Sentence examples for code dimensions from inspiring English sources

We adopt a tensor-based formulation for the proposed SFSM MIMO system that incorporates space, frequency, time, and code dimensions by means of the parallel factor model.

This figure shows that increasing r L rate (i.e., increasing the number E), the average decoding inefficiency ratio quickly approaches 1 (i.e., ideal code) as E=3 (i.e., (r_{L}=frac {2}{3})), even for very small code dimensions.

Figure 14 shows the average (over 1000 different codes) decoding inefficiency ratio for various object sizes or equivalently code dimensions K (both are equal here as the object is encoded in a single pass), when (r_{G} =frac {1}{2}).

For this system, we adopt a tensorial formulation of the transmitted and received signals that jointly incorporates space, frequency, time, and code dimensions by means of a PARAFAC tensor model.

A comparison of the proposed 3D construction with existing 3D constructions shows lower bit error rate for equivalent code dimension.

For this purpose, finding out the code parameters such as code length, code dimension, and code generator is essential.

This independence with respect to the code dimension is a key practical benefit (e.g., LDPC codes are known to be asymptotically good only).

We show that this class of RS codes features very low construction times, which means that GLDPC-Staircase codes can be generated on the fly, with the exact code dimension and length values.

This is done with an RS (n m,k m ) encoding over G F(2 b ) with 0≤e(m)≤E and m=1,...,M L. Here, E, k m, and n m are respectively the maximum number of extra-repair symbols per generalized check node, the RS code dimension and length for the generalized check node m.

If we are also interested in achieving large minimum distance, then we can take n strictly greater than (kfrac {r + ell ^{2}}{r}) and attain the following relationship between the minimum distance (d_{min }) and the code dimension k [9] begin{array}{*{20}l} d_{min}({mathcal C}) = n - k + 1 - ellleft(frac{kell}{r} - 1right).

This is done with an RS (n m,k m ) encoding over G F(2 b ) with 0≤e(m)≤E and m=1,...,M L. Here, E, k m, and n m are respectively the maximum number of extra-repair symbols per generalized check node, the RS code dimension and length for the generalized check node m. Figure 1 illustrates the bipartite graph of a GLDPC-Staircase (left (N_{G}, K right)) code of length N G and dimension K.