Efficient Computation and Optimization of the Free Distance of Variable-Length Finite-State Joint Source-Channel Codes

Abstract

This paper considers the optimization of a class of joint source-channel codes described by finitestate encoders (FSEs) generating variable-length codes. It focuses on FSEs associated to joint-source channel integer arithmetic codes, which are uniquely decodable codes by design. An efficient method for computing the free distance of such codes using Dijkstra's algorithm is proposed. To facilitate the search for codes with good distance properties, FSEs are organized within a tree structure which allows the use of efficient branch-and-prune techniques avoiding a search of the whole tree.

On the Design of Variable-Length Error-Correcting Codes

“…12 Notably different from our work and also the main referenced works in this paper (i.e., Buttigieg …”

“…Go to Step 2. It should be emphasized that the above construction algorithm focuses only on prefix-free VLECs as most previous works did [7], [9], [11], [12], [23], [26], [30]. Although non-prefix-free but uniquely decodable VLECs can also be constructed, they are not herein considered due to the added complexity in testing their unique decodability.…”

“…One important property of the HEAP structure is that it can access the node with the minimal metric (i.e., the top node in the Encoding Stack) within O( log(n) ) complexity, where n denotes the number of nodes in the HEAP. 4 In order to check this condition efficiently, the lower bound on the free distance given in (3) is first computed; if it is less than d * free , then Dijkstra's algorithm [12] is adopted to determine the exact free distance. This is realized by transforming the finite-state VLEC encoder into a pairwise distance graph and applying Dijkstra's algorithm to find the graph's shortest path, where the resulting shortest path yields the VLEC's free distance.…”

“…In [11], [13], [18], Diallo et al proposed several algorithms for obtaining VLECs with maximal d free under the premise that all codeword lengths are known in advance. A similar approach was used in [12] for developing good errorcorrecting arithmetic codes.…”

Optimizing the free distance of Error-Correcting Variable-Length Codes

“…In recent work [11], we introduced a Pairwise Distance Graph (PDG), which is a modified and reduced product graph of the B-FSE and tracks the Hamming distances in P. This PDG is defined such that the free distance can be found by applying Dijkstra's algorithm [12].…”