An iterative decoding threshold analysis for terminated regular LDPC convolutional (LDPCC) codes is presented. Using density evolution techniques, the convergence behavior of an iterative belief propagation decoder is analyzed for the binary erasure channel and the AWGN channel with binary inputs. It is shown that for a terminated LDPCC code ensemble, the thresholds are better than for corresponding regular and irregular LDPC block codes.

Potentially large storage requirements and long initial decoding delays are two practical issues related to the decoding of low-density parity-check (LDPC) convolutional codes using a continuous pipeline decoder architecture. In this paper, we propose several reduced complexity decoding strategies to lessen the storage requirements and the initial decoding delay without significant loss in performance. We also provide bit error rate comparisons of LDPC block and LDPC convolutional codes under equal processor (hardware) complexity and equal decoding delay assumptions. A partial syndrome encoder realization for LDPC convolutional codes is also proposed and analyzed. We construct terminated LDPC convolutional codes that are suitable for block transmission over a wide range of frame lengths. Simulation results show that, for terminated LDPC convolutional codes of sufficiently large memory, performance can be improved by increasing the density of the syndrome former matrix.

An ensemble of$(J,K)$-regular low-density parity- check (LDPC) convolutional codes is introduced and existence-type lower bounds on the minimum distance$d _ {\rm L}$of code segments of finite length$L$and on the free distance$d _{\rm free}$are derived. For sufficiently large constraint lengths$\nu$, the distances are shown to grow linearly with$\nu$and the ratio$d_ {\rm L}/\nu$approaches the ratio$d _{ {\rm free}}/\nu$for large$L$. Moreover, the ratio of free distance to constraint length is several times larger than the ratio of minimum distance to block length for Gallager's ensemble of (J,K)-regular LDPC block codes.

An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is analyzed for binary-input output-symmetric memoryless channels using density evolution techniques. We observe that the structured irregularity in the Tanner graph of the codes leads to significantly better thresholds when compared to corresponding LDPC block codes

Stereo correspondence is maybe the most prominent step in extraction of three dimensional structure of a scene from two or more images taken from distinct viewpoints. The correspondence problem consists of determining the locations in each image that are projections of the same physical point in space. This paper introduces a novel model based stereo matching algorithm using System of Associative Relations (SOAR) computational model. SOAR makes use of pair-wise pixel interactions to determine the underlying structure of associations within the token. The proposed stereo correspondence algorithm utilizes feature vectors (tokens) formed by direction of derivatives which constitute SOAR feature vectors. The algorithm proposed here is simple and easily realizable in hardware. Proposed algorithm is observed to yield equivalent matching performance at lower computation cost.

A lower bound on the free distance of LDPC convolutional codes defined by syndrome former matrices comprised of MtimesM permutation matrices is derived. We show that asymptotically, i.e., as Mrarrinfin, for almost all codes in the ensemble the free distance grows linearly with constraint length

A class of algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse parity-check matrices comprised of blocks of circulant matrices. The sparse parity-check representation allows for practical graph-based iterative message-passing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described.

We present an analog rotating ring decoder for decoding an LDPC convolutional code. The decoder architecture uses a window of soft received L-values, K time units in the past and K time units in the future, to decode a given bit. The window of 2K+1 time units is arranged in a ring structure, and decoding proceeds in a continuous fashion by rotating around the ring. Simulation results indicate performance almost identical to that achieved with digital decoding.

Low density parity check (LDPC) block codes have been shown to achieve near capacity performance for binary transmission over noisy channels. Block codes, however, require splitting the data to be transmitted into frames, which can be a disadvantage in some applications. Convolutional codes, on the other hand, have no such requirement, and are well suited for continuous transmission. Felstrom and Zigangirov (1999) proposed the construction of periodic time-varying convolutional codes with LDPC matrices. A set of time-invariant LDPC convolutional codes was described by Sridharan et al. (2002). The codes of Felstrom and Zigangirov were obtained by random construction techniques whereas those of Sridharan et al. were essentially algebraic constructions. The new LDPC convolutional codes described here are obtained by introducing a degree of randomness into the latter construction.