Multi-stage encoding and multi-stage decoding of information bits

A multi-stage decoder comprising m sub-decoders, the decoder being configured to:

• receive, over a communication channel (302), a vector y comprising a set of N symbols, wherein each of m and N is an integer and m≤N, wherein each received symbol yi(l) corresponds to one of a set of constellation points of a bi-dimensional modulation format, wherein the set of constellation points is divided into two subsets of constellation points including a first subset assigned to a bit of value 0 and a second subset assigned to a bit of value 1, such that a minimum distance d in the same subset is maximized, and wherein the vector y has coordinates (α, β) and components yi(l), i=1, . . . , N, and l=1, . . . , m;
• determine a log-likelihood-ratio on the basis of a respective received symbol yi(l);
• determine a bit value on the basis of the log-likelihood-ratio li(l) by means of a l-level sub-decoder;
• obtain a new symbol yi(l+1) for each symbol yi(l) on the basis of the bit value and by performing a transformation on the symbol yi(l), wherein the transformation comprises a rotation and a shift;
• determine a next log-likelihood-ratio on the basis of the new symbol yi(l+1);
• determine a next bit value on the basis of the next log-likelihood-ratio ;
• and
• decode the vector y on the basis of the bit value and the next bit value.

A method for a multi-stage encoder comprising m sub-encoders for encoding K information bits by means of m component codes, each of length N, in a codeword having a total length of mN, wherein each of m, K and N is an integer, wherein m≤N and K≤N, and wherein the method comprises:

• storing the K information bits into a message u;
• dividing the message u into m sub-information vectors u(i), i=1, . . . , m of length K(1), . . . , K(m), respectively, wherein K(1)+ . . . +K(m)=K;
• encoding, by means of the m sub-encoders, each of the m sub-information vectors u(i) into m sub-codewords c(1), . . . , c(m);
• mapping the m sub-codewords c(1), . . . , c(m) into N symbols taken from 2m constellation points of a modulation format to form a vector x;
• labelling each of the N symbols into a string of m bits;
• and
• transmitting the vector x through a communication channel.