## A Circuit-Based Interpretation of Analog MAP Decoding with Binary Trellises (2000)

Venue: | Proc. 3rd ITG Conference Source and Channel Coding, Munchen |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Hagenauer00acircuit-based,

author = {Joachim Hagenauer and Matthias Mörz and Elke Offer},

title = {A Circuit-Based Interpretation of Analog MAP Decoding with Binary Trellises},

booktitle = {Proc. 3rd ITG Conference Source and Channel Coding, Munchen},

year = {2000},

pages = {175--180}

}

### OpenURL

### Abstract

The maximum a posteriori (MAP) decoding algorithm for convolutional codes is reformulated in terms of probabilities and log-likelihood ratios. This is shown to be a precise circuit description of an analog decoder in terms of currents and voltages which inspires different circuit designs. I. INTRODUCTION Recently several proposals for analog decoders were made in [1], [2], [3], [4], [5], which is in contrast to common practice where decoding is performed by digital processors. The implementation of `soft-in/soft-out' decoders which accept soft input from the demodulator and deliver soft output for the information bits require that soft values are processed throughout the decoder [6]. Such decoders are useful for serial or parallel concatenated decoding schemes, e.g., `turbo'-decoding. In the digital domain the soft values are represented by a hard decision for the corresponding bit combined with additional quantized reliability information about the decision. Especially in combination...

### Citations

1201 |
Optimal decoding of linear codes for minimizing symbol error rate
- Bahl, Cocke, et al.
- 1974
(Show Context)
Citation Context ...esult. The speed of such networks is only limited by parasitic resistor and capacitor values of integrated circuits. The symbol-by-symbol maximum a posteriori (MAP) decoding algorithm as presented in =-=[8]-=- requires multiplications of probabilities and probability densities, respectively. Moreover summations of the resulting products are performed. We reformulate this so called BCJR or Bahl-algorithm by... |

456 | Papke L, “Iterative decoding of binary block and convolutional codes
- Hagenauer, Offer
- 1996
(Show Context)
Citation Context ...plementation of `soft-in/soft-out' decoders which accept soft input from the demodulator and deliver soft output for the information bits require that soft values are processed throughout the decoder =-=[6]-=-. Such decoders are useful for serial or parallel concatenated decoding schemes, e.g., `turbo'-decoding. In the digital domain the soft values are represented by a hard decision for the corresponding ... |

57 |
A precise four-quadrant multiplier with subnanosecond response
- Gilbert
- 1968
(Show Context)
Citation Context ...ential input voltages. For the very restricted input voltage range where these voltages are much less than V T one can use the linear approximation of the hyperbolic tangent to build a multiplier. In =-=[10]-=- an extension of the cell was introduced resulting in a linear and temperature independent four-quadrant multiplier. In contrast to this we use the characteristic non-linear function of the basic Gilb... |

43 |
Tailbiting map decoders
- Anderson, Hladik
- 1998
(Show Context)
Citation Context ...e the decoding algorithm can be implemented by using analog and highly parallel networks which are operating in continuous time. Iterative decoding algorithms or the tail-biting wrap around algorithm =-=[7]-=- are naturally carried out in analog networks with feedback. There is no discrete timing and no iteration. The soft values from the channel are used to load the decoding network which then floats free... |

27 |
The analog decoder
- Hagenauer, Winkelhofer
- 1998
(Show Context)
Citation Context ...e circuit description of an analog decoder in terms of currents and voltages which inspires different circuit designs. I. INTRODUCTION Recently several proposals for analog decoders were made in [1], =-=[2]-=-, [3], [4], [5], which is in contrast to common practice where decoding is performed by digital processors. The implementation of `soft-in/soft-out' decoders which accept soft input from the demodulat... |

21 | Decoding and equalization with analog nonlinear networks
- Hagenauer, Offer, et al.
- 1999
(Show Context)
Citation Context ...iption of an analog decoder in terms of currents and voltages which inspires different circuit designs. I. INTRODUCTION Recently several proposals for analog decoders were made in [1], [2], [3], [4], =-=[5]-=-, which is in contrast to common practice where decoding is performed by digital processors. The implementation of `soft-in/soft-out' decoders which accept soft input from the demodulator and deliver ... |

14 | BiCMOS circuits for analog Viterbi decoders
- Shakiba, Johns, et al.
- 1998
(Show Context)
Citation Context ...cuit description of an analog decoder in terms of currents and voltages which inspires different circuit designs. I. INTRODUCTION Recently several proposals for analog decoders were made in [1], [2], =-=[3]-=-, [4], [5], which is in contrast to common practice where decoding is performed by digital processors. The implementation of `soft-in/soft-out' decoders which accept soft input from the demodulator an... |

7 |
Iterative sum-product decoding with analog VLSI
- Loeliger, Helfenstein, et al.
- 1998
(Show Context)
Citation Context ...recise circuit description of an analog decoder in terms of currents and voltages which inspires different circuit designs. I. INTRODUCTION Recently several proposals for analog decoders were made in =-=[1]-=-, [2], [3], [4], [5], which is in contrast to common practice where decoding is performed by digital processors. The implementation of `soft-in/soft-out' decoders which accept soft input from the demo... |

6 |
An analog decoding technique for digital codes
- Lustenberger, Helfenstein, et al.
- 1999
(Show Context)
Citation Context ...description of an analog decoder in terms of currents and voltages which inspires different circuit designs. I. INTRODUCTION Recently several proposals for analog decoders were made in [1], [2], [3], =-=[4]-=-, [5], which is in contrast to common practice where decoding is performed by digital processors. The implementation of `soft-in/soft-out' decoders which accept soft input from the demodulator and del... |

1 |
Turbo decoding with tail-biting trellises
- Wei, Riedel, et al.
- 1998
(Show Context)
Citation Context ...encoder state s n depends on the entire information sequence, hence, one has to use the state space representation of the encoder to solve this problem. Further information about this can be found in =-=[9]-=-. IV. THE MAP-ALGORITHM The code sequence x = (x 0 ; : : : ; x t ; : : : ) is used as binary input to a transmission channel where the real valued output sequence is denoted with y = (y 0 ; : : : ; y ... |