Yu-Cheng He

An analysis of the orthogonality structures of convolutional codes for iterative decoding

The structures of convolutional self-orthogonal codes and convolutional self-doubly-orthogonal codes for both belief propagation and threshold iterative decoding algorithms are analyzed on the basis of difference sets and computation tree. It is shown that the double orthogonality property of convolutional self-doubly-orthogonal codes improves the code structure by maximizing the number of independent observations over two successive decoding iterations while minimizing the number of cycles of lengths 6 and 8 on the code graphs. Thus, the double orthogonality may improve the iterative decoding in both convergence speed and error performance. In addition, the double orthogonality makes the computation tree rigorously balanced. This allows the determination of the best weighing technique, so that the error performance of the iterative threshold decoding algorithm approaches that of the iterative belief propagation decoding algorithm, but at a substantial reduction of the implementation complexity.

A New Approach for the Construction of Powerful LDPC Convolutional Codes

A novel approach for the algebraic construction of low-density parity-check (LDPC) convolutional codes is presented. It is based on the orthogonality structures of the codes. The proposed code construction leads to a girth of at least 10 in the Tanner graph. The error performance of these codes compares favorably with the usual LDPC convolutional codes, especially at low signal-to-noise ratio range.

Forward-only iterative decoding of convolutional self-orthogonal codes

A class of forward-only iterative belief propagation algorithms for decoding convolutional self-orthogonal codes is presented, which perform successively a number of one-step decoding and thus have only an initial decoding delay. The one-step belief propagation decoders can be realized in a similar way to one-step threshold decoders. The error performance of the algorithms is easily improved by using a weighing technique. These iterative algorithms allow good tradeoffs between complexity, latency, and error performance of the coding scheme.

A serial design of iterative belief propagation decoders for convolutional codes

The belief propagation (BP) decoding algorithm may be suitable for the decoding of convolutional self-orthogonal codes which were originally proposed for one-step threshold de- coding. In this paper, a serial design of iterative BP decoder for convolutional self-orthogonal codes is presented. Using the alge- braic structures of convolutional codes, the iterative BP decoder is designed as a serial concatenation of several one-step BP de- coders. These one-step BP decoders are implemented using mainly the shift registers in a structure similar to that of type-II threshold decoders. The iterative BP decoder performs a non- trellis-based forward-only algorithm and has only an initial de- coding delay, thus avoiding intermediate decoding delays that usually accompany BP or turbo decoding of data frames. As shown by simulation results, the use of weighing techniques has provided substantial improvements to the error performance of the iterative BP decoding at a cost of several multipliers in hard- ware implementation. The iterative BP decoder may be attrac- tive to the practical applications in very high data rate areas.

Reduced-Complexity Convolutional Self-Doubly Orthogonal Codes for Efficient Iterative Decoding

A variant of convolutional self doubly orthogonal codes that can be decoded using an iterative threshold decoding algorithm is presented. These new codes are called degenerate convolutional self-doubly orthogonal codes since not all the double orthogonality conditions required to obtained convolutional self doubly orthogonal codes defined in the wide sense are satisfied. The memory lengths or spans of the degenerate convolutional self-doubly orthogonal codes are substantially shorter than those of the usual convolutional self doubly orthogonal codes defined in the wide sense, at the cost of only a slight degradation of the error performances. As a consequence, very low complexity implementations are possible with these error correcting schemes. Several new degenerate convolutional self doubly orthogonal codes have been determined and their error performances evaluated using computer simulations

Performance Comparison of Iterative BP and Threshold Decoding for Convolutional Self-Doubly-Orthogonal Codes

The forward-only iterative decoding techniques for convolutional self-doubly-orthogonal codes are systematically presented based on one-step belief propagation (BP) decoding and one-step threshold decoding. A feedback mechanism and a weighing technique are examined in order to improve both the convergence speed and error performance. Computer simulation results show that compared with the iterative threshold decoding over an additive white Gaussian noise channel, the iterative BP decoding for these codes achieves essentially the same error performance while requiring only about half the number of iterations. Therefore, these two iterative decoding techniques can provide a tradeoff between the latency and the complexity of decoding and allow for the applications of these codes in very high speed wireless communications.

Parallel processing for fast iterative decoding of orthogonal convolutional codes

An efficient parallel processing mode is proposed for fast decoding of orthogonal convolutional codes using the forward-only iterative belief propagation algorithm. This iterative decoding can approach the speed of one-step decoding while providing useful tradeoffs between decoding speed and error performance. The error performances of two convolutional self-doubly-orthogonal codes are obtained by simulation, and compared to their asymptotic performances

Parallel iterative decoding for orthogonal convolutional codes

A parallel design for the iterative belief propagation decoding of convolutional self-orthogonal codes is presented. This parallel structure allows a substantial increase in the speed of iterative decoding, approaching that of one-step decoding at the cost of only a negligible degradation of coding gain. Together with its low encoding complexity, this coding scheme may be especially attractive for very high data rate applications. The parallel structure can also be generalized to the iterative threshold decoding of convolutional self doubly orthogonal codes, providing a more flexible tradeoff between decoding speed and error performance.

A Class of Low-Density Parity-Check Convolutional Codes Based on Difference Families

An algebraic construction for a class of low-density parity-check (LDPC) convolutional codes is presented on the basis of difference families associated with the code generator matrix. It can be shown that these codes have girth of at least 10 on the Tanner graph which is independent of either the size of the code generator matrix or the minimum Hamming distance of the codes. The code construction guarantees the independence of the messages exchanged in the belief propagation decoding process during two successive decoding iterations. Computer simulations show that over the additive white Gaussian noise channel, the best error performance of these codes at moderate signal-to- noise ratio values is practically obtained using only three to five iterations.

Error performances of multi shift-register convolutional self-doubly-orthogonal codes

A class of orthogonal convolutional codes using a multi shift-register encoder and featuring self-doubly-orthogonal properties is analyzed under iterative decoding. The lower bounds of error performances of these codes can be approached within typically three to five iterations at moderate signal-to-noise ratios using either iterative threshold (TH) decoding or belief propagation (BP) decoding. Compared with iterative BP decoding, it is shown that iterative threshold decoding for these codes yields a much lower complexity at the same decoding latency.