Maximal Free Distance Research Articles

New Free Distance Bounds and Design Techniques for Joint Source-Channel Variable-Length Codes

This paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length codes.

High-Rate Punctured Convolutional Codes for Soft Decision Viterbi Decoding

The high-rate punctured codes of rates 2/3 through 13/14 are derived from rate 1/2 specific convolutional codes with maximal free distance. Coding gains of derived codes are compared based on their bit error rate performances under soft decision Viterbi decoding.

Short unit-memory byte-oriented binary convolutional codes having maximal free distance (Corresp.)

It is shown that (n_{o},k_{o}) convolutional codes with unit memory always achieve the largest free distance among all codes of the same rate k_{o}/n_{o} and same number 2^{Mk_{o} of encoder states, where M is the encoder memory. A unit-memory code with maximal free distance is given at each place where this free distance exceeds that of the best code with k_{o} and n_{o} relatively prime, for all Mk_{o} \leq 6 and for R = l/2, 1/3, 1/4, 2/3 . It is shown that the unit-memory codes are byte oriented in such a way as to be attractive for use in concatenated coding systems.

Short binary convolutional codes with maximal free distance for rates 2/3 and 3/4 (Corresp.)

A search procedure is developed to find good short binary <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(N,N - 1)</tex> convolutional codes. It uses simple rules to discard from the complete ensemble of codes a large fraction whose free distance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d_{free}</tex> either cannot achieve the maximum value or is equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d_{free}</tex> of some code in the remaining set. Farther, the search among the remaining codes is started in a subset in which we expect the possibility of finding codes with large values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d_{free}</tex> to be good. A number of short, optimum (in the sense of maximizing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d_{free}</tex> ), rate-2/3 and 3/4 codes found by the search procedure are listed.

Short convolutional codes with maximal free distance for rates 1/2, 1/3, and 1/4 (Corresp.)

This paper gives a tabulation of binary convolutional codes with maximum free distance for rates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{1}{2}, \frac{1}{3}</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{1}{4}</tex> for all constraint lengths (measured in information digits) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\nu</tex> up to and including <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nu = 14</tex> . These codes should be of practical interest in connection with Viterbi decoders.