Interleavers for turbo code

[0002] This is a utility patent application claiming priority from provisional application Serial No. 60/095,085 filed on Aug. 3, 1998.

[0003] This invention relates to the field of electronic communications systems and, more particularly, to interleavers for performing code modulation.

[0004] Techniques for encoding communication channels, known as coded modulation, have been found to improve the bit error rate (BER) of electronic communication systems such as modem and wireless communication systems. Turbo coded modulation has proven to be a practical, power-efficient, and bandwidth-efficient modulation method for “random-error” channels characterized by additive white Gaussian noise (AWGN) or fading. These random-error channels can be found, for example, in the code division multiple access (CDMA) environment.

[0005] The key innovation of turbo codes is an interleaver which permutes the original received or transmitted data frame before input to a second encoder. Permuting is accomplished by a processor performing a randomizing algorithm, the construction of which is well known. Combining the permuted data frames with the original data frames has shown to achieve low bit-error rates in AWGN and fading channels. The interleaving process increases the diversity in the data in such a way that if the modulated symbol is distorted in transmission the error may be recoverable with the use of error correcting algorithms in the decoder.

[0006] A conventional interleaver collects, or frames, the signal points to be transmitted into a matrix, where the matrix is sequentially filled up a row at a time. After a predefined number of signal points have been framed, the interleaver is emptied by sequentially reading out the columns of the matrix for transmission. As a result, signal points in the same row of the matrix that were near each other in the original signal point flow are separated by a number of signal points equal to the number of rows in the matrix. Ideally, the number of columns and rows would be picked such that interdependent signal points, after transmission, would be separated by more than the expected length of an error burst for the channel. However, this may not be practicable. As the number of rows is increased, so is the signal delay due to the framing of the signal points. As a result, there is a system constraint on the size of the interleaver in order to keep the signal delay within acceptable limits. On the other hand, constraining the size of the interleaver limits the separation of the time-diverse interdependent signal points and thus limits the improvement in error performance achieved by the interleaver.

[0007] There are two conventional interleaving methods; uniform interleaving (i.e. a regular interleaving pattern); and non-uniform interleaving (i.e. a pseudo-irregular interleaving pattern). In the case of uniform interleaving, finite code words (FC) of higher weight can be constructed from FCs of lower weight. Therefore a certain “repetitive pattern” of low-weight FC output sequences can occur in the output stream of a uniform-interleaving turbo coder. However, uniform interleaving does not sufficiently de-correlate the output of the two encoders, hence the minimum distance of the resulting turbo code does not increase as one might expect.

[0008] On the other hand, non-uniform interleaving achieves better “maximum scattering” of data and “maximum disorder” of the output sequence, which means that the redundancy introduced by the two convolutional codes is more equally spread in the output sequence of the turbo encoder. The minimum distance is increased to much higher values than for uniform interleaving. A persistent problem for non-uniform interleaving is how to achieve sufficient “non-uniformity”, since the interleaving algorithms can only be based on pseudo-irregular patterns. Besides this, the effort for implementing the scheme should be reasonable for practical applications. Furthermore, conventional interleavers require a significant amount of memory in the encoder. Conventional interleaving matrices also require delay compensations, which limit their use for applications with real-time requirements.

[0009] Accordingly there exists a need for systems and methods of interleaving codes that improve non-uniformity.

[0010] There also exists a need for systems and methods of interleaving codes that require minimal delay compensations.

[0011] It is thus an object of the present invention to provide systems and methods of interleaving codes that improve non-uniformity.

[0012] It is also an object of the present invention to provide systems and methods of interleaving codes that require minimal delay compensations.

[0013] In accordance with the teachings of the present invention, these and other objects may be accomplished by the present invention, which interleaves a data frame, where the data frame has a predetermined size and is made up of portions. An embodiment of the invention includes a memory configured to receive and store the data frame. Once received, the data frame is indexed by a plurality of rows having a predetermined row size and a plurality of columns having a predetermined column size. The product of the predetermined row size and the predetermined column size equals the predetermined size of the data frame.

[0014] A processor is coupled to the memory and used for separating the data frame into a plurality of portions. The processor also is used for generating a permuted sequence of the plurality of portions which are indexed by the plurality of rows in accordance with i₁(n₁)=α₁{circumflex over ( )}(n₁)mod(P₁), where P₁is a prime number greater than the predetermined row size, where n₁is an integer in the range of 1 through and including P₁−1, and where α₁is a root of P₁. This algorithm enables i₁(n₁) to be a unique number between 1 and the predetermined row size.

