Joachim Hagenauer

Rate-compatible punctured convolutional codes (RCPC codes) and their applications

The concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P+l), where l can be varied between 1 and (N-1)P. A rate-compatibility restriction on the puncturing tables ensures that all code bits of high rate codes are used by the lower-rate codes. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame. Families of RCPC codes with rates between 8/9 and 1/4 are given for memories M from 3 to 6 (8 to 64 trellis states) together with the relevant distance spectra. These codes are almost as good as the best known general convolutional codes of the respective rates. It is shown that the same Viterbi decoder can be used for all RCPC codes of the same M. the application of RCPC codes to hybrid ARQ/FEC schemes is discussed for Gaussian and Rayleigh fading channels using channel-state information to optimise throughput. >

A Viterbi algorithm with soft-decision outputs and its applications

The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated.<<ETX>>

Applications of error-control coding

An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video transmission. Examples, both historical and current, are given that typify the different approaches used in each application area. Although no attempt is made to be comprehensive in the coverage, the examples chosen clearly illustrate the richness, variety, and importance of error-control coding methods in modern digital applications.

Optimization of symbol mappings for bit-interleaved coded Modulation with iterative decoding

We investigate bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth efficient transmission, where the bit error rate is reduced through iterations between a multilevel demapper and a simple channel decoder. In order to achieve a significant turbo-gain, the assignment strategy of the binary indices to signal points is crucial. We address the problem of finding the most suitable index assignments to arbitrary, high order signal constellations. A new method based on the binary switching algorithm is proposed that finds optimized mappings outperforming previously known ones.

Iterative Network and Channel Decoding for the Two-Way Relay Channel

We introduce an extension of the relay channel that we call two-way relay channel. The two-way relay channel consists of two users which want to communicate to each other with the help of one relay. We consider the time-division two-way relay channel without power control, where the broadcast channels are orthogonalized in time and where the two users and the relay use the same transmission power. We describe a joint network-channel coding method for this channel model, where channel codes are used at both users and a network code is used at the relay. The channel code of one user and the network code form a distributed turbo code which we call turbo network code and which can be iteratively decoded at the other user. Moreover, we conjecture closed expressions for lower bounds for the channel capacities of the time-division relay and two-way relay channel without power control and deliver simulation results of the proposed turbo network code.

The performance of rate-compatible punctured convolutional codes for digital mobile radio

The unequal error protection capabilities of convolutional codes belonging to the family of rate-compatible punctured convolutional codes (RCPC codes) are studied. The performance of these codes is analyzed and simulated for the first fading Rice and Rayleigh channels with differentially coherent four-phase modulation (4-DPSK). To mitigate the effect of fading, interleavers are designed for these unequal error protection codes, with the interleaving performed over one or two blocks of 256 channel bits. These codes are decoded by means of the Viterbi algorithm using both soft symbol decisions and channel state information. For reference, the performance of these codes on a Gaussian channel with coherent binary phase-shift keying (2-CPSK) is presented. A number of examples are provided to show that it is possible to accommodate widely different error protection levels within short information blocks. Unequal error protection codes for a subband speech coder are studied in detail. A detailed study of the effect of the code and channel parameters such as the encoder memory, the code rate, interleaver depth, fading bandwidth, and the contrasting performance of hard and soft decisions on the received symbols is provided. >

On the equivalence between SOVA and max-log-MAP decodings

It is shown that after a proper simple modification, the soft-output Viterbi algorithm (SOVA) proposed by Hagenauer and Hoeher (1989) becomes equivalent to the max-log-maximum a posteriori (MAP) decoding algorithm. Consequently, this modified SOVA allows to implement the max-log-MAP decoding algorithm by simply adjusting the conventional Viterbi algorithm. Hence, it provides an attractive solution to achieve low-complexity near-optimum soft-input soft-output decoding.

Separable MAP "filters" for the decoding of product and concatenated codes

Very efficient signaling in radio channels requires the design of very powerful codes having special structure suitable for practical decoding schemes. Powerful codes are obtained by using simple block codes to construct multidimensional product codes. The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a posteriori filters, is described. Simulation results are presented for three-dimensional product codes constructed with the (16,11) extended Hamming code. The extension of the concept to concatenated convolutional codes is given and some simulation results are presented. Potential applications are briefly discussed.<<ETX>>

Subband speech coding and matched convolutional channel coding for mobile radio channels

The effects of digital transmission errors on a family of variable-rate embedded subband speech coders (SBC) are analyzed in detail. It is shown that there is a difference in error sensitivity of four orders of magnitude between the most and the least sensitive bits of the speech coder. As a result, a family of rate-compatible punctured convolutional codes with flexible unequal error protection capabilities have been matched to the speech coder. These codes are optimally decoded with the Viterbi algorithm. Among the results, analysis and informal listening tests show that with a 4-level unequal error protection scheme transmission of 12 kb/s speech is possible with very little degradation in quality over a 16 kb/s channel with an average bit error rate (BER) of 2*10/sup -2/ at a vehicle speed of 60 m.p.h. and with interleaving over two 16 ms speech frames. >

On variable length codes for iterative source/channel decoding

We focus on a trellis-based decoding technique for variable length codes (VLCs) which does not require any additional side information besides the number of bits in the coded sequence. A bit-level soft-in/soft-out decoder based on this trellis is used as an outer component decoder in an iterative decoding scheme for a serially concatenated source/channel coding system. In contrast to previous approaches using this kind of trellis we do not consider the received sequence as a concatenation of variable length codewords, but as one long code word of a (weak) binary channel code which can be soft-in/soft-out decoded. By evaluating the distance properties of selected variable length codes we show that some codes are more suitable for trellis-based decoding than others. Finally we present simulation results which show the performance of the iterative decoding approach.