Variable-length Error-correcting Codes Research Articles

On the Design of Near-Optimal Variable-Length Error-Correcting Codes for Large Source Alphabets

In this paper, we focus on near-optimal designs for variable-length error-correcting (VLEC) codes, while considering the performance in terms of both the average codeword length (ACL) and the symbol-error rate (SER). The criteria for narrowing the search space and enhancing the SER performance are investigated. An efficient code construction algorithm is then devised based on a random search process. Taking advantage of the significantly reduced search complexity, we are able to construct near-optimal VLEC codes for large source alphabets. Numerical results obtained for various free distance values and alphabet sizes show that constructed VLEC codes have both reduced ACL values and enhanced SER performances. Performance improvement is more notable for large source alphabets.

An Efficient Tree Search Algorithm for the Free Distance of Variable-Length Error-Correcting Codes

We propose an efficient tree search algorithm for determining the free distance of variable-length error-correcting codes (VLECs). A main idea behind the algorithm is to structure all pairs of code word-concatenated sequences as a tree, in which we seek the pair of sequences that determine the free distance. In order to speed up the algorithm, we establish constraints that do not compromise optimality in determining the free distance. Experimental results on VLECs algorithmically constructed for the English alphabet show that our algorithm requires a considerably smaller number of bitwise distance computations and covers a much smaller number of tree nodes than Dijkstra’s algorithm operating over the pairwise distance graph while being a hundred times faster in terms of execution time.

On the Design of Variable-Length Error-Correcting Codes

A joint source-channel coding problem that combines the efficient compression of discrete memoryless sources with their reliable communication over memoryless channels via binary prefix-free variable-length error-correcting codes (VLECs) is considered. Under a fixed free distance constraint, a priority-first search algorithm is devised for finding an optimal VLEC with minimal average codeword length. Two variations of the priority-first-search-based code construction algorithm are also provided. The first one improves the resilience of the developed codes against channel noise by additionally considering a performance parameter Bdfree without sacrificing optimality in average codeword length. In the second variation, to accommodate a large free distance constraint as well as a large source alphabet such as the 26-symbol English data source, the VLEC construction algorithm is modified with the objective of significantly reducing its search complexity while still yielding near-optimal codes. A low-complexity sequence maximum a posteriori (MAP) decoder for all VLECs (including our constructed optimal code) is then proposed under the premise that the receiver knows the number of codewords being transmitted. Simulations show that the realized optimal and suboptimal VLECs compare favorably with existing codes in the literature in terms of coding efficiency, search complexity and error rate performance.

Soft-decision priority-first decoding algorithms for variable-length error-correcting codes

Joint source-channel decoding has recently received extensive attention due to the rise in the applications of multimedia wireless communication. Based on a code trellis rather than on a code tree, this work presents a maximum a posteriori (MAP) soft-decision priority-first decoding algorithm and its approximations for variable-length error-correcting codes. Simulation results indicate that for the code with average codeword length 6.269 bits and free distance 3, under moderate signal-to-noise ratio, one of the proposed algorithms almost reaches the lowest decoding complexity, and has nearly the same performance on symbol error probability as the MAP decoding.

Joint Decoding of Concatenated VLEC and STTC System

We consider the decoding of wireless communication systems with both source coding in the application layer and channel coding in the physical layer for high-performance transmission over fading channels. Variable length error correcting codes (VLECs) and space time trellis codes (STTCs) are used to provide bandwidth efficient data compression as well as coding and diversity gains. At the receiver, an iterative joint source and space time decoding scheme are developed to utilize redundancy in both STTC and VLEC to improve overall decoding performance. Issues such as the inseparable systematic information in the symbol level, the asymmetric trellis structure of VLEC, and information exchange between bit and symbol domains have been considered in the maximum a posteriori probability (MAP) decoding algorithm. Simulation results indicate that the developed joint decoding scheme achieves a significant decoding gain over the separate decoding in fading channels, whether or not the channel information is perfectly known at the receiver. Furthermore, how rate allocation between STTC and VLEC affects the performance of the joint source and space-time decoder is investigated. Different systems with a fixed overall information rate are studied. It is shown that for a system with more redundancy dedicated to the source code and a higher order modulation of STTC, the joint decoding yields better performance, though with increased complexity.

Iterative Construction of Reversible Variable-Length Codes and Variable-Length Error-Correcting Codes

We propose a generic algorithm for the construction of efficient reversible variable-length codes (RVLCs) and variable-length error-correcting (VLEC) codes, which optimizes the codeword length distribution. The algorithm may be applied to any existing codeword selection mechanism, and it is capable of generating codes of higher efficiency in comparison to the algorithms disseminated in the literature.

Variable-length error-correcting codes

Variable-length error-correcting codes, suitable to perform joint source-channel coding, are presented. A maximum likelihood decoding algorithm for these codes is given. Some performance bounds are derived and it is shown that these codes are similar to convolutional codes. The free distance of these codes is defined and it is shown that it is the most important parameter that determines their performance at high E/sub b//N/sub 0/. It is shown that the performance of these codes can be better than a standard cascade of a Huffman code followed by a BCH code with the same code parameters.

A lower bound on average codeword length of variable length error-correcting codes

Codes of variable length that are capable of error correction are studied. A lower bound on the average length of such codes under the criterion of promptness is obtained. This generalizes the celebrated result due to C.E. Shannon (1948) for the noiseless case. The bound obtained provides a measure of optimality for variable-length, error-correcting codes. >