# Coding theorems for 'turbo-like' codes

@inproceedings{Divsalar1998CodingTF, title={Coding theorems for 'turbo-like' codes}, author={Dariush Divsalar}, year={1998} }

#### 571 Citations

General coding theorems for turbo-like codes

- Mathematics
- 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)
- 2000

In this paper we prove that for general memoryless binary input channels, most ensembles of parallel and serial turbo codes, with fixed component codes, are "good" in the sense that with maximum… Expand

Coding Theorems for Generalized Repeat Accumulate Codes Background ❍ Turbo Codes ( Berrou et al . ) ❒ Analysis uses the Uniform Random Interleaver

- 2000

In this paper, we present a coding theorem for the ensemble of Generalized Repeat Accumulate (GRA) codes. These codes are the serial concatenation of a terminated convolutional code andm interleaved… Expand

Coding Theorems for Convolutional Accumulate-m Codes 3.1 Introduction

- 2003

It is well-known that long random codes achieve reliable communication at noise levels up to the Shannon limit, but they provide no structure for efficient decoding. The introduction and analysis of… Expand

Chapter 2 The Serial Concatenation of Rate-1 Codes Through Uniform Interleavers 2

- 2003

Since the introduction of turbo codes by Berrou, Glavieux, and Thitimajshima [3], iterative decoding has made it practical to consider a myriad of different concatenated codes, and the use of… Expand

Coding theorems for turbo code ensembles

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 2002

It is proved that ensembles of parallel and serial turbo codes are "good" in the following sense: for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than /spl gamma//sub 0/, the average maximum-likelihood (ML) decoder block error probability approaches zero. Expand

RA Codes Achieve AWGN Channel Capacity

- Mathematics, Computer Science
- AAECC
- 1999

It is proved that on the AWGN channel, RA codes have the potential for achieving channel capacity, and as the rate of the RA code approaches zero, the average required bit Eb/N0 for arbitrarily small error probability with maximum-likelihood decoding approaches log 2, which is the Shannon limit. Expand

The Minimum Distance of Turbo-Like Codes

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2009

It is proven that depth-three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good. Expand

Product accumulate codes: a class of codes with near-capacity performance and low decoding complexity

- Computer Science
- IEEE Transactions on Information Theory
- 2004

This work proposes PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2, and shows that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Expand

Turbo-like codes for the block-fading channel

- Computer Science
- International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.
- 2004

It is shown that standard block codes obtained by trellis-termination of convolutional codes have a gap from outage that increases with the block length: this is a different and more subtle manifestation of the so-called "interleaving gain" of turbo-like codes. Expand

The serial concatenation of rate-1 codes through uniform random interleavers

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 2003

This paper constructs "good" binary linear block codes at any rate r<1 by serially concatenating an arbitrary outer code of rate r with a large number of rate-1 inner codes through uniform random interleavers and proves that long codes from this ensemble will achieve the Gilbert-Varshamov (1952) bound with high probability. Expand

#### References

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A method for computing a conjectured interleaving gain exponent and for optimizing the effective free distance of d2, a class of concatenated coding communications systems built from convolutional codes and interleavers. Expand

Unveiling turbo codes: some results on parallel concatenated coding schemes

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A method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length is proposed and used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes. Expand

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Improved union bound on linear codes for the input-binary AWGN channel, with applications to turbo codes

- Mathematics
- Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252)
- 1998

While improved bounds have been central to proofs of the coding theorem and the tightness of the random coding bound for rates near capacity, most results for specific codes, both block and… Expand

Serial concatenation of interleaved codes: performance analysis, design and iterative decoding

- Computer Science
- Proceedings of IEEE International Symposium on Information Theory
- 1996

Upper bounds to the average maximum-likelihood bit error probability of serially concatenated coding schemes are derived and a highly-performing iterative decoding algorithm is proposed. Expand

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Error-Correcting Codes, 2nd. ed

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