[0015] The processor is also configured to generate a permuted sequence of the plurality of portions indexed by the plurality of columns in accordance with i₂(n₂)=α₂{circumflex over ( )}(n₂)mod(P₂), where P₂is a prime number greater than the predetermined column size, where n₂is an integer in the range of 1 through and including P₂−1, and where α₂is a root of P₂. This algorithm enables i₂(n₂) to be a unique number between 1 and the predetermined column size. The result is interleaved portions of the dataframe.

[0016] The invention will be more clearly understood by reference to the following detailed description of an exemplary embodiment in conjunction with the accompanying drawings, in which:

[0017] FIG. 1 is a diagram of a typical turbo encoder.

[0018] FIGS. 2aand 2bare flowchart diagrams illustrating the operation of the improved interleaver for turbo codes in accordance with the present invention.

[0019] FIG. 3 is a flow chart diagram illustrating another embodiment of the improved interleaver for turbo codes in accordance with the present invention.

[0020] The present invention is an apparatus and method for interleaving codes. The interleaver takes each incoming data frame of N data bits and rearranges them in a pseudo-random fashion prior to encoding by a second encoder. This invention can be used in satellite communication systems, wireless telephone systems, modems, computers, and the like.

[0021] The interleaver sorts the bits in a manner that lacks any apparent order. The present invention will perform better than conventional interleavers even if the data frame is small (i.e., N on the order of a few thousand). This is accomplished by obtaining more diverse “scattering” than conventional interleavers. FIG. 1 depicts a standard turbo encoder. It consists of two encoders 10 and 20 and an interleaver 30. The encoders 10 and 20 are arranged in a parallel concatenation with the interleaver 30 before the second encoder 20. The output of the first encoder 10 is a low-weight code 50 and the output of the second encoder 20 is a high-weight code 60. These outputs may go to a device such as a code puncturing mechanism (not shown) to periodically delete selected bits to reduce coding overhead. In addition the output of the interleaver 70 may also be transmitted directly to the puncturing mechanism, but it is not necessary. In addition the present invention may also be used with other non turbo code systems that require code interleaving.

[0022] The present invention discloses two embodiments of an interleaver which can improve the performance of conventional turbo codes. The first embodiment will be referred to as a Galya interleaver and the second embodiment will be referred to as a frequency hopping (FH) interleaver. Both of these embodiments are based on number theory and both of these embodiments may be realized in software or hardware (i.e. application specific integrated circuits (ASIC), programmable logic arrays (PLA), or any other suitable logic devices, the construction of which is well known).

[0023] In the first embodiment, the Galya interleaver, the information bit matrix has N₁rows and N₂columns such that N₁*N₂=N. Further, there exist prime numbers P₁and P₂which are respectively greater than N₁and N₂(i.e. P₁>N₁and P₂>N₂). It is preferred that these prime numbers should be the lowest prime numbers greater than N₁and N₂, respectively, but it is not required. Initial roots α₁and α₂may be determined for these prime numbers using conventional methods. Employing the above noted parameters, the bit sequence generation for the Galya interleaver is defined by the following equations:

[0024] i₁(n₁)=α₁{circumflex over ( )}(n₁)mod(P₁), wherein n₁=1,2, . . . ,P₁−1; and i₁(n₁)≦N₁; and,

[0025] i₂(n₂)=α₂{circumflex over ( )}(n₂)mod(P₂), wherein n₂=1,2, . . . ,P₂−1; and i₂(n₂)≦N₂.

[0026] For N=256, we have N₁=N₂=16, P₁=P₂=17, α₁=α₂=3.

[0027] FIGS. 2aand 2bshow the implementation of the above embodiment in either software or hardware. The above equations may be performed in a parallel or serial manner. In FIG. 2a, step 200 defines a parameter representing block length N₁. An array i₁(n₁) for storing the bit sequence is defined (step 210) to size N₁and initialized. Next, a prime number P₁is defined (step 220) which is greater than N₁. Step 230 defines the initial root of N₁called α₁. A counter n₁is defined and initialized to one (step 240) and incremented (step 270) for each pass of the loop. As step 260 shows, the counter determines when to break out of a loop which calculates (step 250) the bit sequence, i₁(n₁), for each symbol in the data frame. The loop is conditioned to break when the entire data frame has been permuted. The loop can also be adjusted to interleave a portion of the received or transmitted data frames.

