(defun bit-array-serialize (bit-array)
  (format nil "~S~%~:{~A*~A~:^ ~}~%"
          (array-dimensions bit-array)
          (bit-vector-rle (make-array (reduce (function *) (array-dimensions bit-array))
                                      :displaced-to bit-array))))

(bit-array-serialize (make-sparse-bit-array '(100 200 50) 1/10000))

(defun bit-array-deserialize (data)
  (with-input-from-string (*standard-input* data)
    (let ((dimensions (read)))
      (check-type dimensions list)
      (assert (every (function integerp) dimensions))
      (let* ((bit-array  (make-array dimensions :element-type 'bit :initial-element 0))
             (bit-vector (make-array (reduce (function *) dimensions) :displaced-to bit-array)))
        (loop
          :for run := (read *standard-input* nil)
          :while run
          :do (let ((srun (string run)))
                (multiple-value-bind (start star) (parse-integer srun :junk-allowed t)
                  (let ((length (parse-integer srun :start (1+ star))))
                    (fill bit-vector 1 :start start :end (+ start length))))))
        bit-array))))

(let ((small-bit-array (make-sparse-bit-array '(4 5 6)  1/10)))
  (assert (equalp small-bit-array (bit-array-deserialize (bit-array-serialize small-bit-array)))))