A method comprising: performing one of: (a) receiving a signal, encoding at least a portion of a codeword from a signal based value using an approximation of a combinatorial function based on a linear combination of a set of basis functions, wherein the signal based value is a pulse vector and represents one or more aspects of the signal that is received, and transmitting that codeword; or (b) receiving a code word, decoding at least a portion of the code word to a signal based value using an approximation of a combinatorial function based on a linear combination of a set of basis functions, wherein the signal based value is a pulse vector and represents one or more aspects of a signal, and transmitting the signal; wherein in addition to performing (a) or (b), the method further comprises: receiving at least one vector characteristic value; and determining a length of the code word or portion thereof from the approximation of the combinatorial function by using at least one vector characteristic value, wherein the at least one vector characteristic value is one of a pulse count m and a vector length n; wherein m and n are related by: m ≡ ∑ i = 0 n − 1 x i, and wherein each x i is an integer element of the pulse vector or a portion of the pulse vector; wherein the pulse vector or a portion thereof has a length given by n, and the method further comprises determining the approximation of the combinatorial function as G ̃ n m = ∑ k = 0 l − 1 C k i ⋅ f k m m i < m ≤ m i + 1, wherein each multiplier C k i is a constant, each range limit m i is a positive integer, m i+ 1 > m i +1, and l is the total quantity of basis functions f k ( m); wherein the method further comprises determining G̃ n (m) as an approximation of the combinatorial function G n m = log 2 ∑ d = 1 min m n F n d F m − 1, d − 1 2 d, wherein F ( n,d) is the number of combinations of d non-zero vector elements over n positions, and F ( m - 1, d - 1) is the number of combinations of d -1 non-zero vector elements over m -1 positions; and wherein the signal is a signal selected from the group of signals consisting of an audio signal, a video signal, an image signal, and a telemetry signal. performing one of: (a) receiving a signal, encoding at least a portion of a codeword from a signal based value using an approximation of a combinatorial function based on a linear combination of a set of basis functions, wherein the signal based value is a pulse vector and represents one or more aspects of the signal that is received, and transmitting that codeword; or (b) receiving a code word, decoding at least a portion of the code word to a signal based value using an approximation of a combinatorial function based on a linear combination of a set of basis functions, wherein the signal based value is a pulse vector and represents one or more aspects of a signal, and transmitting the signal; (a) receiving a signal, encoding at least a portion of a codeword from a signal based value using an approximation of a combinatorial function based on a linear combination of a set of basis functions, wherein the signal based value is a pulse vector and represents one or more aspects of the signal that is received, and transmitting that codeword; or (b) receiving a code word, decoding at least a portion of the code word to a signal based value using an approximation of a combinatorial function based on a linear combination of a set of basis functions, wherein the signal based value is a pulse vector and represents one or more aspects of a signal, and transmitting the signal; wherein in addition to performing (a) or (b), the method further comprises: receiving at least one vector characteristic value; and determining a length of the code word or portion thereof from the approximation of the combinatorial function by using at least one vector characteristic value, wherein the at least one vector characteristic value is one of a pulse count m and a vector length n; receiving at least one vector characteristic value; and determining a length of the code word or portion thereof from the approximation of the combinatorial function by using at least one vector characteristic value, wherein the at least one vector characteristic value is one of a pulse count m and a vector length n; wherein m and n are related by: m ≡ ∑ i = 0 n − 1 x i, and wherein each x i is an integer element of the pulse vector or a portion of the pulse vector; wherein the pulse vector or a portion thereof has a length given by n, and the method further comprises determining the approximation of the combinatorial function as G ̃ n m = ∑ k = 0 l − 1 C k i ⋅ f k m m i < m ≤ m i + 1, wherein each multiplier C k i is a constant, each range limit m i is a positive integer, m i+ 1 > m i +1, and l is the total quantity of basis functions f k ( m); wherein the method further comprises determining G̃ n (m) as an approximation of the combinatorial function G n m = log 2 ∑ d = 1 min m n F n d F m − 1, d − 1 2 d, wherein F ( n,d) is the number of combinations of d non-zero vector elements over n positions, and F ( m - 1, d - 1) is the number of combinations of d -1 non-zero vector elements over m -1 positions; and wherein the signal is a signal selected from the group of signals consisting of an audio signal, a video signal, an image signal, and a telemetry signal.