A Better Understanding of the Performance of Rate-1/2 Binary Turbo Codes that Use Odd-Even Interleavers

The effects of the odd-even constraint - as an interleaver design criterion - on the performance of rate-1/2 binary turbo codes are revisited. According to the current understanding, its adoption is favored because it makes the information bits be uniformly protected, each one by its own parity bit. In this paper, we provide instances that contradict this point of view suggesting for a different explanation of the constraint's behavior, in terms of distance spectrum

Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and $C$-symmetric, and make a connection to finite graph covers of the 3D-TC factor graph. This connection is used to show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a finite-length minimum pseudoweight analysis for small cover degrees. Also, an explicit description of the fundamental cone of the 3D-TC polytope is given. Finally, we present an extensive numerical study of small-to-medium block length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the minimum distance $d_{\rm min}$ and/or the stopping distance $h_{\rm min}$ is high, the minimum pseudoweight (on the additive white Gaussian noise channel) is strictly smaller than both the $d_{\rm min}$ and the $h_{\rm min}$, and 2) the minimum pseudoweight grows with the block length, at least for small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication

Iterative channel equalization, channel decoding and source decoding

The performance of soft source decoding is evaluated over dispersive AWGN channels. By employing source codes having error-correcting capabilities, such as Reversible Variable-Length Codes (RVLCs) and Variable-Length Error-Correcting (VLEC) codes, the softin/soft-out (SISO) source decoder benefits from exchanging information with the MAP equalizer, and effectively eliminates the inter-symbol interference (ISI) after a few iterations. It was also found that the soft source decoder is capable of significantly improving the attainable performance of the turbo receiver provided that channel equalization, channel decoding and source decoding are carried out jointly and iteratively. At SER = 10-4, the performance of this three-component turbo receiver is about 2 dB better in comparison to the benchmark scheme carrying out channel equalization and channel decoding jointly, but source decoding separately. At this SER value, the performance of the proposed scheme is about 1 dB worse than that of the ½-rate convolutional coded non-dispersive AWGN channel.<br/

Hybrid concatenated codes and iterative decoding

Several improved turbo code apparatuses and methods. The invention encompasses several classes: (1) A data source is applied to two or more encoders with an interleaver between the source and each of the second and subsequent encoders. Each encoder outputs a code element which may be transmitted or stored. A parallel decoder provides the ability to decode the code elements to derive the original source information d without use of a received data signal corresponding to d. The output may be coupled to a multilevel trellis-coded modulator (TCM). (2) A data source d is applied to two or more encoders with an interleaver between the source and each of the second and subsequent encoders. Each of the encoders outputs a code element. In addition, the original data source d is output from the encoder. All of the output elements are coupled to a TCM. (3) At least two data sources are applied to two or more encoders with an interleaver between each source and each of the second and subsequent encoders. The output may be coupled to a TCM. (4) At least two data sources are applied to two or more encoders with at least two interleavers between each source and each of the second and subsequent encoders. (5) At least one data source is applied to one or more serially linked encoders through at least one interleaver. The output may be coupled to a TCM. The invention includes a novel way of terminating a turbo coder