This paper addresses the problem of increasing the robustness to bit errors for two description scalar quantizers. Our approach is to start with an m-diagonal index assignment and further apply a permutation to the indexes of each description to increase the minimum Hamming distance dminof the set of valid index pairs. In particular, we show how to construct linear permutation pairs achieving dmin3, and establish a lower bound in terms of the description rate R, for the highest value of m for which such permutations exist. For the case when one description is known to be correct, we propose a new performance measure, denoted by dside,min. This represents the minimum Hamming distance of the set of indexes of one description, when the index of the other description is fixed. We prove the close connection between the problem of robust permutations design under the new criterion and the anti-bandwidth problem in a certain graph derived from a hypercube. Leveraging this connection, we settle the problem of existence of permutations achieving dside,min≥ 2, respectively dmin≥ 2, and show their construction. Further, we develop a technique for constructing linear permutation pairs achieving dside,min≥ h based on linear (R, ⌈log2 m⌉) channel codes of minimum Hamming distance h + 1. In addition, tight bounds in terms of R, on the maximum achievable value of dside,minare derived for m = 2, 3, 4.

This work addresses the problem of increasing the robustness to bit errors for two description scalar quantizers. To this aim a permutation is applied to the indices of each description. We show how to construct permutation pairs that increase the minimum Hamming distance of the set of valid index pairs to 3 when the redundancy is sufficiently high. Additionally, for the case when one description is known to be correct we propose a new performance criterion, denoted by dside,min. This represents the minimum Hamming distance of the set of valid indices of one description, when the index of the other description is fixed. We develop a technique for constructing permutation pairs achieving dside,min≥ h based on a linear (R, [log2m]) channel code of minimum Hamming distance h + 1, where R is the rate of each description and m is the number of diagonals occupied by the valid index pairs in the matrix of the initial index assignment.