The performance of either structured or random turbo-block codes and binary, systematic block codes operating over the additive white Gaussian noise (AWGN) channel, is assessed by upper bounds on the error probabilities of maximum likelihood (ML) decoding. These bounds on the block and bit error probability which depend respectively on the distance spectrum and the input-output weight enumerati...

In the matter of channel coding and spectral efficiency, up to invention turbo codes, 3 dB or more stood between what theory promised real systems were able offer. This gap has now been removed, allowing communication be designed with quasi-optimum performance. Ten years after first publication on this new technique, codes have commenced their practical service.

In this paper we introduce the iterative decoding principle, “the turbo principle”, for the bidimensional Turbo Product Codes (TPC’s). The constituent codes used for encoding on rows and columns are two concatenated (7,4) Hamming block codes. Several Soft Input Soft Output (SISO) algorithms can be used for the iterative decoding process. At each iteration, the two decoders decode all rows, then...

This paper describes an application of turbo codes in conjunction with 16QAM in high speed mobile satellite communications. The channel characteristics, the architecture of the modem and the performance curves for the selected turbo codes are presented.

A statistical theory of turbo-codes, treated as a special family of convolutional codes with a low-density parity-check matrix, is developed. The basic ideas are: the representation of the transposed parity-check matrix of turbo-codes as a product of a sparse (multiple) scrambler matrix and the transposed parity-check matrix of the basic code, the introduction of a special statistical ensemble ...

A full-parallel architecture for turbo decoding, which achieves ultrahigh data rates when using product codes as error correcting codes, is proposed. This architecture is able to decode product codes using binary BCH or m-ary Reed-Solomon component codes. The major advantage of our architecture is that it enables the memory blocks between all half-iterations to be removed. Moreover, the latency...

Bandwidth efficient coding schemes employing bit interleaved coded modulation and low complexity multiple turbo codes are investigated. The BER performance of these designs is shown to be superior to bit interleaved coded modulation schemes using conventional turbo codes.

Recently a coding scheme, termed turbo-codes was proposed, which achieves results very close to the Shannon-limit. The encoding and decoding of turbo-codes is reviewed. In particular, a comparison of the current methods used for terminating the trellis of the turbo-code are described. A novel approach to termination of the code is introduced which removes the need to transmit tail bits across t...

Turbo-decoding of nonbinary codes Jens Berkmann and Frank Burkert Dept. of Communications Engineering, Technical University of Munich Arcisstr. 21, 80290 Munich, Germany Email [email protected] Abstract | It is shown how parallel concatenation of nonbinary codes can be put into the same framework of iterative decoding as in the binary case. The turbocode(turbo-decoding-) idea is...

Low rate convolutional and turbo codes that output non-linear cyclic (NLC) codewords of length n1⁄4 2, m being a positive integer, are described. These codes have a very low coding rate, which makes them especially suitable for spread spectrum systems where they can be used for simultaneously achieving error correction and bandwidth expansion. Due to the cyclic properties and codeword length of...