The design of double serially concatenated convolutional codes with S-type permutors, i.e., permutors that provide a nontrivial separation, is considered. Based on a newly introduced parameter, namely, the so-called symbol span, a joint design of the outer and inner permutor is presented and its impact on the minimum distance of the overall code is analyzed. It is shown that a lower bound on the minimum distance that is given by the product of the free distances of all three component codes can be guaranteed. Design tables and simulation results are presented that include comparisons with single serially concatenated convolutional codes. In addition, a comparison with double/generalized repeat accumulate codes is briefly sketched.

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.

The free distance of convolutional codes is the most important parameter determining their performance under good channel conditions. In this paper, we investigate the free distance properties of turbo-like codes generated by non-terminated convolutional encoders and convolutional permutors. In particular, we prove the existence of such codes whose free distance exhibits the same asymptotic growth rate in the permuter memory as block turbo codes in the permuter size

In this paper we address the extrinsic information transfer functions of inner decoders for a serially concatenated coding scheme. For the case of an AWGN channel, we give a universal proof for the fact that only inner encoders yielding an infinite output weight for a weight-one input sequence, such as recursive convolutional encoders, lead to perfect extrinsic information at the output of the corresponding SISO decoder. As an example we consider bit-interleaved coded modulation with iterative demapping (BICM-ID) and insert an additional recursive precoder prior to the mapping operation. Simulation results show that the proposed system does not suffer from an error floor and thus significantly outperforms BICM-ID systems that solely use mappings as inner encodings, even when they are optimized

In this paper the impact of S-type permutors, i.e., permutors that provide a non-trivial separation, on the minimum distance of double serially concatenated convolutional codes is considered. A joint design of the outer and inner permutor is presented on the basis of a newly introduced permutor parameter - the so-called symbol span. This design guarantees that the minimum distance of the overall code is lower bounded by the product of the free distances of all three component codes. Simulation results are presented and comparisons with single serially concatenated and double/generalized repeat accumulate codes are briefly sketched.

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.

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 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((dfreeo)lfloorrho/2rfloor+1) is proved for serially concatenated convolutional encoders with permutors having large separations of order rho

In this paper we introduce a new coding scheme - so-called laminated turbo codes. It is characterized by a block-convolutional structure that enables us to combine the advantages of a convolutional encoder memory and a block-oriented decoding method. We show that this block-convolutional structure is superior in terms of its error correction capability compared to the pure block structure of the corresponding self-concatenated code. Comparisons to turbo codes and multiple turbo codes are also included. Finally, the impact of the inter-block memory is investigated.

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.

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.