Error detection/correction and fault detection/recovery – Pulse or data error handling – Digital data error correction
Reexamination Certificate
1999-08-20
2002-09-17
Decady, Albert (Department: 2784)
Error detection/correction and fault detection/recovery
Pulse or data error handling
Digital data error correction
C714S788000, C714S701000
Reexamination Certificate
active
06453442
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to Parallel (Turbo codes) or Serial Concatenated Convolutional codes. More specifically, the invention relates to interleavers for parallel or serial concatenated convolutional codes.
BACKGROUND OF THE INVENTION
Both parallel and serial concatenated convolutional codes are referred to herein as Turbo codes for simplicity. Several techniques for using interleaving for Turbo codes have been addressed in the prior art. A random interleaver is the most common interleaver design for Turbo codes. A random interleaver of length N selects random integers between 1 and N for a block of data of length N, i.e., the random interleaver is a permutation of N integers that, for each i, there is a corresponding random integer &pgr;(i), without repetition. For large values of N, most random interleavers perform well. However, when the interleaver block size decreases, the performance of the Turbo codes degrades substantially up to a point that its BER performance is worse than the convolutional codes with similar computational complexity. Most random interleavers demonstrate an acceptable bit error rate (BER) performance; however, research has been conducted to design interleavers for Turbo codes that can outperform random interleavers.
One approach was introduced in “Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations,” by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara,
TDA Report
p. 42-122, Aug. 15, 1995, wherein the interleaver was called an S_random interleaver. In this approach, for each integer i, where 1≦i≦N, a random number is chosen between 1 and N that maps the i-th bit to a new location in the interleaver. When a value is chosen, the value is compared to the S previously selected integers. If the current selection is equal to any of S previous selections within a distance ±S, then the current selection is rejected. Any selected integer should be chosen only once in the interleaver. The process repeats until all N integers are selected in a random order. Computer simulation results have shown that if S≦{square root over (N/2)}, then the process will converge. This interleaver design assures that the short cycle events are avoided. A short cycle event occurs when two bits are close to each other before and after interleaving. This approach was considered to provide the best interleaver for Turbo codes for a long time, especially for short block length interleavers.
Recently, a new approach was developed that is based on the S random interleaver, but that also attempts to maximize the minimum effective free distance of the code. The new approach, described in “Combined Turbo Codes and Interleaver Design,” by J. Yuan, B. Vucetic and W. Feng,
IEEE Trans.on Communication
, Vol. 47, No. 4, April, 1999, not only selects the integers in the interleaver based on the S_random criteria, but also attempts to provide an interleaver with a minimum effective free distance that is larger than a preselected value.
A new interleaver design was recently proposed by J. Hokfelt, O. Edfors, and T. Maseng, “Turbo Codes: Correlated Extrinsic Information and its Impact on Iterative Decoding Performance,” Proceeding of IEEE VTC '99, Houston, Tex., based on the performance of iterative decoding algorithm in Turbo codes. Turbo codes utilize an iterative decoding algorithm based on a MAP algorithm (described by L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimum decoding of linear codes for minimizing symbol error rate,” IEEE Trans. On Inf. Theory, vol. IT-20, pp. 284-287, Mar. 1974, and hereby incorporated by reference) or any algorithm that provides soft output. At each decoding step, some information related to the parity bits of one decoder is fed into the next decoder together with the systematic data sequence and the parity bits corresponding to that decoder, as is known by those skilled in the art of using turbo codes. The inputs to each decoder are input data sequence d
k
, the parity bits y
1
k
or y
2
k
, and the logarithm of likelihood ratio (LLR) associated with the parity bits from the other decoder (W
1
k
or W
2
k
). All these inputs are utilized by the MAP decoder to create three outputs corresponding to the weighted versions of these inputs. The output {circumflex over (d)}
k
of the first decoder represents the weighted version of the input data sequence d
k
. Also, the input data sequence is fed into the second decoder after interleaving. The input to each decoder from the other decoder is used as a priori probability in the next decoding step. This information is more effective in the performance of the iterative decoding when it is less correlated to the input data sequence (or interleaved input data sequence). Thus, this criterion is used for designing the interleaver. For large block interleavers, most random interleavers provide a low correlation between W
i
k
and the input data sequence d
k
. The correlation coefficient r
W
k1
1
,d
k2
1
is defined as the correlation coefficient between W
i
k
and d
k2
. J. Hokfelt, O. Edfors, and T. Maseng, “Turbo Codes: Correlated Extrinsic Information and its Impact on Iterative Decoding Performance,” Proceeding of IEEE VTC '99, Houston, Tex., have shown that r
W
k1
1
,d
k2
1
can be analytically approximated as
r
^
W
k
1
1
,
d
k
2
1
=
{
a
exp
-
c
&LeftBracketingBar;
k1
-
k2
&RightBracketingBar;
if
k1
≠
k2
&RightBracketingBar;
0
if
k1
=
k2
(
1
)
where a and c are two constants that depend on the encoder feedback and feedforward polynomials. The correlation coefficient at the output of the second decoder is approximated as
{circumflex over (r)}
W
2
,d
2
=½
{circumflex over (r)}
W1,d
1
P
(
I+{circumflex over (r)}
W1,d
1
) (2)
where the two terms on the right hand side of (2) correspond to the correlation coefficients between W
2
and the two input data, i.e., W
1
and d. Similar correlation coefficients can be computed regarding the de-interleaver. The correlation matrix corresponding to the de-interleaver {circumflex over (r)}′
W
2
,d
2
is the same as (2), except P is substituted by
Then V
k
1
, which is the variance of the correlation coefficients, is defined as
V
k
1
=
1
N
-
1
∑
k
2
=
1
N
(
r
^
W
k
1
2
,
d
k
2
2
-
r
^
_
W
,
d
k
2
2
)
2
(
3
)
where
r
^
_
W
,
d
k
2
2
=
1
N
-
1
∑
k
2
=
1
N
r
^
W
k
1
2
,
d
k
2
2
(
4
)
V′
k1
is defined similarly using {circumflex over (r)}′
W
2
,d
2
.
The iterative decoding suitability (IDS) measure is then defined as
IDS
=
1
2
N
∑
k
1
=
1
N
(
V
k
1
+
V
k
1
′
)
(
5
)
A low value of IDS is an indication that correlation properties between W
1
and d are equally spread along the data sequence of length N. An interleaver design based on the IDS condition is suggested by J. Hokfelt, O. Edfors, and T. Maseng, “Interleaver Design for Turbo Codes Based on the Performance of Iterative Decoding,” Proceeding of IEEE ICC '99, Vancouver, Canada.
However, there is a need for a more efficient S_random interleaver.
SUMMARY OF THE INVENTION
The current invention is based on two optimization criteria using an S_random interleaver. The first criterion is to maximize the distance spectrum properties of the code by designing an interleaver that increases the minimum effective free distance of the code. The second criterion is to design the interleaver in a way to reduce the correlation properties of the extrinsic information that is fed into the next stage decoder. The present invention utilizes different techniques to achieve these two properties based on a S_random interleaver. This design maximizes the bit error rate (BER) performance of the code with respect to iterative decoding in Turbo codes.
REFERENCES:
patent: 6298463 (2001-10-01), Bingeman et al.
“Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations,” by S. Bendetto, D. Divsalar, G. Montorsi and F. Pollar,TDA Reportp. 42-122, Aug. 15, 1995;.
“Combined
Sadjadpour Hamid R.
Salehi Masoud
Sloane Neil James Alexander
AT&T Corp.
Banner & Witcoff , Ltd.
De'cady Albert
Dooley Matt
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