[0028] In FIG. 2b, step 400 defines a parameter representing block length N₂. An array for storing the bit sequence is defined (step 410) to size N₂and initialized. Next, a prime number P₂is defined (step 420) which is greater than N₂. Step 430 defines the initial root of N₂called α₂. A counter n₂is defined and initialized to one (step 440) and incremented (step 470) for each pass of the loop. As step 460 shows, the counter determines when to break out of a loop which calculates (step 450) the bit sequence, i₂(n₂), for each symbol in the data frame. The loop is conditioned to break when the entire data frame has been permuted. The loop can also be adjusted to interleave a portion of the received or transmitted data frames.

[0029] In the second embodiment, the FH interleaver, assume that the block length (or data frame size) is length N. Further, there exists a prime number P which is greater than N. It is preferred that the prime number should be the lowest prime number greater than N, but it is not required. For a given prime number it is possible to find an initial root a using conventional methods. Thus, for example, if N=256, then P=257 and α=3. Employing the above noted parameters, the bit sequence generation for the FH interleaver is defined by the following equation:

[0030] i(n)=α{circumflex over ( )}(n)mod (P), wherein n=1,2, . . . , P−1, i(n)≦N.

[0031] FIG. 3 is an implementation of the above embodiment in either software or hardware. Step 300 defines a parameter representing block length N. An array for storing the bit sequence is defined (step 310) to size N and initialized. Next, a prime number P is defined (step 320) which is greater than N. Step 330 defines the initial root of N called α. A counter n is defined and initialized to one (step 340) and incremented (step 370) for each pass of the loop. As step 360 shows, the counter determines when to break out of a loop which calculates (step 350) the bit sequence, i(n), for each symbol in the data frame. The loop is conditioned to break when the entire data frame has been permuted. The loop can be adjusted to interleave a portion of the received or transmitted data frames.

[0032] Those skilled in the art will realize that any initialization value for the array i(n), i₁(n₁), i₂(n₂) can be used and still be within the scope of the invention. For example the initialization data can consist of zeros, ones, twos, etc., or a template may be created with different initialization data. In addition, it is common in programming to use indexes of different starting values. Thus, n, n₁, and n₂can be any integer and the loop break conditions n≦N, n₁≦N₁, and n₂≦N₂can be adjusted accordingly and still be within the scope of this invention.

[0033] The disclosed interleavers are compatible with existing turbo codes structure and are compatible with the current decoding algorithm. These interleavers offer superior performance without increasing system complexity.

[0034] In addition, those skilled in the art will realize that de-interleavers can be used to decode the interleaved data frames. The construction of de-interleavers used in decoding turbo codes is also well known in the art. As such they are not further discussed herein. Accordingly, a de-interleaver corresponding to the first embodiment can be constructed using the permuted sequences:

[0035] i₁(n₁)=α₁{circumflex over ( )}(n₁)mod(P₁), wherein n₁=1,2, . . . ,P₁−1; and i₁(n₁)≦N₁; and,

[0036] i₂(n₂)=α₂{circumflex over ( )}(n₂)mod(P₂), wherein n₂=1,2, . . . ,P₂−1; and i₂(n₂)≦N₂

[0037] for deinterleaving. It follows, a de-interleaver corresponding to the second embodiment can also be constructed using the permuted sequence:

[0038] i(n)=α{circumflex over ( )}(n)mod (P), wherein n=1,2, . . . , P−1, i(n)≦N

[0039] for deinterleaving.

[0040] It will thus be seen that the invention efficiently attains the objects set forth above, among those made apparent from the preceding description. In particular, the invention provides systems and methods of interleaving codes.

[0041] It will be understood that changes may be made in the above construction and in the foregoing sequences of operation without departing from the scope of the invention. It is accordingly intended that all matter contained in the above description or shown in the accompanying drawings be interpreted as illustrative rather than in a limiting sense.

[0042] It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention as described herein, and all statements of the scope of the invention which, as a matter of language, might be said to fall therebetween.