Apparatus and method for representing a sequence of content as projections for reconstructing the sequence at full or lower quality
View Patent ↗A content presentation system comprising content playing apparatus and content providing apparatus operative to receive an array of digitally represented numbers, representing content as P points in D-dimensional space, to generate therefrom a plurality of projections on at least one sub-space of a vector space comprising a span of at least one D-dimensional vector, and to provide the plurality of projections to the content playing apparatus, the content playing apparatus being operative to reconstruct the array of digitally represented numbers from the plurality of projections and to expose human users to content accordingly.
1. A method for retrieving a sequence of P×D×L[>]=M raw digital entertainment content bits from a received sequence of 1<e<=E data elements, each data element comprising P sets of d k L-tuples of bits,
each data element ELEMENT k (1<=k<=e) comprising a projection of substantially all of P points defined in a coordinate system having an origin, onto a d k -dimensional subspace s k of D-dimensional space, thereby to define subspaces defining a span,
wherein the subspaces are characterized in that the dim(span(S 1 , . . . ,Sk))<=M/(P×L),
the method comprising:
if dim(S 1 )+. . . +dim(Se)>M/(P×L) discarding data elements at random until dim(S 1 )+. . . +dim(Se)=M/(P×L), and then continuing as in the case where dim(span(S 1 , . . . , Se))=M/(P×L);
repeating for p=1, . . . P:
a. retrieving a p′th point comprising D L-tuples of bits, wherein retrieving the p′th point comprises, for each data element ELEMENT h (1<=h<=e) in said sequence of e data elements, taking the intersection of all O p,1 , O p,2 , . . . , O p,e where O p,h (1<=p<=P, 1<=h<=e) is a translated subspace orthogonal to s h that contains the point PNTh,p, the dimension of the subspace being D−d h , the intersection of all of said translated subspaces orthogonal to s h defining an intersection translated subspace comprising a translated subspace of dimension D-dim(span(s 1 ,s 2 , . . . , s[k]e)); and
b. choosing a D-dimensional point q p within said intersection translated subspace, wherein each dimension of the D-dimensional point is represented at a 2 L -level resolution, such that the point is defined by D L-tuples of bits; and
decoding the P D-dimensional points into M raw digital entertainment bits by setting the (i×D+j)-th L-tuple of bits to hold the L-bit binary representation of the j-th coordinate of the i-th point (1<=j<=D) (1<=i<=P), thereby obtaining P×D×L bits,
wherein, if dim(span(S 1 , . . . , Se)) =M/(P×L), the intersection of all of said translated subspaces orthogonal to s h defines a single point q p and said M raw digital entertainment bits are identical to the bits that were encoded.
2. A method according to claim 1 wherein span(s 1 , . . . se)=D such that all subspaces s k (1<=k<=E) intersect at a single D-dimensional point, each dimension having L levels, said point being the exact encoding of M.
3. A method according to claim 1 wherein q p is chosen so as to minimize its Euclidian distance from the origin.
4. A method according to claim 1 wherein M bits are permuted by a predefined permutation after decoding them.