of a code generated by a WCE with OW and designed permutors is presented that considerably exceeds those with known designs.

On permutations with second order separations between cascaded convolutional encoders

A new set of permutation parameters is introduced. It is called the set of second order separations and is a generalization of the well-known symbol separation. A construction method is presented that allows us to generate permutors with large second order separations. Additionally, we derive a lower bound on the minimum distance of serially concatenated codes with a permutation of sufficiently large second order separations.

Laminated Turbo Codes: A New Class of Block-Convolutional Codes

In this paper, a new class of codes is presented that features a block-convolutional structure-namely, laminated turbo codes. It allows combining the advantages of both a convolutional encoder memory and a block permutor, thus allowing a block-oriented decoding method. Structural properties of laminated turbo codes are analyzed and upper and lower bounds on free distance are obtained. It is then shown that the performance of laminated turbo codes compares favorably with that of turbo codes. Finally, we show that laminated turbo codes provide high rate flexibility without suffering any significant performance degradation.

A new cycle-based joint permutor design for multiple turbo codes

In this letter, a permutor design parameter, called the weight of a cycle through J-1 permutation matrices, for multiple turbo codes is introduced. Analogously to the single-permutor case of conventional turbo codes, we show the connection of the new parameter to the minimum distance of special classes of multiple turbo codes. In addition, simulation results are presented for multiple turbo codes based on the new design

A simple method of approximating the error floor of turbo codes with S-type permutors

An efficient method for calculating some of the first coefficients of the distance spectrum of turbo codes is presented. It is based on the evaluation of cycles in the permutation matrix that are of a special type. For S-type permutors, the calculated coefficients in the distance spectrum include the minimum distance and other low weight terms. Therefore, by applying the union bound, this method is capable of giving a very tight approximation to the error floor behavior of the corresponding turbo code - even for large permutor sizes.

On higher order permutors for serially concatenated convolutional codes

A new parameter set for designing permutors is introduced. It is called the set of higher order separations and can be considered as a generalization of the well-known symbol separation (spreading factor). The respective permutor is called a higher order permutor and we show how such a permutor can be constructed. For a second-order permutor in a serially concatenated convolutional encoding scheme we give a lower bound on the minimum distance of the resulting overall code. The integers that determine the sufficiently large separations, i.e., the smallest separations for which the distance properties can be guaranteed, are derived from the active distances of the convolutional component encoders. Additionally, a growth rate of the minimum distance like O((dfree o)lfloorrho/2rfloor+1) is proved for serially concatenated convolutional encoders with permutors having large separations of order rho

On cycle-based permutor designs for serially concatenated convolutional codes

A permutor design for serially concatenated convolutional codes is presented. It is based on the construction of a permutation matrix without short cycles of special types. For a serially concatenated convolutional code with such a permutor a lower bound on the minimum distance is given that conspicuously exceeds that achievable with first order separation. Additionally, the minimum distance can be attuned with the permutation length.