## Energy limited channels: Coding, multiaccess, and spread spectrum (1987)

Citations: | 43 - 1 self |

### BibTeX

@TECHREPORT{Gallager87energylimited,

author = {Robert G. Gallager},

title = {Energy limited channels: Coding, multiaccess, and spread spectrum},

institution = {},

year = {1987}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1476 |
Information Theory and Reliable Communication
- Gallager
- 1968
(Show Context)
Citation Context ...d, however, that these exponents are the same, showing that impractically large bandwidths are not required to approach the best exponents. In the next sub-section, we analyze the random coding bound =-=[1]-=- for these channels, using a fixed value of 8. We next find the reliability function at 0 rate and use this, along with known results about the relationship of lower and upper bounds to error probabil... |

886 | Information Theory: Coding Theorems for Discrete Memoryless Systems - Csiszár, Körner - 1981 |

167 |
A Perspective on Multiaccess Channels
- Gallager
- 1985
(Show Context)
Citation Context ... exception of sequential decoding as developed by Arikan [20]. The random coding bound to error probability for this case was derived by Slepian and Wolf [21] and was extended to shell constraints in =-=[22]-=-. We now develop this bound using a shell constraint, for the multiaccess channels under consideration here. The probability of error, Pe, for one or more of the J code words can be expressed as P, = ... |

140 |
Multi-way Communication Channels
- Ahlswede
- 1971
(Show Context)
Citation Context ...ess channel with energy constraints and establish the converge to the coding theorem. The coding theorem and converse for multiaccess channels without an energy constraint was established by Ahlswede =-=[10]-=- and Liao [11] and has been extended in many subsequent papers, for example [12-14]. However, none of the converses use bit error probability and none include general energy constraints. The inclusion... |

80 |
Lower bounds to error probability for coding on discrete memoryless channels
- Shannon, Gallager
(Show Context)
Citation Context ...2 ln J p(pl() dy] (35) Note that the quantity in brackets is E0(1) = Er(O). Also this exponent for two code words is an upper bound to E(O), so we have established that Er(O) = E(O). It is well known =-=[6]-=- that for any DMC (and thus any value of 6>0) the reliability function is upper bounded bys10 the sphere packing exponent and by the straight line exponent. The sphere packing exponent is given by Es(... |

54 |
A Coding Theorem for Multiple Access Channels With Correlated Sources
- Slepian, Wolf
- 1973
(Show Context)
Citation Context ...n for simultaneous decoding, with the possible exception of sequential decoding as developed by Arikan [20]. The random coding bound to error probability for this case was derived by Slepian and Wolf =-=[21]-=- and was extended to shell constraints in [22]. We now develop this bound using a shell constraint, for the multiaccess channels under consideration here. The probability of error, Pe, for one or more... |

24 |
The capacity region of the totally asynchronous multiple access channel
- Hui, Humblet
- 1985
(Show Context)
Citation Context ...ity, but the exponents are somewhat smaller than those for simultaneous decoding. These results remain valid if the blocks used by the different transmitters are not synchronized (see Hui and Humblet =-=[23]-=- for a discussion of the unsynchronized case), but again we note that our model is not sufficient to discuss the problem of lack of component synchronization. For rates that are achievable only as con... |

21 |
A coding theorem for multiple access communications
- Liao
- 1972
(Show Context)
Citation Context ...th energy constraints and establish the converge to the coding theorem. The coding theorem and converse for multiaccess channels without an energy constraint was established by Ahlswede [10] and Liao =-=[11]-=- and has been extended in many subsequent papers, for example [12-14]. However, none of the converses use bit error probability and none include general energy constraints. The inclusion of an energy ... |

16 |
Practical codes for photon communication
- McEliece
- 1981
(Show Context)
Citation Context ... Er(R) is positive for all R > O; that is, the capacity in bits per unit energy of the channel is infinite. A special case of this phenomenon was first observed for a model of quantum optical channel =-=[7,8,9]-=-. It does not suggest that there is anything wrong with the concept of capacity for such channels and in no way gives added importance to the computational cut off rate (see [9] for a more complete di... |

14 |
Capacity cutoff rate, and coding for direct detection optical channel
- Massey
- 1981
(Show Context)
Citation Context ... Er(R) is positive for all R > O; that is, the capacity in bits per unit energy of the channel is infinite. A special case of this phenomenon was first observed for a model of quantum optical channel =-=[7,8,9]-=-. It does not suggest that there is anything wrong with the concept of capacity for such channels and in no way gives added importance to the computational cut off rate (see [9] for a more complete di... |

13 |
Communication over fading dispersive channels
- Richters
- 1967
(Show Context)
Citation Context ...ather than bandwidth limitations. These situations have been widely studied for additive Gaussian noise channels (for example [1-3]) and to a lesser extent for fading dispersive channels (for example =-=[4,5]-=-. There is no cohesive treatment of the class of such channels, and this paper is intended to provide at least the beginning of such a cohesive treatment. For multiaccess communication, in which a lar... |

11 | Multiple user information theory - Gama1, Cover |

11 |
Frequency-hop transmission for satellite packet switching and terrestrial packet radio neworks
- Pursley
- 1986
(Show Context)
Citation Context ...er j independently chooses each component of each code word to be 1 with probability 8j subject to a shell constraint. This can be viewed as an abstraction of spread spectrum coding (see, for example =-=[16,17]-=-. In practice, a spread spectrum transmitter pseudorandomly chooses a subset of the available N components and then uses algebraic or convolutional coding to select code words within that subset; all ... |

10 |
Maximum likelihood sequence detection for intersymbol interference channels: A new upper bound on error probability
- Verdú
- 1987
(Show Context)
Citation Context ...t decodes the code word for J- 1, and so forth down to the code word for transmitter 1. Viterbi [18] has investigated this decoding strategy for an additive white Gaussian noise channel. He and Verdu =-=[19]-=- consider also the problems of synchronization for this channel. We shall consider the reliability function for this type of decoding shortly, but first treat the final possibility for decoding. Suppo... |

4 |
Sequential decoding for multiple access channels
- Arikan
- 1988
(Show Context)
Citation Context ...lihood decoding on the set of J codes. No computationally attractive decoding techniques are known for simultaneous decoding, with the possible exception of sequential decoding as developed by Arikan =-=[20]-=-. The random coding bound to error probability for this case was derived by Slepian and Wolf [21] and was extended to shell constraints in [22]. We now develop this bound using a shell constraint, for... |

3 | Error exponents for direct detection optical channel,” Report LIDS-P-1337, Laboratory for Information and Decision Systems, Mass
- Humblet
- 1983
(Show Context)
Citation Context ... Er(R) is positive for all R > O; that is, the capacity in bits per unit energy of the channel is infinite. A special case of this phenomenon was first observed for a model of quantum optical channel =-=[7,8,9]-=-. It does not suggest that there is anything wrong with the concept of capacity for such channels and in no way gives added importance to the computational cut off rate (see [9] for a more complete di... |

2 | der Meulen, "A survey of multi-way channels in information theory: 1961 - 1976 - van - 1977 |

2 |
Graph theoretic approaches to the code construction for the two-user multiple-access binary adder channel
- Kasami, Lin, et al.
- 1983
(Show Context)
Citation Context ...ntirely realistic model since the output of a multiaccess channel usually depends on how many transmitters are simultaneously transmitting a one. Thus a more realistic model would be an adder channel =-=[15]-=- cascaded with a point to point channel with the input alphabet { 0,1,...,J}. We have chosen the simpler model here since our objective is to gain insight into multiaccess coding in the simplest conte... |

1 |
Fading Dispersive Channels
- Kennedy
- 1969
(Show Context)
Citation Context ...ather than bandwidth limitations. These situations have been widely studied for additive Gaussian noise channels (for example [1-3]) and to a lesser extent for fading dispersive channels (for example =-=[4,5]-=-. There is no cohesive treatment of the class of such channels, and this paper is intended to provide at least the beginning of such a cohesive treatment. For multiaccess communication, in which a lar... |

1 |
Spread Spectrum Multiple Access with Binary Modulation can Approach Shannon Capacity for the Aggregate Gaussian Channel" Manuscript
- Viterbi
(Show Context)
Citation Context ...such a set of codes by first decoding for transmitter J. Conditioning on the decoded word for J, one next decodes the code word for J- 1, and so forth down to the code word for transmitter 1. Viterbi =-=[18]-=- has investigated this decoding strategy for an additive white Gaussian noise channel. He and Verdu [19] consider also the problems of synchronization for this channel. We shall consider the reliabili... |

1 |
Asynchronous Multi-access channel Capacity
- Cover, McEliece, et al.
- 1980
(Show Context)
Citation Context ...ly achievable. This of course requires block synchronization. As shown in [23], only directly achievable (R,6) pairs are achievable with no block synchronization between the transmitters. As shown in =-=[24]-=-, however, if there is a bounded uncertainity between the components of the different transmitters, time sharing can still be used by using block lengths large relative to the maximum uncertainity.sRE... |